Physics 200+ formulas and concepts

Physics
Handbook
1
200+Physics Formulas and Concepts

1 | Physics Handbook Part 1
Physics Formulas
1. Acceleration Formula
2. Force Formula
3. Frequency Formula 6
4. Velocity Formula
5. Wavelength Formula
6. Angular Velocity Formula 7
7. Displacement Formula
8. Density Formula
9. Kinematic Equations Formula 8
10.Tangential Velocity Formula
11.Kinetic Energy Formula
12.Angular Speed Formula
13.Buoyancy Formula 9
14.Efficiency Formula
15.Static Friction Formula 10
16.Potential Energy: Elastic Formula
17.Friction Formula
18.Tangential Acceleration Formula 11
19.Potential Energy: Earth's Gravity Formula
20.Potential Energy: Electric Potential Formula
21.Potential Energy: Two-Body Gravitation Formula 12
22.Potential Energy: Electrostatic Point Particles Formula
23.Average Speed Formula 13
24.Doppler Shift Formula
25.Current Density Formula
26.Heat Transfer Formula 14
27.Wavelength to Frequency Formula
28.Centripetal Force Formula
29.Deceleration Formula 15
30.Angular Displacement Formula
31.Average Force Formula
32.Acceleration Due to Gravity Formula 16
33.Momentum Formula
34.Power Formula 17
35.Specific Gravity Formula
36.Projectile Motion Formulas 18
37.Torque Formula (Moment of Inertia and Angular Acceleration)
38.Spring Constant Formula
39.Specific Heat Formula 19
40.Amplitude Formula
41.Torque Formula (Force at a Distance) 20
42.Elastic Potential Energy Formula
43.Free Fall Formula

44.Average Acceleration Formula
45.Elastic Collision Formula 21
46.Heat Capacity Formula
47.Gravity Formula 22
48.Tension Formula
49.Centripetal Acceleration Formula
50.Gravitational Potential Energy Formula
51.Impulse Formula 23
52.Capacitance Formula
53.Distance Speed Time Formula 24
54.Orbital Velocity Formula
55.Resistance Formula 25
56.Reynold's Number Formula
57.Angular Momentum Formula 26
58.Initial Velocity Formula
59.Inverse Square Law Formula 27
60.Work Formula
61.Air Resistance Formula 28
62.Angular Momentum Formula(Moment of Inertia and Angular Velocity)
63.Center of Mass Formula
64.Flow Rate Formula 29
65.Stopping Distance Formula
66.Escape Velocity Formula 30
67.Inelastic Collision Formula
68.Kinetic Friction Formula
69.Newton's Law of Cooling Formula 31
70.Pressure Formula
71.Average velocity (constant acceleration) Formula
72.Average Velocity Formula (displacement over time) 32
73.De Broglie Wavelength Formula
74.Linear Speed Formula (Rotating Object)
75.Angular Acceleration Formula 33
76.Linear speed Formula (straight line motion)
77.Horizontal Range Formula 34
78.Instantaneous Speed Formula
79.Instantaneous Velocity Formula 35
80.Kinetic Energy Formula
81.Maximum Height Formula
82.Rotational Kinetic Energy Formula 36
83.Strain Formula (general form)
84.Time of Flight Formula 37
85.Trajectory Formula
86.Capacitors in Parallel Formula 38
87.Capacitors in Series Formula
88.Electric Power Formula

89.Resistors in Parallel Formula 39
90.Resistors in Series Formula
91.Coulomb's Law Formula 40
92.Gravitational Force Formula
93.Length Contraction Formula 41
94.Snell's Law Formula
95.Time Dilation Formula 42
96.Electric Field Formula
97.Kirchhoff's Junction Rule Formula 43
98.Kirchhoff's Loop Rule Formula
99.Ohm's Law Formula
100. Relativity Formula 44
101. Centripetal Acceleration Formula
102. Conservation of Energy Formula 45
103. Decibel Formula
104. Doppler Effect Formula 46
105. Hooke's Law Formula
106. Average Angular Velocity Formula 47
107. Gravitational Field Formula
108. Ideal Gas Law Formulas
109. Impulse Formula 48
110. Einstein's Mass-Energy Equivalence Formula
111. Kinetic Energy of Gas Formula 49
112. Impulse-Momentum Theorem Formula
113. Moment of Inertia Formula (common shapes) 50
114. One-Dimensional Kinematics Formula 51
115. Simple Harmonic Motion Formula
116. Magnetic Field Formula 52
117. Magnetic Force Formula (Charge-Velocity) 53
118. Magnetic Force Formula (Current-Length)
119. Parallel Axis Theorem Formula 54
120. Rotational Kinematics Formula 55
121. Angular Frequency Formula
122. Bernoulli's Equation Formula 56
123. Drag Formula
124. Dynamic Viscosity Formula
125. Kinematic Viscosity Formula 57
126. Mass Continuity Formula
127. Mass Flow Rate Formula
128. Volume Continuity Formula 58
129. Volume Flow Rate Formula
130. Pressure in a Fluid Formula
131. Bulk modulus Formula 59
132. Froude number Formula
133. Latent Heat Formula 60

134. Liquid Expansion Formula
135. Sensible Heat Formula
136. Shear modulus Formula 61
137. Solid Expansion Formula
138. Entropy Formula 62
139. Surface tension Formula
140. Young's modulus Formula
141. Heat Flow Rate Formula 63
142. Internal Energy Formula
143. Maxwell-Boltzmann Distribution Formula 64
144. Molecular Kinetic Energy Formula
145. Molecular Speed Formula
146. Stephan-Boltzmann Law Formula 65
147. Thermal Conduction Formula
148. Thermodynamic Work Formula
149. Wien Displacement Law Formula 66
150. Capacitor potential energy Formula
151. Cylindrical capacitor Formula 67
152. Electric Current Formula
153. Electric resistance Formula
154. Image position Formula 68
155. Image size Formula
156. Plate capacitor Formula
157. Resistivity-Conductivity Formula 69
158. Spherical capacitor Formula
159. Spherical mirror Formula 70
160. Biot-Savart Law Formula
161. Electric Flux Formula 71
162. Gauss law Formula
163. Induced Electromotive Force Formula
164. Magnetic Flux Formula 72
165. Motional Electromotive Force Formula
166. No one's Formula
167. Magnetic Force Between Parallel Wires Formula 73
168. Solenoid Formula
169. Straight Wire Magnetic Field Formula
170. Ampere's Law Formula 74
171. Energy momentum Formula
172. Photoelectric Effect Formula 75
173. Photon Energy Formula
174. Photon Momentum Formula
175. Relative Velocity Formula 76
176. Relativistic Doppler Effect Formula
177. Relativistic Energy Formula 77
178. Relativistic Mass Formula

179. Relativistic Momentum Formula
180. Equations of motion Formula 78
181. Half-Life Formula
182. Rydberg Formula
183. Schrodinger Equation Formula 79
184. Uncertainty Principle Formula
185. Archimedes Principle Formula 80
186. Critical angle Formula
187. Cross product Formula 81
188. Friction loss Formula 82
189. Linear acceleration Formula
190. Orbital speed Formula 83
191. Sound intensity Formula 84
192. Speed of sound Formula
193. Transformer Formula 85
194. Voltage divider Formula 86
195. Distance Traveled Formula
196. Electrical Formula
197. Energy Density Formula 87
198. Gravitational Acceleration Formula
199. Intensity Formula 88
200. Resonant Frequency Formula
201. Temperature Formula
202. Thermal Expansion Formula 89
203. Wave Formula
204. Force of attraction Formula 90
205. Inductance Formula
206. Celsius to Kelvin Formula
207. Mass Formula 91
208. Position Formula
209. Thermal Energy Formula 92
210. Vector Projection Formula
211. Weight Formula 93
212. Work done by gravity Formula
213. Period of a Pendulum Formula 94

Acceleration Formula
Acceleration is a measure of how quickly the velocity of an object changes. So, the acceleration is the
change in the velocity, divided by the time. Acceleration has a magnitude (a value) and a direction.
The direction of the acceleration does not have to be the same as the direction of the velocity. The
units for acceleration are meters per second squared (m/s2
).
a = acceleration (m/s2
)
vf = the final velocity (m/s)
vi = the initial velocity (m/s)
t = the time in which the change occurs (s)
Δv = short form for "the change in" velocity (m/s
Force Formula
Force is the mass of an object, multiplied by its acceleration. The unit of force is . This is called a
Newton, with the symbol N. Force has a magnitude and a direction.
force = mass x acceleration
F = ma
F = force
m = mass
a = acceleration
Frequency Formula
Frequency is the number of cycles in a unit of time. The "cycles" can be movements of anything with
periodic motion, like a spring, a pendulum, something spinning, or a wave. Frequency is equal to 1
divided by the period, which is the time required for one cycle.
The derived SI unit for frequency is hertz, named after Heinrich Rudolf Hertz (symbol hz). One hz is
one cycle per second.

f = frequency, the cycles in a unit of time
T = period, the time required for one cycle
N = a number of cycles
t = an amount of time
Velocity Formula
Velocity is a measure of how quickly an object moves. So, the velocity is the change in the position of
an object, divided by the time. Velocity has a magnitude (a value) and a direction. The unit for velocity
is meters per second (m/s).
b
v = velocity (m/s)
xf = the final position (m)
xi = the initial position (m)
t = the time in which the change occurs (s)
Δx = short form for "the change in" position (m
Wavelength Formula
Wavelength is the distance between the crests of a wave. Many different things can move like waves,
like strings, water, the air (sound waves), the ground (earthquakes), and light can be treated as a
wave. Wavelength is represented with the Greek letter lambda: λ. It is equal to the velocity of the
wave, divided by the frequency. Wavelength is expressed in units of meters (m).
λ = wavelength, the distance between wave crests (m)
v = wave velocity, the speed that waves are moving in a direction (m/s)
f = frequency, the wave crests that go through a point in a certain time (cycles/s or Hz)
Angular Velocity Formula
Angular Velocity is a measure of how quickly an object moves through an angle. It is the change in
angle of a moving object (measured in radians), divided by time. Angular velocity has a magnitude (a
value) and a direction.

Angular velocity = (final angle) - (initial angle) / time = change in position/time
ω = (θf - θi) / t
ω = angular velocity
θf = the final angle
θi = the initial angle
t = time
Δθ = short form for 'the change in angle
Displacement Formula
Displacement is the change in an object's position from the origin. Displacement is a vector quantity,
and thus has both magnitude and direction.
Displacement = (final position) - (initial position) = change in position
D = Xf -Xi
D = displacement
Xf = final position
Xi = initial position
ΔX = short form for change in position
Density Formula
Density is a measure of relative compactness, or how heavy an object is relative to its size. Density is
defined as mass, m, in a given unit volume, V.
ρ = m/V
ρ = density, kg/m3
, or g/(cm)3
m = mass, in kg or g
V = volume, in m3
or (cm)3
Kinematic Equations Formula
Kinematics is the study of objects in motion and their inter-relationships. There are four (4) kinematic
equations, which relate to displacement, D, velocity, v, time, t, and acceleration, a.
a) D = vit + 1/2 at2
b) (vi +vf)/2 = D/t
c) a = (vf - vi)/t d) vf
2
= vi
2
+ 2aD
D = displacement
a = acceleration
t = time

vf = final velocity
vi = initial velocity
Tangential Velocity Formula
The tangential velocity is the velocity measured at any point tangent to a turning wheel. Thus
tangential velocity, vt is related to the angular velocity of the wheel, ω, and the radius of the wheel, r.
Vt = ω r
Vt = tangential velocity
ω = angular velocity
r = radius of wheel
Kinetic Energy Formula
The Kinetic energy is the energy that an object has due to its motion. Ek, is the energy of a mass, m, in
motion, v2
.
Ek = 1/2 mv2
Ek = Kinetic energy
m = mass
v = velocity
Angular Speed Formula
Angular speed is the rate at which an object changes its angle (measured) in radians, in a given time
period. Angular speed has a magnitude (a value) only.
Angular speed = (final angle) - (initial angle) / time = change in position/time
ω = θ /t
ω = angular speed in radians/sec
θ = angle in radians (2π radians = 360 degrees)
t = time, sec
Angular speed and angular velocity use the same formula; the difference between the two is that
Angular speed is a scalar quantity, while angular velocity is a vector quantity.
Buoyancy Formula
Liquid exerts a force on objects immersed or floating in it. This force is equal to the weight of the liquid
that is displaced by an object. This is also known as Archimedes' principle. The unit for the buoyant
force (like other forces) is the Newton (N).
buoyant force =(density of liquid)(gravitational acceleration)(volume of liquid)

= (density)(gravitational acceleration)(height of liquid)(surface area of object)
Fb = ρgV = ρghA
Fb = buoyant force of a liquid acting on an object (N)
ρ = density of the liquid(kg/m3
)
g = gravitational acceleration(9.80 m/s2
)
V = volume of liquid displaced (m3
or liters, where 1 m3
= 1000 L)
h = height of water displaced by a floating object(m)
A = surface area of a floating object(m2
)
Efficiency Formula
Efficiency is a measure of how much work or energy is conserved in a process. In many processes,
work or energy is lost, for example as waste heat or vibration. The efficiency is the energy output,
divided by the energy input, and expressed as a percentage. A perfect process would have an
efficiency of 100%.
η = efficiency (Greek letter "eta")
Wout = the work or energy produced by a process. Units are Joules (J).
Win = the work or energy put in to a process. Units are Joules (J).
Static Friction Formula
Static friction is a force that keeps an object at rest. It must be overcome to start moving the object.
Once an object is in motion, it experiences kinetic friction. If a small amount of force is applied to an
object, the static friction has an equal magnitude in the opposite direction. If the force is increased, at
some point the value of the maximum static friction will be reached, and the object will move. The
coefficient of static friction is assigned the Greek letter "mu" (μ), with a subscript "s". The maximum
force of static friction is μs times the normal force on an object.
force of static friction ≤ (coefficient of static friction)(normal force) maximum force of static friction =
(coefficient of static friction)(normal force)
Fs ≤ μs η , and Fs
m
ax
= μs η
Fs = force of static friction
μs = coefficient of static friction
η = normal force (Greek letter "eta")
≤ means "less than or equal to"

Fs
m
ax
= maximum force of static frictio
Potential Energy: Elastic Formula
Potential energy is energy that is stored in a system. There is the possibility, or potential, for it to be
converted to kinetic energy. Elastic potential energy is stored in a spring that has been stretched or
compressed by a distance x away from its equilibrium position. Position x = 0 must always be the
position where the spring is most relaxed. Springs have their own natural "spring constants" that
define how stiff they are. The letter k is used for the spring constant, and it has the units N/m. Like all
work and energy, the unit of potential energy is the Joule (J), where 1 J = 1 N∙m = 1 kg m2
/s2
.
potential energy = 1/2(spring constant)(distance from equilibrium)2
U = 1/2kx2
U = potential energy of a spring at a certain position
k = the spring constant, specific to the spring, with units N/m.
x = distance the spring is stretched or compressed away from equilibrium
Friction Formula
Friction is caused by one surface moving over another. It is a force that can resist the motion of an
object. Friction can cause energy of motion to be lost in the form of heat. The amount of force created
depends on the materials involved, and every combination is different. The coefficient of friction is
used to describe the way two surfaces interact. The coefficient of friction is assigned the Greek letter
"mu" (μ), and it is unitless. The force of friction is μ times the normal force on an object. The unit for
friction is the Newton (N).
force of friction = (coefficient of friction)(normal force)
Ff = μη
Ff = force of friction
μ = coefficient of friction
Tangential Acceleration Formula
In rotational motion, tangential acceleration is a measure of how quickly a tangential velocity changes.
It always acts perpendicular to the centripetal acceleration of a rotating object. It is equal to the
angular acceleration α, times the radius of the rotation.
tangential acceleration = (radius of the rotation)(angular acceleration)
atan = rα
atan = tangential acceleration

r = radius of the object's rotation
α = angular acceleration, with units radians/s
Potential Energy: Earth's Gravity Formula
converted to kinetic energy. Gravitational potential energy exists when an object has been raised
above the ground. If the object is released from its position it will fall, converting the potential energy to
kinetic energy. Like all work and energy, the unit of potential energy is the Joule (J), where 1 J = 1 N∙m
= 1 kg m2
/s2
.
potential energy = (mass of the object)(acceleration due to gravity)(height)
U = mgh
U = potential energy of an object due to Earth's gravity
m = the mass of the object
g = acceleration due to gravity (9.8 m/s2
)
h = height above position with U = 0 (the ground, or floor typically
Potential Energy: Electric Potential Formula
Potential energy is energy that is stored in a system, based on the position of objects. A charged
particle in an electric field has potential energy because of the electrostatic force that can act on it. It is
often useful to be able to describe the potential energy per unit charge at a certain position. This
potential energy per unit charge is called electric potential (or simply "potential"). Like all work and
energy, the unit of potential energy is the Joule (J), where 1 J = 1 kg∙m2
/s2
. The unit of charge is the
Coulomb (C), and the unit of electric potential is the Volt (V), which is equal to a Joule per Coulomb
(J/C).
potential energy = (charge of particle)(electric potential)
U = qV
U = potential energy, with units J (Joules)
q = the charge of the point particle, with units C (Coulombs)
V = an electric potential, with units V = J/C (Volts, equal to Joules per Coulomb)
Potential Energy: Two-Body Gravitation Formula
converted to kinetic energy. Any two objects with mass are attracted to each other by gravity. In
space, it is possible to find the potential energy of gravity between two objects separated by a

distance. This potential energy formula contains a constant, G, which is called the "universal
gravitational constant". Its value is = 6.673 x 10-11
(N∙m2
)/kg2
. The unit of potential energy is the Joule
(J), where 1 J = 1 N∙m = 1 kg m2
/s2
.
U = potential energy of gravity between two objects
G = the universal gravitational constant, G = 6.673 x 10-11
(N∙m2
)/kg2
m1 = mass of one of the objects
m2 = mass of the second object
r = the distance between the centers of mass of the two objects
Potential Energy: Electrostatic Point Particles Formula
converted to kinetic energy. Point particles with charge exert forces on each other. For opposite
charges, the force is attractive. For same charges, the force is repulsive. In both cases, there is a
potential energy related to the position of charges relative to each other. The unit of electric charge is
the Coulomb, C. Like all work and energy, the unit of potential energy is the Joule (J), where 1 J = 1 kg
m2
/s2
.
U = potential energy of electrostatic point particles
k = the Coulomb constant, k = 8.99 x 109
N∙m2
/C2
. Can be written = 1/(4πϵ0 ) .
ϵ0 = the permittivity of free space, ϵ0 = 8.854 x 10-12
C2
/(N∙m2
)
q1 = charge of one of the point particles
q2 = charge of the other point particle
r = distance between the two point charges
Average Speed Formula

The Average Speed of an object is a measure of the distance covered by that object in a set period of
time. It is the distance covered, divided by time. Average speed has a magnitude, and is a scalar
quantity
sAvg = ΔD/Δt
D = distance, meters (m)
t = time,sec (s)
Δ = short form for 'the change'
ΔD = short form for 'the change in distance'
ΔD = D1 + D2 + D3 + ...Dn
Δt = short form for 'the change in time'
Δt = t1 + t2 + t3 + ... tn
Doppler Shift Formula
The Doppler Shift, when associated with sound, is the change in frequency of a source as it moves:
the frequency will appear to increase as the source comes towards a listener and will appear to
decrease as the source moves away from a listener. (This formula is also used to calculate the motion
of stars.)
f = fs (v + vL)/(v - vs)for sound
f = frequency heard by listener
fs = frequency of the source
v = velocity of sound
vs = velocity of the source
(positive if moving towards listener, negative if moving away from listener)
vL = velocity of listener
(positive if moving toward the source, negative if moving away from the source)
Current Density Formula
In the field of electromagnetism, Current Density is the measurement of electric current (charge flow in
amperes) per unit area of cross-section (m2
). This is a vector quantity, with both a magnitude (scalar)
and a direction.
J = I/A
J = current density in amperes/m2
I = current through a conductor, in amperes

A = cross-sectional area of the conductor, m2
Heat Transfer Formula
Heat, a measure of thermal energy, can be transferred from one point to another. Heat flows from the
point of higher temperature to one of lower temperature. The heat content, Q, of an object depends
upon its specific heat, c, and its mass, m. The Heat Transfer is the measurement of the thermal
energy transferred when an object having a defined specific heat and mass undergoes a defined
temperature change.
Heat transfer = (mass)(specific heat)(temperature change)
Q = mcΔT
Q = heat content in Joules
m = mass
c = specific heat, J/g °C
T = temperature
ΔT = change in temperature
Wavelength to Frequency Formula
The velocity of light, v, is the product of its wavelength, λ , and its frequency, f. This means that the
wavelength is the velocity, v, divided by the frequency, f.
Wavelength of light = velocity of light / frequency of light
λ = v/f
λ = Wavelength of light, meters
v = Velocity of light (c = 3.0 x 108
m, for speed of light if not otherwise defined)
f = frequency of light, Hz
Centripetal Force Formula
The Centripetal ('center-seeking') force is the force which keeps an object moving along the axis of
rotation of a curved path. This force always acts towards the center.
Centripetal force = (mass of the object)(velocity of the object)2
/ radius
Fc = mv2
/ r
Fc = centripetal force
m = mass
v = velocity
r = radius of circular path

Deceleration Formula
Deceleration is the opposite of acceleration. It is the rate at which an object slows down. Deceleration
is the final velocity minus the initial velocity, with a negative sign in the result because the velocity is
dropping. The formula for acceleration can be used, recognizing that the final result must have a
negative sign.
deceleration = (final velocity - initial velocity) / time
d = (vf - vi)/t
d = deceleration
vf = final velocity
t = time
Angular Displacement Formula
The angular displacement is defined as the angle through which an object moves on a circular path. It
is the angle, in radians, between the initial and final positions.
(θf - θi) = angular displacement
θ = s/r
θ = angular displacement through which movement has occurred
s = distance travelled
r = radius of the circle
Average Force Formula
The average force is the force exerted by a body moving at a defined rate of speed (velocity) for a
defined period of time. The word 'average' is used to indicate that this is not an 'instantaneous' or
precisely measured velocity. Thus, average Force is equal to the mass of the body multiplied by the
average velocity over the defined time.
F = m (vf - vi)/t
F = force
m = mass
vavg = average velocity
vf = final velocity
t = time
Acceleration Due to Gravity Formula

Near the Earth's surface, the acceleration due to gravity is approximately constant. However, at large
distances from the Earth, or around other planets or moons, the acceleration is different. The
acceleration due to gravity depends on the mass of the body, the distance from the center of mass,
and a constant G, which is called the "universal gravitational constant". Its value is = 6.673 x 10-
11
N·m2
/kg2
.
g = acceleration due to gravity (units m/s2
)
G = the universal gravitational constant, G = 6.673 x 10-11
N·m2
kg2
m = mass of a large body (for example, Earth)
r = the distance from the center of mass of the large body
Momentum Formula
Momentum is a quantity with a value and a direction. It is the product of the mass of an object and its
velocity. Momentum is conserved in elastic collisions. The unit of momentum is a kg·m/s, which is also
equivalent to a J·s (a Joule·second).
momentum = (mass)(velocity)
p = mv
p = momentum (kg·m/s)
m = mass (kg)
v = velocity (m/s)
Power Formula
Power is a rate at which work is done, or energy is used. It is equal to the amount of work done
divided by the time it takes to do the work. The unit of power is the Watt (W), which is equal to a Joule
per second (J/s).
P = power (W, or J/s)
∆W = the work done, or energy used (J)
∆t = the time taken to do the work (s)

Specific Gravity Formula
Specific gravity is a measure of relative density. The specific gravity is the density of a substance
divided by the density of water. Density is measured in the units kg/m3
. The density of water at 4.0°C is
1000 kg/m3
. So, the specific gravity is a unitless number.
SG = specific gravity (unitless)
ρsubstance = the density of the substance (kg/m3
)
ρwater = the density of water at 4.0°C, 1000 kg/m3
Projectile Motion Formulas
A projectile is an object that is given an initial velocity, and is acted on by gravity. The path the object
follows is determined by these effects (ignoring air resistance). This path is the object's trajectory. The
trajectory has horizontal (x) and vertical (y) components. Velocity is a vector (it has magnitude and
direction), so the overall velocity of an object can be found with vector addition of the x and y
components: v2
= vx
2
+ vy
2
. The units to express the horizontal and vertical distances are meters (m).
The horizontal and vertical velocities are expressed in meters per second (m/s).
Horizontal distance
horizontal distance = (initial horizontal velocity)(time)
x = vxo t
Vertical distance
Horizontal velocity
horizontal velocity = initial horizontal velocity
vx = vxo
Vertical velocity
vertical velocity = initial vertical velocity - (acceleration due to gravity)(time)
vy = vyo - gt
x = horizontal distance (m)
y = vertical distance (m)
v = velocity (combined components, m/s)
vx = horizontal velocity (m/s)

vy = vertical velocity (m/s)
vxo = initial horizontal velocity (m/s)
vyo = initial vertical velocity (m/s)
t = time (s)
)
Torque Formula (Moment of Inertia and Angular Acceleration)
In rotational motion, torque is required to produce an angular acceleration of an object. The amount of
torque required to produce an angular acceleration depends on the distribution of the mass of the
object. The moment of inertia is a value that describes the distribution. It can be found by integrating
over the mass of all parts of the object and their distances to the center of rotation, but it is also
possible to look up the moments of inertia for common shapes. The torque on a given axis is the
product of the moment of inertia and the angular acceleration. The units of torque are Newton-meters
(N∙m).
torque = (moment of inertia)(angular acceleration)
τ = Iα
τ = torque, around a defined axis (N∙m)
I = moment of inertia (kg∙m2
)
α = angular acceleration (radians/s2
)
Spring Constant Formula
Springs have their own natural "spring constants" that define how stiff they are. The letter k is used for
the spring constant, and it has the units N/m. By Newton's Third Law of Motion, as a spring is pulled, it
pulls back with a restoring force. This force follows Hooke's Law, which relates the force of the spring
to the spring constant, and the displacement of the spring from its original position.
force of the spring = -(spring constant k)(displacement)
F = -kx
F = restoring force of the spring (directed toward equilibrium)
k = spring constant (units N/m)
x = displacement of the spring from its equilibrium position
Specific Heat Formula
When heat energy is added to a substance, the temperature will change by a certain amount. The
relationship between heat energy and temperature is different for every material, and the specific heat
is a value that describes how they relate.

heat energy = (mass of substance)(specific heat)(change in temperature)
Q = mc∆T
Q = heat energy (Joules, J)
m = mass of a substance (kg)
c = specific heat (units J/kg∙K)
∆ is a symbol meaning "the change in"
∆T = change in temperature (Kelvins, K)
Amplitude Formula
For an object in periodic motion, the amplitude is the maximum displacement from equilibrium. For
example, a pendulum swings through its equilibrium point (straight down), then swings to a maximum
distance away from the center. This distance is the amplitude, A. The full range of the pendulum has a
magnitude of 2A. Periodic motion also applies to things like springs and waves. The sine function
oscillates between values of +1 and -1, so it is used to describe periodic motion. The unit for amplitude
is meters (m).
position = amplitude x sine function(angular frequency x time + phase difference)
x = A sin(ωt + ϕ)
x = displacement (m)
A = amplitude (m)
ω = angular frequency (radians/s)
t = time (s)
ϕ = phase shift (radians)
Torque Formula (Force at a Distance)
A force that acts on a moment arm, and is used to cause rotational motion is called torque. Torque is
the cross product of a length and a force. The length is between a center of rotation and the point
where a force is applied. The cross product can only be applied between two vectors (magnitude and
direction). The solution to a cross product is: , where is a vector that is
perpendicular to the other two. The Greek letter tau ( ) is used to represent it. The units of torque are
Newton-meters (N∙m).
torque = (distance between a center of rotation and a force) x (force)
= torque (N∙m)
= force vector (N)

= length vector, directed from the center of rotation to the force point (meters)
Elastic Potential Energy Formula
Elastic potential energy is the stored energy of a compressible or stretchable object like a spring or
rubber band or molecule. Elastic potential energy is equal to the force times the distance of
movement.
Elastic potential energy = force x distance of displacement.
W = Fs
W = elastic potential energy, in Joules
F = force, in Newtons
s = displacement, m
Because the force is = spring constant x displacement, then the Elastic potential energy = spring
constant x displacement squared.
F = 1/2 ks
k = spring constant, Newtons/m
So W = (1/2 ks)s
W = 1/2ks2
= PE
Free Fall Formula
Free fall means that an object is falling freely with no forces acting upon it except gravity, a defined
constant, g = -9.8 m/s2
. The distance the object falls, or height, h, is 1/2 gravity x the square of the time
falling. Velocity is defined as gravity x time.
h = 1/2gt2
, m
v = gt, m/s
Average Acceleration Formula
Acceleration is the rate of change for velocity, that is, change in velocity over a specified period of
time. Average acceleration is the final velocity minus the initial velocity per time taken.
Aav g = Δv / Δt
Aavg = Average acceleration, m/s2
Δv = vf - vi, m/s
Δt = tf - ti, s
Elastic Collision Formula

An elastic collision is a collision where both kinetic energy, KE, and momentum, p, are conserved. This
means that KE0 = KEf and po = pf. Recalling that KE = 1/2 mv2
, we write 1/2 m1(v1i)2
+ 1/2 m2(vi)2
= 1/2
m1(v1f)2
+ 1/2 m2 (v2f)2
, the final total KE of the two bodies is the same as the initial total KE of the two
bodies. And, since p = linear momentum = mv, then we write m1v1i + m2v2i = m1v1f + m2v2f.
[A] m1v1i + m2v 2i = m1v1f + m2v2f
[B] 1/2 m1(v1i)2
+ 1/2 m2(vi)2
= 1/2 m1(v1f)2
+ 1/2 m2 (v2f)2
KE = kinetic energy
p = momentum
m = mass, kg
mi = mass of 1st object
m2= mass of 2nd object
v = velocity, m/s
v1 = velocity of 1st object
v2 = velocity of 2nd object
vf = final velocity
Heat Capacity Formula
The heat capacity, or 'thermal mass' of an object, is defined as the Energy in Joules required to raise
the temperature of a given object by 1º C. This is the 'specific heat' of the object (a defined
physical/chemical property) multiplied by its mass and the change in temperature.
Heat capacity = mass x specific heat x change in temperature
Q = mc Δ T
Q = heat capacity, J
m = mass, g
c = specific heat of object, J/(g-ºC)
ΔT = change in temperature, ºC
Gravity Formula
Gravity is the Force of attraction between two objects times the gravitational constant, and inversely
related to the square of the distance between the objects.
Force = [gravitational constant x masses (m1 x m2)] / (radius)2
F = [Gm1m2] / r2
F = force of gravity, N/kg
G = gravitational constant, 6.67 x 10-11
N-m2
/kg2

m1 = 1st mass, kg
m2 = 2nd mass, kg
r = distance between the two masses, m
Tension Formula
The tension on an object is equal to the mass of the object x gravitational force plus/minus the mass x
acceleration.
T = mg + ma
T = tension, N, kg-m/s2
m = mass, kg
g = gravitational force, 9.8 m/s2
a = acceleration, m/s2
Centripetal Acceleration Formula
The centripetal ('center-seeking') acceleration is the motion inwards towards the center of a circle. The
acceleration is equal to the square of the velocity, divided by the radius of the circular path.
ac = v2
/r
ac = acceleration, centripetal, m/s2
v = velocity, m/s
r = radius, m
Gravitational Potential Energy Formula
The gravitational potential energy of an object is the 'stored energy' that the object has by being at that
height. This is equivalent to its mass times the force of gravity, g (a defined constant of 9.8 m/s2) times
the height of the object.
Potential energy = mass x gravity x height.
Egrav = PE = mgh
PE = potential energy, J or kg.m2/s2
m = mass, kg
g = gravity = 9.8 m/s2
h = height, m
Impulse Formula

An impulse is a force applied for a specified period of time. Thus I, the impulse, is equal to a force, F, x
time, t.
I = Ft
I = impulse, N-sec
F = force, N
t = time, sec
Capacitance Formula
Electrical capacitance is a property of objects that can hold electric charge. A capacitor is an electric
component that results from creating a small gap between charge-carrying layers, for example, a
parallel-plate capacitor. The capacitance is the collected charge divided by the voltage difference
across the capacitor. Capacitance is measured in Farads (F), charge is measured in Coulombs (C),
and voltage is measured in Volts (V). Be careful not to confuse capacitance: C, and the unit
Coulombs: C.
C = capacitance (Farads, F)
Q = the charge built up on the capacitor (Coulombs, C)
V = voltage difference between two sides of a capacitor (Volts, V)
Distance Speed Time Formula
Speed is a measure of how quickly an object moves from one place to another. It is equal to the
distance traveled divided by the time. It is possible to find any of these three values using the other
two. This picture is helpful:
The positions of the words in the triangle show where they need to go in the equations. To find the
speed, distance is over time in the triangle, so speed is distance divided by time. To find distance,
speed is beside time, so distance is speed multiplied by time.

, ,
, ,
s = speed (meters/second)
d = distance traveled (meters)
t = time (seconds)
Orbital Velocity Formula
Objects that travel in uniform circular motion around the Earth are said to be "in orbit". The velocity of
this orbit depends on the distance from the object to the center of the Earth. The velocity has to be just
right, so that the distance to the center of the Earth is always the same.The orbital velocity formula
contains a constant, G, which is called the "universal gravitational constant". Its value is = 6.673 x 10-
11
N∙m2
/kg2
.The radius of the Earth is 6.38 x 106
m.
v = the orbital velocity of an object (m/s)
G = the universal gravitational constant, G = 6.673x10(-11)
N∙m2
/kg2
mE = the mass of the Earth (5.98 x 1024
kg)
r = the distance from the object to the center of the Earth
Resistance Formula
Electrical resistance is a property of materials that allow electric current to flow. Resistance opposes
the flow of current. The unit of resistance is Ohms, which is represented with the Greek uppercase
letter omega: Ω. Resistors are components of electric circuits. The resistance depends on the voltage
across the resistor, and the current flowing through it.
R = resistance (Ohms, Ω)
V = voltage difference between the two ends of a resistor (Volts, V)
I = the current flowing through a resistor (Amperes, A)

Reynold's Number Formula
The Reynold's number is used to describe fluid flow. Flow can be laminar, turbulent, or between these
two states (a transient flow). It is found by dividing the fluid's inertial force by its viscous force. The
Reynold's number is unitless. Low Reynold's numbers indicate laminar flow, meaning it is smooth and
constant. High Reynold's numbers indicate turbulent flow, meaning it is chaotic. Values in between
indicate transient flow, meaning the flow changes with time. The Reynold's number can be used for a
number of fluid flow situations, as well as objects moving through fluids.
R = Reynold's number (unitless)
ρ = the density of the fluid (kg/m3
)
v = the velocity of the fluid (m/s)
L = the "characteristic length"or diameter of the fluid flow (m)
μ = the viscosity of the fluid
For a circular pipe, the characteristic length is the diameter of the pipe. The boundaries between the
types of flow are:
 Laminar flow when R < 2300
 Transient flow when 2300 < R < 4000
 Turbulent flow when R > 4000
Angular Momentum Formula
Angular momentum relates to how much an object is rotating. An object has a constant angular
momentum when it is neither speeding up nor slowing down. It is equal to the cross product of a length
and a linear momentum. The length is between a center of rotation and a point where the linear
momentum is present. The cross product can only be applied between two vectors (magnitude and
direction), and the solution to a cross product is: , where is a vector that is
perpendicular to the other two. The units of angular momentum are kg∙m2
/s.
angular momentum = (distance from the center of rotation) x (linear momentum)
angular momentum (kg∙m2
/s)
length vector, directed from the center of rotation to the momentum point(meters)
linear momentum vector (kg∙m/s)

Initial Velocity Formula
Velocity is the rate that the position of an object changes relative to time. Forces acting on an object
cause it to accelerate. This acceleration changes the velocity. The initial velocity,vi is the velocity of the
object before acceleration causes a change. After accelerating for some amount of time, the new
velocity is the final velocity, vf.
initial velocity = final velocity - (acceleration×time)
vi = vf - at
vi = initial velocity (m/s)
vf = final velocity (m/s)
a = acceleration (m/s2
)
t = time between the start and end of the acceleration (s)
Inverse Square Law Formula
The inverse square law describes the intensity of light at different distances from a light source. Every
light source is different, but the intensity changes in the same way. The intensity of light is inversely
proportional to the square of the distance. This means that as the distance from a light source
increases, the intensity of light is equal to a value multiplied by 1/d2
,. The proportional symbol, , is
used to show how these relate. The relationship between the intensity of light at different distances
from the same light source can be found by dividing one from the other. The formula for this is shown
below. Visible light is part of the electromagnetic spectrum, and the inverse square law is true for any
other waves or rays on that spectrum, for example, radio waves, microwaves, infrared and ultraviolet
light, x rays, and gamma rays. The intensity of visible light is measured in candela units, while the
intensity of other waves is measured in Watts per meter squared (W/m2
).
Proportional:
I = light intensity (candela, W/m2
)
means "is proportional to"
d = distance from a light source (m)
Intensity at different distances:

I1 = light intensity at distance 1
I2 = light intensity at distance 2
d1 = distance 1 from light source (m)
d2 = distance 2 from light source (m)
Work Formula
Work is the result when a force acts on an object and moves it by some distance. Sometimes, the
direction an object moves is not the same as the direction of the force. In that case, only the
component of the force that acts in the direction of the movement causes work to be done. The work
formula includes the cosine of the angle between the force and distance for this reason. If the force
and movement are in the same direction, than the angle is equal to 0 radians (or 0°). The cosine of
zero is: cos0 = 1. The units of work are Joules (J), where 1 J = 1 N∙m = 1 kg∙m2
/s2
.
work = force x distance×cosine(the angle between force and movement directions)
W = Fd cosθ
W = work (units J)
k = force (units N)
d = distance (m)
θ = the angle between the force direction and movement direction
Air Resistance Formula
Air resistance is a force that affects objects that move through the air. Often physics problems used in
teaching ignore it, but it is very important for understanding the motion of fast-moving objects like
airplanes. It depends on the density of the air, the area of the object, the velocity it is moving, and a
"drag coefficient" that accounts for other properties of the object like the surface roughness, and
turbulence. Air resistance is also called "drag", and the unit for this force is Newtons (N).
F = force due to air resistance, or drag (N)
k = a constant that collects the effects of density, drag, and area (kg/m)
v = the velocity of the moving object (m/s)
ρ = the density of the air the object moves through (kg/m3
)
CD = the drag coefficient, includes hard-to-measure effects (unitless)
A = the area of the object the air presses on (m2
)

Angular Momentum Formula(Moment of Inertia and Angular Velocity)
Angular momentum relates to how much an object is rotating. An object has a constant angular
momentum when it is neither speeding up nor slowing down. The angular momentum of an object
depends on the distribution of the mass of the object. The moment of inertia is a value that describes
the distribution. It can be found by integrating over the mass of all parts of the object and their
distances to the center of rotation, but it is also possible to look up the moments of inertia for common
shapes. The angular momentum is the product of the moment of inertia and the angular velocity
around an axis.The units of angular momentum are kg∙m2
/s.
angular momentum = (moment of inertia)(angular velocity)
L = Iω
L = angular momentum (kg∙m2
/s)
)
ω = angularvelocity (radians/s)
Center of Mass Formula
The center of mass is a point of balance of an object or a group of objects. The center of mass can be
found for any one, two-, or three-dimensional object, and so the units are meters (m) in each
dimension. The formula given here is for the center of mass in one dimension.
X = center of mass (m)
mi = mass of a part of an object (kg)
xi = position of the part of an object (m)
Flow Rate Formula
The flow rate of a liquid is a measure of the volume of liquid that moves in a certain amount of time.
The flow rate depends on the area of the pipe or channel that the liquid is moving through, and the
velocity of the liquid. If the liquid is flowing through a pipe, the area is A = πr2, where r is the radius of
the pipe. For a rectangle, the area is A = wh where w is the width, and h is the height. The flow rate
can be measured in meters cubed per second (m3
/s), or in liters per second (L/s). Liters are more
common for measures of liquid volume, and 1 m3
/s = 1000 L/s.
fluid flow rate = area of the pipe or channel×velocity of the liquid
Q = Av

Q = liquid flow rate (m3
/s or L/s)
A = area of the pipe or channel (m2
)
v = velocity of the liquid (m/s)
Stopping Distance Formula
If a driver puts on the brakes of a car, the car will not come to a stop immediately. The stopping
distance is the distance the car travels before it comes to a rest. It depends on the speed of the car
and the coefficient of friction (μ) between the wheels and the road. This stopping distance formula
does not include the effect of anti-lock brakes or brake pumping. The SI unit for stopping distance is
meters.
d = stopping distance (m)
v = velocity of the car (m/s)
μ = coefficient of friction (unitless)
)
Escape Velocity Formula
The escape velocity is the minimum velocity required to leave a planet or moon. For a rocket or other
object to leave a planet, it must overcome the pull of gravity. The formula for escape velocity contains
a constant, G, which is called the "universal gravitational constant". Its value
is . The unit for escape velocity is meters per second (m/s).
escape velocity (m/s)
G = universal gravitational constant ( )
M = mass of the planet or moon (kg)
R = radius of the planet or moon (m)

Inelastic Collision Formula
An inelastic collision is any collision between objects in which some energy is lost. A special case of
this is sometimes called the "perfectly" inelastic collision. In a perfectly inelastic collision, two objects
collide and stick together. The momentum of the objects before the collision is conserved, but the total
energy is not conserved. The final velocity of the combined objects depends on the masses and
velocities of the two objects that collided. The units for the initial and final velocities are m/s, and the
unit for mass is kg.
mass of a first object (kg)
mass of a second object (kg)
initial velocity of the first object (m/s)
initial velocity of the second object (m/s)
final velocity of the combined objects (m/s)
Kinetic Friction Formula
Kinetic friction is a force that acts between moving surfaces. An object that is being moved over a
surface will experience a force in the opposite direction as its movement. The magnitude of the force
depends on the coefficient of kinetic friction between the two kinds of material. Every combination is
different. The coefficient of kinetic friction is assigned the Greek letter "mu" (μ), with a subscript "k".
The force of kinetic friction is μk times the normal force on an object, and is expressed in units of
Newtons (N).
force of kinetic friction = (coefficient of kinetic friction)(normal force)
Fk = μk η
Fk = force of kinetic friction
μk = coefficient of kinetic friction
Newton's Law of Cooling Formula
Sir Isaac Newton created a formula to calculate the temperature of an object as it loses heat. The heat
moves from the object to its surroundings. The rate of the temperature change is proportional to the
temperature difference between the object and its surroundings. The formula can be used to find the
temperature at a given time. The SI unit of temperature is the Kelvin (K), but degrees Celsius ( ) is
common.

T(t) = Ts + (T0 - Ts ) e(-kt)
T(t) = temperature of an object at a certain time (Kelvin, K)
t = time (s)
Ts = temperature of the surroundings (Kelvin, K)
T0 = starting temperature of the object (Kelvin, K)
k = a cooling constant, specific to the object (1/s)
Pressure Formula
Pressure is a force per unit area that acts on an object. It can be expressed simply as P = F/A,
where F is a force, and A is the area it acts on. Pressure is often calculated for gases and fluids. The
pressure under a liquid or gas is equal to the density of that fluid multiplied by the acceleration due to
gravity and the height (or depth) of the fluid above the certain point. The unit for pressure is the Pascal
(Pa), and
pressure = density of a fluid x acceleration due to gravity x height of fluid column
P = ρgh
P = pressure (Pa)
ρ = density of a gas or fluid (kg/m3
)
)
h = the height of a column of gas or fluid (m)
Average velocity (constant acceleration) Formula
Velocity is the rate at which an object moves. It has both a magnitude (a value) and a direction. When
a velocity is changing as a result of a constant acceleration, the average velocity can be found by
adding the initial and final velocities, and dividing by 2. The unit for velocity is meters per second (m/s).
Note that this formula applies for constant acceleration only.
vavg = average velocity (m/s)
vi = the initial velocity (m/s)
vf = the final velocity (m/s)

Average Velocity Formula (displacement over time)
The velocity of an object is the rate at which it moves from one position to another. The average
velocity is the difference between the starting and ending positions, divided by the difference between
the starting and ending times. Velocity has a magnitude (a value) and a direction. The unit for velocity
is meters per second (m/s).
vavg = average velocity (m/s)
x1 = the start position of an object (m)
x2 = the end position of an object (m)
t1 = the start time of the motion (s)
t2 = the end time of the motion(s)
Linear Speed Formula (Rotating Object)
The linear speed of a point on a rotating object depends on its distance from the center of rotation.
The angular speed is the angle that an object moves through in a certain amount of time. The angular
speed has units of radians per second (rad/s). There are 2π radians in a full circle. At a distance r from
the center of the rotation, a point on the object has a linear speed equal to the angular speed
multiplied by the distance r. The units of linear speed are meters per second, m/s.
linear speed = angular speed x radius of the rotation
v = ωr
v = linear speed (m/s)
ω = angular speed (radians/s)
r = radius of the rotation (m)
angular Acceleration Formula
The angular acceleration of a rotating object is the rate at which the angular velocity changes with
respect to time. It is the change in the angular velocity, divided by the change in time. The average
angular acceleration is the change in the angular velocity, divided by the change in time. The angular
acceleration is a vector that points in a direction along the rotation axis. The magnitude of the angular
acceleration is given by the formula below. The unit of angular acceleration is radians/s2
.

α = angular acceleration, (radians/s2
)
Δω = change in angular velocity (radians/s)
Δt = change in time (s)
ω1 = initial angular velocity (radians/s)
ω2= final angular velocity (radians/s)
t1 = initial time (s)
t2= final time (s)
Linear speed Formula (straight line motion)
Linear speed is the rate at which an object travels along a straight path. It is the distance an object
travels in a certain amount of time. The units of linear speed are meters per second, m/s.
v = linear speed (m/s)
Δs = short form for "the change in" position (m)
Δt = short form for "the change in" time (s)
Horizontal Range Formula
A projectile is an object that is given an initial velocity, and is acted on by gravity. The horizontal range
of a projectile is the distance along the horizontal plane it would travel, before reaching the same
vertical position as it started from. The horizontal range depends on the initial velocity v0, the launch
angle θ, and the acceleration due to gravity. The unit of horizontal range is meters (m).
R = horizontal range (m)
v0 = initial velocity (m/s)
)

θ = angle of the initial velocity from the horizontal plane (radians or degrees)
Instantaneous Speed Formula
Speed is the rate of change of position with time. The speed of an object can change as it moves. The
instantaneous speed is the speed of an object at a certain instant of time. If the position is a function of
time, then the speed depends on the change in the position as time changes. The instantaneous
speed can be found as this change in time becomes small. Calculating the instantaneous speed
requires finding the limit of the position function as the change in time approaches zero. Speed is a
scalar quantity, meaning that it has a magnitude (a value), but no direction. For that reason, speed can
never be negative. The unit for speed is meters per second (m/s).
v = instantaneous speed (m/s)
Δ = "the change in", represented with the Greek letter "delta" (unitless)
x(t) = position as a function of time (m)
t = time (s)
Instantaneous Velocity Formula
Velocity is a measure of how quickly an object moves from one position to another. If an object is
accelerating or decelerating, the velocity of the object changes with time. The instantaneous velocity of
an object is the velocity at a certain instant of time. Velocity is the change in position divided by the
change in time, and the instantaneous velocity is the limit of velocity as the change in time approaches
zero. This is equivalent to the derivative of position with respect to time. Instantaneous velocity is a
vector, and so it has a magnitude (a value) and a direction. The unit for instantaneous velocity is
meters per second (m/s).
= instantaneous velocity (m/s)
= vector change in position (m)
Δt = change in time (s)

= derivative of vector position with respect to time (m/s)
Kinetic Energy Formula
Kinetic energy is the energy of moving objects. An object's kinetic energy depends on the object's
mass and velocity. The unit of kinetic energy is Joules (J). In terms of other units, one Joule is equal to
one kilogram meter squared per second squared ( ).
K = kinetic energy ( )
m = mass (kg)
v = velocity (m/s)
Maximum Height Formula
A projectile is an object that is given an initial velocity, and is acted on by gravity. The maximum height
of the object is the highest vertical position along its trajectory. The maximum height of the projectile
depends on the initial velocity v0, the launch angle θ, and the acceleration due to gravity. The unit of
maximum height is meters (m).
H = maximum height (m)
)
Rotational Kinetic Energy Formula
Kinetic energy is the energy of moving objects, including objects that are rotating. The kinetic energy
of a rotating object depends on the object's angular (rotational) velocity in radians per second, and on
the object's moment of inertia. Moment of inertia is a measure of how easy it is to change the rotation
of an object. Moments of inertia are represented with the letter I, and are expressed in units of kg∙m2
.
The unit of kinetic energy is Joules (J). In terms of other units, one Joule is equal to one kilogram
meter squared per second squared ( ).

K = kinetic energy ( )
)
ω = angular velocity (radians/s)
Strain Formula (general form)
Strain is a measure of the amount an object deforms as a result of a force. There are a number of
types of strain, but in general, strain is the change in a dimension divided by the original value of that
dimension. Some types are:
1. longitudinal strain. The longitudinal strain is the change in length divided by the original length.
2. shearing strain. The shearing strain is the result of a bend in an object, so it is the change in
position of one side of an object divided by the distance between the sides.
3. volumetric strain. The volumetric strain is the result of pressure on a fluid (liquid or gas), and is
equal to the change in volume divided by the original volume.
Strain is a unitless quantity, since the values in the numerator and denominator always have the same
units.
S = strain (unitless)
Δx = change in dimension (m for longitudinal or shearing strain, m3
for volumetric strain)
X = original dimension (m for longitudinal or shearing strain, m3 for volumetric strain)
Time of Flight Formula
A projectile is an object that is given an initial velocity, and is acted on by gravity. The amount of time it
spends in the air is called the time of flight. If the ground from which the projectile is launched is level,
the time of flight only depends on the initial velocity v0, the launch angle θ, and the acceleration due to
gravity. The unit for the time of flight is seconds (s).
t = time of flight (s)

)
Trajectory Formula
A projectile is an object that is given an initial velocity, and is acted on by gravity. The path the object
follows is called its trajectory. The trajectory has horizontal (x) and vertical (y) position components. If
a projectile is launched with an initial velocity v0, at an angle θ from the horizontal plane, then its
vertical position can be found from its horizontal position using the following formula. The units of
horizontal and vertical position are meters (m).
y = vertical position (m)
x = horizontal position (m)
v0 = initial velocity (combined components, m/s)
)
Capacitors in Parallel Formula
In electric circuits, it is often possible to replace a group of capacitors with a single, equivalent
capacitor. The equivalent capacitance of a number of capacitors in parallel is the sum of the individual
capacitances. The unit of capacitance is the Farad (F), which is equal to a Coulomb per Volt (1 F = 1
C/V), though most electronic circuits use much smaller capacitors. Picofarad (1 pF = 10-12
F),
nanofarad (1 nF = 10-9
F), and microfarad (1 µF = 10-6
F) capacitors are common.
Ceq = equivalent capacitance (F or smaller units)
C1 = capacitance of first capacitor (F)
C2 = capacitance of second capacitor (F)
C3 = capacitance of third capacitor (F)

Capacitors in Series Formula
In electric circuits, it is often possible to replace a group of capacitors with a single, equivalent
capacitor. The equivalent capacitance of a number of capacitors in series can be found using the
reciprocal of capacitance, 1/C. The reciprocal of the equivalent capacitance is equal to the sum of the
reciprocals of each capacitance. The unit of capacitance is the Farad (F), which is equal to a Coulomb
per Volt (1 F = 1 C/V), though most electronic circuits use much smaller capacitors. Picofarad (1 pF =
10-12
F), nanofarad (1 nF = 10-9
F), and microfarad (1 µF = 10-6
F) capacitors are common.
Ceq = equivalent capacitance (F or smaller units)
C1 = capacitance of first capacitor (F)
C2 = capacitance of second capacitor (F)
C3 = capacitance of third capacitor (F)
Electric Power Formula
Electric power is the rate at which energy is transferred to or from a part of an electric circuit. A battery
can deliver energy, or a circuit element like a resistor can release energy as heat. For any circuit
element, the power is equal to the voltage difference across the element multiplied by the current. By
Ohm's Law, V = IR, and so there are additional forms of the electric power formula for resistors. Power
is measured in units of Watts (W), where a Watt is equal to a Joule per second (1 W = 1 J/s).
General form:
electric power = voltage difference x current
P = VI
Resistors:
P = electric power (W)
V = voltage difference (V = J/C)
I = electric current (A = C/s)
R = resistance (Ω = V/A)
Resistors in Parallel Formula

In electric circuits, it is often possible to replace a group of resistors with a single, equivalent resistor.
The equivalent resistance of a number of resistors in parallel can be found using the reciprocal of
resistance, 1/R. The reciprocal of the equivalent resistance is equal to the sum of the reciprocals of
each resistance. The unit of resistance is the Ohm (Ω), which is equal to a Volt per Ampere (1 Ω = 1
V/A). Larger resistors with kilo-Ohm (1 kΩ = 103
Ω) or mega-Ohm (1 MΩ = 106
Ω) resistances are
common, as well.
Req = equivalent resistance (Ω or larger units)
R1 = resistance of first resistor (Ω)
R2 = resistance of second resistor (Ω)
R3 = resistance of third resistor (Ω)
Resistors in Series Formula
In electric circuits, it is often possible to replace a group of resistors with a single, equivalent resistor.
The equivalent resistance of a number of resistors in series is the sum of the individual resistance
values. The unit of resistance is the Ohm (Ω), which is equal to a Volt per Ampere (1 Ω = 1 V/A).
Larger resistors with kilo-Ohm (1 kΩ = 103
Ω) or mega-Ohm (1 MΩ = 106
Ω) resistances are common,
as well.
equivalent resistance = resistor 1 + resistor 2 + resistor 3 + ...
Req = equivalent resistance (Ω or larger units)
R1 = resistance of first resistor (Ω)
R2 = resistance of second resistor (Ω)
R3 = resistance of third resistor (Ω)
Coulomb's Law Formula
Objects with electric charge attract and repel each other by exerting forces. Charges with the same
sign repel, and charges with opposite signs attract. The magnitude of the electrostatic force between
charges can be found using Coulomb's Law. The electrostatic force depends on the magnitude of the
charges, the distance between them, and the Coulomb constant, which is .
The Coulomb constant can also be written in terms of the permittivity of free space, . In that form,
the Coulomb constant is . The values of the electric charges have units of Coulombs, C.

Charges are often written as multiples of the smallest possible charge, . The unit of
the electrostatic force is Newtons (N).
F = electrostatic force between two point charges ( )
k = Coulomb constant ( )
q1 = charge of the first point charge (C)
q2 = charge of the second point charge (C)
r = distance between charges (m)
Gravitational Force Formula
Every object in the universe attracts every other object. The gravitational force formula, also known as
Newton's Law of Gravitation, defines the magnitude of the force between any two objects. The formula
for the gravitational force includes the gravitational constant, which has a
value . The unit of the gravitational force is Newtons (N).
Fg = gravitational force between two objects ( )
G = gravitational constant ( )
m1 = mass of the first object (kg)
m2 = mass of the second object (kg)
r = distance between objects (m)
Length Contraction Formula
Special relativity states that the distance between two points can differ in different reference frames.
The distance between points, and therefore the length, depends on the velocity of one reference frame
relative to another. In one reference frame, an object being measured will be at rest. This is called
the proper length, and is labeled Δl0. In another reference frame, an observer will see the object
moving. The length of the object in this reference frame is observed length, and is labeled Δl. The
observed length is always shorter than the proper length. This effect is called length contraction. Both
Δl0 and Δl are measured in meters (m).

Δl = the observed length, in the reference frame in which the object is moving (m)
Δl0 = the proper length, in the reference frame in which the object is at rest (m)
v = velocity (m/s)
c = speed of light (3.0 x 108
m/s)
Snell's Law Formula
When light strikes a smooth barrier between two transparent materials, the light is partly reflected, and
partly refracted (transmitted). The formula that describes refraction is also known as Snell's Law. The
angle of refraction depends on the angle of incidence of the light, and the indexes of refraction of the
two materials. The index of refraction of a material depends on the material's properties. The angles in
Snell's Law are always measured relative to the normal to the barrier, which is perpendicular to the
barrier's surface. The angles are measured in radians or degrees, and the indexes of refraction are
unitless numbers.
na = index of refraction in material a, (unitless)
nb = index of refraction in material b, (unitless)
θa = angle of light relative to normal to the barrier in material a, (radians or degrees)
θb = angle of light relative to normal to the barrier in material b, (radians or degrees)
Time Dilation Formula
Special relativity states that time can pass at different rates in different reference frames. The time
depends on the velocity of one reference frame relative to another. In one reference frame, two events
(for example, two ticks of a clock) will occur at the same position. In this reference frame, the time
between the events is called one-position time or proper time, and is labeled Δt0. In another reference
frame, an observer will see the two events happen in different positions. In the observer's reference
frame, the time between events is called two-position time or observer time, and is labeled Δt. The
observer time is always larger than the proper time. This effect is called time dilation. Both Δt0 and Δt
are measured in seconds (s).

Δt = the observer time, or two-position time (s)
Δt0 = the proper time, or one-position time (s)
v = velocity (m/s)
c = speed of light (3.0 x 108
m/s)
Electric Field Formula
Objects with electric charge emit electric fields. This electric field is the source of the electrostatic force
that nearby charged objects experience. The electric field is a vector quantity, and the direction of the
field lines depends on the sign of the source charge. Electric field vectors point away from positively
charged sources, and toward negatively charged sources. The formula for the electric field includes
the Coulomb constant, which is . The Coulomb constant can also be written
in terms of the permittivity of free space, . In that form, the Coulomb constant is . The unit
of the electric field magnitude is Newtons per Coulomb, N/C.
= electric field vector at a certain position in space (N/C)
k = Coulomb constant ( )
q = charge of a single point source of the electric field (C)
r = distance from the source charge (m)
= unit vector (length is 1), the direction of the electric field (unitless)
Kirchhoff's Junction Rule Formula
In a closed circuit, there can be any number of circuit elements, such as batteries and resistors. The
circuit can branch, creating "junctions", where the circuit separates or recombines. The sum of the
currents in and out of a circuit junction must be zero. This is known as Kirchhoff's Junction Rule.
Current is measured in Amperes (A).

I = current, (Amperes, A)
Kirchhoff's Loop Rule Formula
In any "loop" of a closed circuit, there can be any number of circuit elements, such as batteries and
resistors. The sum of the voltage differences across all of these circuit elements must be zero. This is
known as Kirchhoff's Loop Rule. Voltage differences are measured in Volts (V). When the current I in
the loop is given in Amperes (A) and resistance of circuit elements is given in Ohms (Ω), the voltage
difference across a resistor can be found using the formula .
V = voltage difference, (Volts, V)
Ohm's Law Formula
Ohm's Law relates the voltage across different parts of an electric circuit to the electric current and
resistance. Voltage is a difference in the electric potential between two points in a circuit. For example,
the potential difference (voltage) across a resistor can be found by multiplying its resistance by the
current flowing through it. The unit of voltage is the Volt (V). Current is measured in Amperes (A), and
resistance is measured in Ohms ( ), where one Ohm is equal to one Volt per Ampere ( ).
V = voltage, also known as potential difference (Volts, V)
I = electric current (Amperes, A)
R = resistance (Ohms, )
Relativity Formula
Special relativity states that time, length, energy, and momentum can depend on the velocity of one
reference frame relative to another. An observer on a spaceship moving near the speed of light will
measure time, length, energy, and momentum differently than an observer that is outside the ship. The
formula that relates a value in one reference frame to the value in another is labeled with the Greek
letter ("gamma"). It depends on the velocity, divided by the speed of light. The value is unitless.

= gamma, (unitless)
v = velocity (m/s)
c = speed of light ( )
Centripetal Acceleration Formula
When an object moves along a circular path, the direction of the object's velocity must constantly
change. A changing velocity means that there must be an acceleration. This acceleration is
perpendicular to the direction of the velocity. This is called the radial acceleration, or centripetal
acceleration ("centripetal" means "center seeking"). The radial acceleration is equal to the square of
the velocity, divided by the radius of the circular path of the object. The unit of the centripetal
acceleration is meters per second squared ( ).
= radial, or centripetal, acceleration (m/s2
)
v = velocity (m/s)
r = radius of motion of the object (m)
Conservation of Energy Formula
An object, or a closed system of objects, can have both kinetic and potential energy. The sum of the
kinetic and potential energy of the object or system is called the total mechanical energy. If no outside
forces act on the system, then the total mechanical energy is conserved. Energy can change from
kinetic to potential energy, and back, without reducing the total energy. The sum of the kinetic and
potential energy at an initial time will be equal to the sum of the kinetic and potential energy at any
other time.
Often, a mechanical system is not fully closed. Either the system can do work on the surroundings (for
example, by heating), or work can be done on the system (for example, air resistance, or friction). In
this case, a term for "other work" is added to the formula to account for the change in total mechanical
energy. The unit of energy and work is Joules (J).

K1 = initial kinetic energy (Joules, J)
U1 = initial potential energy (J)
wother = other work, gained or lost to the system (J)
K2 = final kinetic energy (J)
U2 = final potential energy (J)
Decibel Formula
The intensity of a sound wave is the rate at which it transports energy per unit area. This is equivalent
to average power per unit area, expressed as Watts per square meter ( ). A more common way
to express sound intensity is using the decibel scale. The decibel scale uses the logarithmic function to
represent a large range of intensities easily. The unit of the scale is the decibel, dB.
= sound intensity, in decibels (dB)
I = sound intensity ( )
I0 = reference sound intensity ( )
Doppler Effect Formula
The sound that a listener hears can change if the source of the sound and the listener are moving
relative to each other. This is called the Doppler Effect. When the listener and the source are moving
closer, the frequency heard by the listener will be higher than the frequency of the sound emitted by
the source. When the listener and the source are moving away from each other, the frequency heard
by the listener will be lower than the frequency of the sound from the source. The unit of sound
frequency is usually written as Hertz ( ), where one Hertz is a cycle per second (
).
fL = frequency of sound heard by the listener ( , or )
v = speed of sound in the medium (m/s)
vL = listener's velocity (m/s)
vs = velocity of the sound source (m/s)

fs = frequency of sound emitted by the source ( , or )
Hooke's Law Formula
Pulling or pushing a spring away from its equilibrium (resting) position requires a force to be applied.
When the spring is held at a distance x from its equilibrium position, the spring exerts a restoring
force in the negative x direction. For many springs, the restoring force is proportional to the distance
away from equilibrium the spring is held. This is known as Hooke's Law. The relationship between the
force and the distance is determined by a constant. The spring constant k is specific to a certain
spring, and has units Newtons per meter (N/m). The unit of the restoring force is Newtons (N).
F = restoring force of a spring (Newtons, N)
k = spring constant (N/m)
x = displacement of the spring (m)
Average Angular Velocity Formula
The angular velocity of a rotating object is the rate at which the angular coordinate changes with
respect to time. The angular coordinate is the angle of the object relative to a certain coordinate
system, and is usually represented with the Greek letter θ ("theta"). The average angular velocity is
the change in the angular coordinate θ, expressed in radians, divided by the change in time. The
angular velocity is a vector that points in the direction of the axis of rotation. The magnitude of the
angular velocity is given by the formula below. The unit of angular velocity is .
= average angular velocity, ( )
= change in angular coordinate (radians)
= change in time (s)
= initial angular coordinate (radians)
= final angular coordinate (radians)
t1 = initial time (s)
t2 = final time (s)

Gravitational Field Formula
The acceleration due to gravity near the Earth depends on the distance of an object from Earth's
center. The gravitational field formula can be used to find the field strength, meaning the acceleration
due to gravity at any position around the Earth. The radius of the Earth is , and so
values of r in the formula are (typically) greater than this radius. The gravitational field strength is
measured in Newtons per kilogram ( ), or in the same units as acceleration, .
g(r) = Earth's gravitational field strength ( or )
G = gravitational constant ( )
mE = mass of the Earth ( )
r = distance from the center of the Earth (m)
Ideal Gas Law Formulas
In an ideal gas, there are no attractive forces between the gas molecules. This is a good
approximation for most gases. An ideal gas has three variables that define its state. They are:
absolute pressure (P), volume (V), and absolute temperature (T). The ideal gas law defines how these
state variables relate to each other. There are two forms, one defined in terms of the number of moles
(mol) of gas, and one defined in terms of the number of molecules of gas. One mole of a substance
consists of molecules. Pressure is measured in Pascals ( ), volume is measured
in cubic meters (m3
), and temperature is measured in Kelvin (K).
P = pressure (Pa)
V = volume (m3
)
n = number of moles of gas (mol)
R = gas constant ( )
T = temperature (K)
N = number of molecules of gas (unitless)
kB = Boltzmann's constant ( )
Impulse Formula

Impulse is a quantity that is closely related to momentum. Impulse is a vector, with both a value and a
direction, and is represented by the symbol . Impulse is the product of a constant force , and a time
interval . The Greek letter ("delta") is used to mean "the change in", and is the amount of time
for which the force is applied. The unit of impulse is the Newton-second, .
= impulse ( )
= applied force (N)
= time interval for which the force is applied (s)
Einstein's Mass-Energy Equivalence Formula
Albert Einstein's most famous equation shows that mass can be converted to energy, and energy can
be converted to mass. This means, in essence, that mass and energy are equivalent concepts. The
energy produced by complete conversion of mass to energy is equal to the mass of an object times
the speed of light squared. Note that this formula applies to the "rest mass" of an object. For fast-
moving objects, special relativity applies, and a different formula is required to find the total energy.
The unit of energy is Joules (J), where
E = energy (Joules, J)
m = mass (kg)
c = speed of light in vacuum ( )
Kinetic Energy of Gas Formula
In an ideal gas, there are no attractive forces between the gas molecules, and there is no rotation or
vibration within the molecules. The kinetic energy of the translational motion of an ideal gas depends
on its temperature. The formula for the kinetic energy of a gas defines the average kinetic energy per
molecule. The kinetic energy is measured in Joules (J), and the temperature is measured in Kelvin (K).
K = average kinetic energy per molecule of gas (J)
kB = Boltzmann's constant ( )
T = temperature (k)

Impulse-Momentum Theorem Formula
Impulse is a quantity that is closely related to momentum. When an object has a momentum , and a
force is applied for an amount of time, the momentum can change to a new value . The impulse-
momentum theorem states that the impulse is equal to this change in momentum. Impulse is a vector,
with both a value and a direction, and is represented by the symbol . Momentum is equal to the mass
times the velocity of an object ( ). The unit of impulse is the Newton-second, , which is
equivalent to .
= impulse ( , or )
= final momentum ( )
= initial momentum ( )
Moment of Inertia Formula (common shapes)
The moment of inertia is a value that measures how difficult it is to change the state of an object's
rotation. The moment of inertia depends on the mass and shape of an object, and the axis around
which it rotates. The moments of inertia for some common shapes can be found using the following
formulas. The moment of inertia of an object made of a number of these common shapes is the sum of
the moments of inertia of its components. The unit for moment of inertia is the kilogram-meter
squared, .
Object Type Description Formula
Thin rod, axis
through the
center
Thin rod, axis
through one end
Rectangular plate,
axis through
center
Rectangular plate,
axis along edge
Hollow cylinder,

with a wall
thickness
Solid cylinder
Thin-walled
hollow cylinder
Solid sphere
Thin-walled
hollow sphere
I = moment of inertia ( )
M = total mass of the rotating object (kg)
L = the total length of the rod (m)
a = the length of two sides of the plate (m)
b = the length of the other two sides of the plate (m)
R1 = the inner radius of the cylinder (m)
R2 = the outer radius of the cylinder (m)
R = the radius of the cylinder or sphere (m)
One-Dimensional Kinematics Formula
One-dimensional motion can be described using formulas that relate displacement, velocity, and
acceleration. Velocity is the rate of change of displacement with respect to time. Acceleration is the
rate of change of velocity with respect to time. In these formulas, the acceleration is assumed to be
constant. The unit of displacement is the meter (m), the unit of velocity is meters per second (m/s),
and the unit of acceleration is meters per second squared (m/s2
).
Velocity
Displacement
Velocity, Acceleration, Displacement

Displacement and Velocity
x0 = initial displacement (m)
x = final displacement (m)
v0x = initial velocity (m/s)
vx = final velocity (m/s)
ax = acceleration (m/s2
)
t = time (s)
Simple Harmonic Motion Formula
Simple Harmonic Motion (SHM) is a special type of periodic motion that follows a certain pattern. The
position of an object in simple harmonic motion is described by a sine function that depends on an
amplitude of the motion A, an angular frequency , time t, and a starting condition called the phase
shift . The unit for position and amplitude is meters (m), the unit for angular frequency is radians/s,
the unit for time is seconds (s), and the unit for the phase shift is radians.
x = position (m)
A = amplitude (m)
angular frequency (radians/s)
t = time (s)
phase shift (radians)
Magnetic Field Formula
When electric current is carried in a wire, a magnetic field is formed around it. The magnetic field lines
form concentric circles around the wire. The magnetic field direction depends on the direction of the
current. It can be determined using the "right hand rule", by pointing the thumb of your right hand in
the direction of the current. The direction of the magnetic field lines is the direction of your curled

fingers. The magnitude of the magnetic field depends on the amount of current, and the distance from
the charge-carrying wire. The formula includes the constant . This is called the permeability of free
space, and has a value . The unit of magnetic field is the Tesla, T.
B = magnetic field magnitude (Tesla, T)
= permeability of free space ( )
I = magnitude of the electric current (Amperes, A)
r = distance (m)
Magnetic Force Formula (Charge-Velocity)
When a charged particle moves in a magnetic field, a force is exerted on the moving charged particle.
The formula for the force depends on the charge of the particle, and the cross product of the particle's
velocity and the magnetic field. The direction of the force vector can be found by calculating the cross
product if vector directions are given, or by using the "right hand rule". Imagine your right hand with
your index finger pointed in the direction of the particle's velocity vector. Then, curl your fingers in the
direction of the magnetic field vector. The direction of your thumb is the direction of the cross product
of the vectors. If the charge is positive, the direction of the force will be in the direction of your thumb.
If the charge is negative, the direction of the force will be the opposite. The unit of force is Newtons
(N), the unit of charge is Coulombs (C), the unit of velocity is meters per second (m/s), and the unit of
magnetic field is Teslas (T).
= magnetic force vector (Newtons, N)
q = charge of a moving particle (Coulombs, C)
= particle velocity vector (m/s)
v = particle velocity magnitude (m/s)
= magnetic field vector (Teslas, T)
B = magnetic field magnitude (Teslas, T)
= angle between velocity and magnetic field vectors (radians)
= cross product direction vector (unitless)

Magnetic Force Formula (Current-Length)
When a wire carrying electric charge is placed in a magnetic field, a force is exerted on the wire. The
formula for the force depends on the current, the length of the wire, and the magnetic field. The "length
vector" of the wire specifies the direction in which the current is flowing. The direction of the force
vector can be found by calculating the cross product of the length vector and the magnetic field if
vector directions are given, or by using the "right hand rule". Imagine your right hand with your index
finger pointed in the direction of the length vector. Then, curl your fingers in the direction of the
magnetic field vector. The direction of the force will be in the direction of your thumb. The unit of force
is Newtons (N), the unit of current is Amperes (A), the unit of length is meters (m), and the unit of
magnetic field is Teslas (T).
= magnetic force vector (Newtons, N)
I = current magnitude (Amperes, A)
= length vector (m)
L = wire length, magnitude (m)
= magnetic field vector (Teslas, T)
B = magnetic field magnitude (Teslas, T)
= angle between length and magnetic field vectors (radians)
= cross product direction vector (unitless)
Parallel Axis Theorem Formula
The moment of inertia is a value that measures how difficult it is to change the state of an object's
rotation. The same object can have different moments of inertia, depending where the rotational axis
is. If the moment of inertia for an axis through an object's center of mass is known, it is possible to find
the value of the moment of inertia for any other parallel axis. This is called the parallel axis theorem.
The unit for moment of inertia is the kilogram-meter squared, .
Ip = moment of inertia for rotation around a parallel axis ( )
Icm = moment of inertia for rotation around an axis through the center of mass ( )

M = total mass of the object (kg)
d = distance between the two rotation axes (m)
Rotational Kinematics Formula
Motion of a rotating object can be described using formulas that relate angular displacement, angular
velocity, and angular acceleration. Angular displacement is a measure of the change in the angular
coordinate , angular velocity is the rate of change of the angular coordinate with respect to time, and
angular acceleration is the rate of change of angular velocity with respect to time. In these formulas,
the angular acceleration is assumed to be constant. The angular coordinate and angular displacement
are measured in radians. The unit of angular velocity is per second, which can be written as radians/s,
1/s, or as s-1
. The unit of angular acceleration is per second squared, which can be written as
radians/s2
, 1/s2
, or as s-2
.
Angular Velocity
Angular Displacement
Angular Velocity, Angular Acceleration, Angular Displacement
Angular Displacement and Angular Velocity
= initial angular displacement, around the z axis (radians)
= final angular displacement, around the z axis (radians)
= initial angular velocity, around the z axis ( radians/s, 1/s, or s-1
)

= final angular velocity, around the z axis ( radians/s, 1/s, or s-1
)
= angular acceleration, around the z axis ( radians/s2
, 1/s2
, or s-2
)
t = time (s)
Angular Frequency Formula
Angular frequency is associated with the number of revolutions an object performs in a certain unit of
time. In that sense is related to frequency but in terms of how many times it turns a full period of
motion in radians units.
The formula of angular frequency is given by:
Angular frequency = 2 π / (period of oscillation)
ω = 2π / T = 2πf
Where we have:
ω: angular frequency
T: period
f: frequency
If the motion is alone a circle, we have:
Angular frequency = (angle change) / (time it takes to change the angle)
ω = dθ / dt
θ: is the angle change.
If we know the radius of the circle is R, then we can determine the velocity by:
v = Rω
Bernoulli's Equation Formula
The Bernoulli Equation is a different way of the conservation of energy principle, applied to flowing
fluids. It relates the pressure, the kinetics energy and the gravitational potential energy of a fluid in a
container or flowing in a tube.
Describes the lowering of fluid pressure in regions where the flow velocity is increased. In the high
velocity flow through the constriction, kinetic energy must increase at the expense of pressure energy.
Pressure + ½ density * square of the velocity + density * gravity
acceleration* height = constant
The equation is written
P + ½ ρ v2
+ρ g h = constant
That says the whole formula holds along the system, each term can change but the sum is the same.
We have:
P: Pressure

v: velocity of the fluid
ρ: Density of the fluid
h: height of the container or the pipe here the fluid is flowing
Drag Formula
Drag force is the resistance of a fluid, the force that it applies acting opposite to the motion of an object
that is moving submerge in a certain fluid.
Drag = (density) * (square of the velocity) * (Drag coefficient) *(transversal area)
FD = ½ ρ * v2
* CD * A
We have:
FD: Drag force
ρ: fluid density
v: Relative velocity between the fluid and the object
CD: Drag coefficient
A: Transversal area or cross sectional area
Dynamic Viscosity Formula
Dynamic viscosity is the tangential force required to move one horizontal plane of a fluid with respect
to another.
Dynamic viscosity = shearing stress / shearing rate change
η = τ / γ
We have:
η: Dynamic viscosity
τ: Shearing stress
γ: Shear rate
Kinematic Viscosity Formula
Kinematic viscosity is the measure of the inherent resistance of a fluid to flow when no external force
is exerted, except gravity. It is the ratio of the dynamic viscosity to its density, a force independent
quantity. Kinematic viscosity can be obtained by dividing the absolute viscosity of a fluid with the fluid
mass density.
Kinematic viscosity = Dynamic viscosity / Fluid mass density

ν = η / ρ
We have:
ν: Kinematic viscosity
ρ: fluid density
η: Dynamic viscosity
Mass Continuity Formula
This principle is known as the conservation of mass, it claims that if there are no possible discharge of
mass to another system, the mass in the system will remain constant at any time.
Mass entering per unit time = Mass leaving per unit time
The mass is written in terms of the density of a fluid and the volume occupied.
ρE VE = ρL VL
Where we have:
V: Volume of the fluid that is variating and being transfer from one place to another.
Another way to write this formula is,
ρE VE - ρL VL = ρE AE vE - ρ L AL vL = 0
v: Upstream velocity of the fluid
A: Is the transverse area of the pipe
Mass Flow Rate Formula
Mass Flow Rate is the rate of movement of a massive fluid through a unit area. Mass flow depends on
the density, velocity of the fluid and the area of the cross section. Meaning, it is the movement of mass
per unit time. It's units are kg/s. The formula for mass flow rate is given:
Mass Flow Rate = (density)*(velocity)*(area of the cross section)
m = ρ v A
Where we have:
v: Velocity of the fluid
A: Area or cross section
Volume Continuity Formula

This principle is closely related to the conservation of mass, if there are no possible discharge of
mass, and the fluid is incompressible, then, the volume occupied by that mass will remain constant.
Volume occupied initially = Volume occupied finally
The volume is written in terms of the density of a fluid and the mass.
ME/ρE =ML/ρL
Where we have:
M: Mass of the fluid that flowing from one place to another.
Volume Flow Rate Formula
Is the volume of fluid which is transferred or passes per unit time, for example from one container to
other.
It is represented by the symbol Q, with unit m3/s (cubic meters per second). The formula for volume
flow rate is given:
Volume Flow Rate = (variation of volume) / (variation of time)
Q = ΔV/Δt
Where we have:
ΔV: Volume of the fluid that is variating
Δt: Variation of time
Pressure in a Fluid Formula
The pressure exerted by a static fluid or hydrostatic pressure, is the pressure in an equilibrium system
that depends only upon the depth of the fluid, the density of the fluid, and the acceleration of gravity.
Its units are the same as pressure in general, N/m2. The formula for pressure in a fluid is given:
Pressure in a fluid = (density) * (acceleration of gravity) * (depth of the fluid)
P = ρ g h
Where we have:
g: Acceleration of gravity
h: Depth of the fluid
Bulk modulus Formula

When a force is applied on a body in all directions and results in a deformation of the whole volume,
the elastic coefficient is called the Bulk modulus. Is ratio of the change in pressure to the fractional
volume compression:
Bulk modulus = (change in pressure stress)/(fractional volume) = (change in pressure) / (change in
volume / original volume)
The equation is
B = ΔP /(ΔV/V)
We have:
B: Bulk modulus
ΔP: change of the pressure or force applied per unit area on the material
ΔV: change of the volume of the material due to the compression
V: Initial volume of the material
Froude number Formula
The Froude number is a dimensionless value that describes the different flow regimes of an open
channel flow. The Froude number is a ratio of inertial and gravitational forces. This is written as:
Froude number = Velocity of the fluid / √ (gravity acceleration * depth of flow)
The equation is
Fr = v / √ (g l)
We have:
Fr: Froude number
v: Velocity of fluid
l: Depth of flow
g: Gravitational acceleration
Latent Heat Formula
Latent heat is energy released or absorbed, by a body during a constant-temperature process, for
example a phase change of water from liquid to gas. This is written as:
Sensible heat = (mass of the body) * (specific latent heat)
The equation is
Q= m L
We have:
Q: Latent heat
m: Mass of the body
L: Specific latent heat coefficient of the material

Liquid Expansion Formula
Is the coefficient or number associated with the thermal expansion of a liquid due to an increase in
temperature. It compares the space of the occupied when it is measured at different temperatures,
keeping other physical quantities like pressure at a constant value. There are linear, surface and
volumetric expansion, where the linear is the more commonly used. This is written as:
Linear expansion = (initial length) * (coefficient of linear expansion) * (change of the temperature)
The equation is
ΔL= L α ΔT
We have:
ΔL: Expansion of the liquid
L: Length of the liquid before the change o temperature
ΔT: Change of the temperature
α: Coefficient of expansion associated individually to each material
Sensible Heat Formula
Sensible heat is heat exchanged by a thermodynamic system that changes the temperature of the
system without changing some variables such as volume or pressure. As the name implies, sensible
heat is the heat that you can feel. This is written as:
Sensible heat = (mass of the body) * (specific heat capacity) * (change of the temperature)
The equation is
Q= m c ΔT
We have:
Q: Sensible heat
m: Mass of the body
c: Specific heat coefficient of the material
Shear modulus Formula
When a force is applied on a body which results in its lateral deformation, the elastic coefficient is
called the shear modulus. It is the ratio of shear stress to shear strain in a body. Is written as as:
Shear modulus = (shear stress)/(strain) = (Force * no-stress length) / (Area of a section * change in
the lateral length)
The equation is

G= = σ /ϵ = (F L) / (A Δx)
We have:
G: Shear modulus
σ : shear stress
ϵ : strain
F: Force applied
L: lateral length of the material without force applied
A: area of a section of the material
Δx: Change in the lateral length of the material after a force is applied
Solid Expansion Formula
Is the coefficient or number associated with the thermal expansion of a solid due to an increase in
temperature. It compares the large of the solid when it is measured at different temperatures, keeping
other physical quantities like pressure at a constant value. There are linear, surface and volumetric
expansion, where the linear is the more commonly used. This is written as:
Linear expansion = (initial length) * (coefficient of linear expansion) * (change of the temperature)
The equation is
ΔL= L α ΔT
We have:
ΔL: Expansion of the solid
L: Length of the solid before the change o temperature
α: Coefficient of expansion associated individually to each material
Entropy Formula
Entropy is a measure how much the energy of atoms and molecules become more spread out in a
process and can be defined in terms of statistical probabilities of a system or in terms of the other
thermodynamic quantities. The most familiar case is the entropy of an ideal gas.
Entropy = (Boltzmann constant) * logarithm (number of possible states of the system)
The equation is:
S= k Log(Ω)
Where:
S: Entropy
k: Boltzmann constant. (1.38*10(-23)
J/ K)
Ω: The number of states of the system.

Surface tension Formula
Surface tension is defined as the ratio of the surface force F applied on a liquid to the length d along
which the force acts. It is responsible for insects to walk on water, or a paperclip to "float". The
equation is given by:
Surface tension = (surface force)/(length force acts)
The equation is
γ = F /d
We have:
γ: Surface tension
F: Force applied on the liquid
d: length where the force acts
Young's modulus Formula
Young's modulus is used to represents how easy it is to deform a material. A modulus is a numerical
value, which represents a physical property of a material. It compares the tensile stress with the
tensile strain. This is written as:
Young's modulus = (Force * no-stress length) / (Area of a section * change in the length)
The equation is
Y = (F L) / (A ΔL)
We have:
Y: Young's modulus
F: Force applied
L: length of the material without force
A: area of a section of the material
ΔL: Change in the length of the material after a force is applied
Heat Flow Rate Formula
Is the amount of heat that is transferred per unit of time in some material.
The rate of heat flow in a rod of material is proportional to the cross-sectional area of the rod and to
the temperature difference between the ends and inversely proportional to the length.
Heat flow = - (heat transfer coefficient) * (area of the body) * (variation of the tem-perature) / (length
of the material)
The equation is:

Q = -k (A/l) (ΔT)
We have:
Q: heat transfer per unit time
K: The thermal conductivity
A: area of the emitting body
l: the length of the material.
ΔT: Difference of temperature.
Internal Energy Formula
The internal energy is the total of all the energies associated with the motion of the molecules in a
system. Microscopic forms of energy include those due to the rotation, vibration, translation, and
interactions among the molecules of a substance. The more usual formula is given for an ideal gas.
Internal energy = 3/2 (number of moles) * (ideal gas constant) * (Temperature)
The equation is:
E= 3/2 n R T
Where:
E: Internal Energy
R: Ideal gas constant. (8.314 kg*m2
/s2
*mol*K)
T: Absolute Temperature in Kelvin.
n: moles
Maxwell-Boltzmann Distribution Formula
The Maxwell-Boltzmann distribution is the classical function for a distribution of an amount of energy
between identical but distinguishable particles. It gives information about the occurrence of a particle
at a given temperature and a given energy.
Maxwell-Boltzmann distribution = 1 / Exponential(energy/(Boltzma nn constant Temperature))
The equation is:
f= 1/exp(-E/kT)
Where:
f: Energy distribution
E: energy of the system
m2
kg /(s K2
))

Molecular Kinetic Energy Formula
The kinetic energy associated to a system that in obeys the Maxwell-Boltzmann distribution. It is an
average energy.
Average kinetic energy = 3 / 2 (Boltzmann constant) * Temperature
The equation is:
<k>= 3/2 k T
Where:
<K>: Average molecular kinetic energy
m2
kg /(s K2
))
Molecular Speed Formula
The speed associated to a group of molecules in average. It is valid in ideal gas, where the molecules
do not interact with each other.
Average molecular speed = Square root (3 (ideal gas constant) * (Temperature)/m)
The equation is:
v= √ (3 R T/m)
Where:
v: molecular speed
/s2
*mol*K)
m: molar mass
Stephan-Boltzmann Law Formula
The Stephan-Boltzmann Law describes the power radiated a body that absorbs all radiation that falls
on its surface in terms on its temperature. The radiation energy per unit time from a black body is
proportional to the fourth power of the absolute temperature and can be expressed with Stefan-
Boltzmann Law as: The Stefan-Boltzmann Constant.
Radiate energy = (Emissivity) * (Stefan-Boltzmann constant) * (Temperature)4
* (Area)
The equation is:
P = є σ T4
A
P: Radiate energy
σ: The Stefan-Boltzmann Constant
T: absolute temperature in Kelvin
є: Emissivity of the material.

A: Area of the emitting body
Thermal Conduction Formula
The thermal conduction is the direct microscopic exchange of kinetic energy of particles through the
boundary between two systems. Such spontaneous heat transfer always occurs from a region of high
temperature to another region of lower temperature, as described by the second law of the
thermodynamics.
Thermal conduction = -(heat transfer coefficient)*(Area/length)*(difference of temperature)
The equation is:
Q = -h (A/l) (T2-T1)
With:
Q: Heat or thermal conduction
h: The heat transfer coefficient
A: area of the emitting body
l: the length of the material.
T2: Temperature in hot state
T1: Temperature in cold state
Thermodynamic Work Formula
It is the quantity of energy transferred from one system to another. It is a generalization of the concept
of mechanical work in mechanics. It can be related to a variety of physical systems, in the case of an
ideal gas is:
Work = (number of moles) * (ideal gas constant) * (change of temperature)
The equation is:
W= n R ΔT
Where:
W: Thermodynamic work
/s2
*mol*K)
ΔT: Absolute Temperature in Kelvin.
n: moles
Wien Displacement Law Formula

The Wien's Displacement Law provides the wavelength where the spectral radiance has maximum
value. This law states that the black body radiation curve for different temperatures peaks at a
wavelength inversely proportional to the temperature.
Maximum wavelength = Wien's displacement constant / Temperature
The equation is:
λmax= b/T
Where:
λmax: The peak of the wavelength
b: Wien's displacement constant. (2.9*10(−3)
m K)
Capacitor potential energy Formula
The energy stored on a capacitor or potential energy can be expressed in terms of the work done by a
battery, where the voltage represents energy per unit charge. The voltage V is proportional to the
amount of charge which is already on the capacitor. It's expression is:
Capacitor energy = 1/2 (capacitance) * (voltage)2
The equation is:
U = 1/2 C V2
Where:
C: Capacitance
V: Voltage
U: Energy stored in the capacitor
Cylindrical capacitor Formula
The capacitance for a cylindrical geometry, is the capacitance stated as a capacitance per unit length.
The charge resides on the outer surface of the inner conductor and the inner wall of the outer
conductor. It depends on the inner and outer radius.
Capacitance per unit length = 2 * π * (relative permittivity) * (permittivity of space) /Logarithm (outer
radius / inner radius )
The equation is:
C =2 π k ϵ /Log(ro/ri)
Where:
C: Capacitance
ri: inner radius
ro: outer radius

k: relative permittivity
ϵ: permittivity of space
Electric Current Formula
The rate of flow of charge through a cross section of some region of a metallic material is called the
electric current. It is related to the resistance of the material and the voltage applied to move the
charge. It is measured in amperes (A).
Electric current = Voltage / Resistance
The equation is:
I = V/R
Where:
I: Electric Current
V: Voltage
R: Resistance of the material
Electric resistance Formula
The electric resistance is the ability of a material to oppose to the flow of charge current in it. The
electrical resistance experimentally depends upon how long or short is the material, or its cross
sectional area. The resistance of a wire can be expressed as:
Electric resistance = resistivity * length / cross sectional area
The equation is:
R = ρ L/A
Where:
R: Electric Resistance
ρ: Resistivity
L: Length of the material
A: Sectional area of the material
Image position Formula
This equation predicts the formation and position of both real and virtual images in thin lenses. It is
valid only for paraxial rays, rays close to the optic axis, and does not apply to thick lenses.
1/(object distance) + 1/(image distance) = 1/(focal length)
The equation is:
1/o + 1/I = 1/f

Where:
o: Object distance
I: Formed image distance
f: focal length
Image size Formula
The image size formula or magnification equation, relates the ratio of the image distance and object
distance to the ratio of the image height and object height. The magnification equation is:
M= (image height)/(object height) = - (image distance)/(object distance)
The equation is:
M= hi / ho = - I/o
Where:
o: Object distance
hi: image height
ho: object height
Plate capacitor Formula
The capacitance of a parallel plate capacitor depends on the area of the plates A and their separation
d.
Capacitance = (relative permittivity)* (permittivity of space) * (Plates area) / (distance between
plates)
The equation is:
C = k ϵ A/d
Where:
C: Capacitance
A: Area of the plates
d: distance between plates
Resistivity-Conductivity Formula

It is a measure of how strongly a specific material opposes the flow of electric current on resistors or
conductors with a uniform cross-section, where current flows uniformly. As a reciprocal quantity,
conductivity is a measure of how easy a material permits the flow of current. This are related by:
Resistivity = 1 / conductivity
The equation is:
ρ = 1 / σ
Where:
σ: Conductivity
ρ: Resistivity
Spherical capacitor Formula
The capacitance for spherical conductors can be obtained by evaluating the voltage difference
between the conductors for a given charge on each. It depends then on the inner and outer radius of
each sphere.
Capacitance = 4 * π * (relative permittivity) * (permittivity of space) / (1/(inner radius) – 1/(outer
radius) )
The equation is:
C =4 π k ϵ / (1/ri -1/ro)
Where:
C: Capacitance
ri: inner radius
ro: outer radius
Spherical mirror Formula
This equation predicts the formation and position of both real and virtual images in thin spherical
lenses. It is valid only for paraxial rays, rays close to the optic axis, and does not apply to thick lenses.
Also, it can be determined the curvature ratio of the lens.
1/(object distance) + 1/(image distance) = 1/(focal length)
Focal length ≈ curvature radius / 2
The equations are:
1/o + 1/I = 1/f
F ≈ r/2
Where:

o: Object distance
f: focal length
r: Curvature radius
Biot-Savart Law Formula
The Biot-Savart Law relates the currents as sources of the magnetic fields. The magnetic field results
from a current distribution that involves the vector product. Its units are given in Tesla (T). The
expression for the modulus of the differential magnetic field is:
Magnetic field = Integration over the cable path of (vacuum permeability constant/4 π * current *
(sine of the angle between current direction and cable position vector)/ (cable position)2
) * line
element
The equation is:
B = ∫ (μ0 / 4 π) I dl sin(θ)/r2
Where:
μ0: vacuum permeability
B: magnetic field
I: current intensity flowing in the cable
θ: angle between the current path and the position of the cable
r: distance from the origin of coordinates to the cable
dl: line element
Electric Flux Formula
The electric flux through a planar area is defined as the electric field times the component of the area
perpendicular to the field.
Electric flux = Electric field * Area * (angle between the planar area and the electric flux)
The equation is:
Φ = E A cos(θ)
Where:
Φ: Electric Flux
A: Area
E: Electric field
θ: angle between a perpendicular vector to the area and the electric field

Gauss law Formula
Gauss's Law is a general law applying to any closed surface that permits to calculate of the field of an
enclosed charge by mapping the field on a surface outside the charge distribution. It simplifies the
calculation of the electric field if the geometries of sufficient symmetric. The typical case, is a charge
particle with spherical symmetry.
Electric flux = enclosed charge / permittivity
The equation is:
Φ =Q/ϵ
Where:
Φ: Electric flux
Q: Enclosed charge by the surface
ϵ: Permittivity
Induced Electromotive Force Formula
The magnetic field crosses an area formed by a loop, and the flux changes in time, the charges will
move in the conductor and that can be associated with a voltage. This is also known as Faraday's law.
There is a minus sign refered to as the EMF that is generated oppose the change of magnetic flux. For
a single loop, the voltage generated is:
Induced EMF = - Change in the Magnetic flux / change in time
The equation is:
EMF = - ΔΦ /Δt
Where:
EMF: Electromotive force
ΔΦ: Change of the magnetic flux
Δt: change in time
Magnetic Flux Formula
Magnetic flux is the product of the average magnetic field times the perpendicular area that it crosses.
Magnetic flux = Magnetic field * Area * (angle between the planar area and the magnetic flux)
The equation is:
Φ = B A cos(θ)
Where:
Φ: Magnetic Flux
A: Area
B: Magnetic field

θ: angle between a perpendicular vector to the area and the magnetic field
Motional Electromotive Force Formula
The magnetic force exerted on the charges in a moving conductor will generate a motion that can be
associated with a voltage. The generated voltage can be seen to be the work done per unit charge.
Motional EMF = velocity of the charge carriers *Magnetic field * length of the wire
The equation is:
EMF = v B L
Where:
EMF: Electromotive force
v: Velocity of the charge
B: Magnetic field
L: Length of the wire where the charge is moving
No one's Formula
Gauss's Law for magnetism or no one's law, is a general law applying to any closed surface. In the
same sense than the electric case it permits to calculate of the field of an enclosed charge by mapping
the field on a surface outside the magnetic charge distribution. The consequence of the law in this
scenario is that there no exist magnetic charge distributions, or monopoles.
Magnetic flux = zero
The equation is:
Φ = 0
Where:
Φ: Magnetic flux of a close surface
Magnetic Force Between Parallel Wires Formula
For the case of a long straight wire carrying a current I1, and a wire carrying a current I2, the force that
each wire feels due to the presence of the other depends on the distance between them and the
magnitude of the currents.
For per unit length = magnetic permeability * (current 1) *(current 2) / (2 π distance between the
wires)
The equation is:
F/ΔL = μ I1 I2 /2 π r
Where:

μ: permeability
I1: current intensity flowing in the cable one
I2: current intensity flowing in the cable two
r: distance between wires
Solenoid Formula
A solenoid is a coil of wire through which a current flow. The magnetic field is determined by the
contribution of each loop in the solenoid, so the total magnetic field is dependent on the number of
turns and the length of the solenoid. The formula is
Magnetic field = magnetic permeability * current *(Number of turns / Length of the solenoid)
The equation is:
B = μ I N/L
Where:
μ: permeability
B: magnetic field
N: number of turns of the wire
L: Length of the solenoid
Straight Wire Magnetic Field Formula
A long straight wire carrying a current has a magnetic field due to moving charges which will depend
on the right-hand rule. For the case of a long straight wire carrying a current I, the magnetic field lines
wrap around the wire and depends on the distance to the wire.
Magnetic field = magnetic permeability * current / (2 π distance from the wire)
The equation is:
B = μ I /2 π r
Where:
μ: permeability
B: magnetic field
r: distance to the wire (perpendicular to the wire)
Ampere's Law Formula

Ampere's law allows us to calculate magnetic fields from the relation between the electric currents that
generate this magnetic fields. It states that for a closed path the sum over elements of the component
of the magnetic field is equal to electric current multiplied by the empty's permeability.
Integration over the closed path of (magnetic field . infenitesimal segment of the integration path) =
empty's permeability * enclosed electric current by the path
The equation is:
∫B.dl = μ0I
Where:
B: magnetic field
dl: infinitesimal segment of the integration path
μ0: empty's permeability
I: enclosed electric current by the path
Energy momentum Formula
The energy–momentum relation is a relativistic equation that relates an object's rest mass, its total
energy and momentum. Holds for systems such as a particle or macroscopic body, having intrinsic
rest mass m0, total energy E, and a momentum of magnitude p, where the constant c is the speed of
light.
Energy = √( momentum2
(speed of light)2
+ ((rest mass) (speed of light)2
)2
)
The equation is:
E = √ (p2
c2
+ (m0 c2
)2
)
Where:
E: Energy
p: momentum
c: speed of light
m0: rest mass
Photoelectric Effect Formula
A photon is like a tiny blob of pure energy. In the photoelectric effect, an electron is hit by a wandering
blob of energy and is so excited that it breaks its bond with the atom to which it is held.
We can know the energy necessary to breaks the bonds of the electrons as follows:
photon energy = work function + electron kinetic energy
The equation is:
hν = Ee + W
Where:

h: Planck's constant
ν: Frequency of the incident light
Ee: Energy of the electron
W: the work function of the material
Photon Energy Formula
A photon is an elementary particle, it has energy which is directly related to the photon's wavelength
which is inversely proportional to the energy, it means, the longer the photon's wavelength, the lower
its energy
Photon energy = Plank's constant * speed of light / photon's wavelength
The equation is:
E = hc / λ
Where:
E: photon's energy
h:Plank's constant
λ: photon's wavelength
c: speed of light
Photon Momentum Formula
A photon which is an elementary particle and is massless, it has a linear momentum which is related
to its energy and wavelength.
Photon momentum = Plank's constant / photon's wavelength
The equation is:
p = h / λ
Where:
P: photon momentum
h:Plank's constant
λ: photon's wavelength
Relative Velocity Formula
Let us consider two bodies A and B which are moving relative to each other. The relative velocity is
the velocity that the body A would appear to an observer on the body B and vice versa. Mathematically
speaking the relative velocity is the vector difference between the velocities of two bodies.
Relative velocity = velocity of the body A – velocity of the body B

The equation is:
vAB = vA – vB
Where:
vAB: relative velocity of the body A respect body B
vA: velocity of the body A
vB: velocity of the body B
Relativistic Doppler Effect Formula
The normal Doppler shift for waves such as sound which move with velocities v much less than the
speed of light. For light and other electromagnetic waves, the relationship must be modified to be
consistent with the Lorentz transformation. The Doppler effect is observed with visible light and all
other electromagnetic waves. It relates the frequency observed by an observer in motion and the
frequency emitted by the source. The formula is given by,
frequency observed = (frequency emitted) √((1+velocity/speed of light)/(1-velocity/speed of light))
The equation is:
fO = fE√ ((1+v/c)/(1-v/c))
Where:
fO: Frequency observed
fE: Frequency emitted
c: speed of light
v: velocity of the observer respect to the source
Relativistic Energy Formula
The relativistic energy is the way that Einstein showed that the law of conservation of energy is valid
relativistically, it means, the law of conservation of energy is valid in all inertial frames in high velocities
approaching to the speed of light.
Relativistic energy = rest mass * speed of light squared / squared root [one minus (velocity / speed
of light) squared]
The equation is:
E = mc2
/ sqrt (1 – v2
/ c2
)
Where:
E: relativistic energy
m: rest mass (invariant mass)
v: velocity of the body
c: speed of light

Relativistic Mass Formula
Relativistic mass refers to mass of a body which change with the speed of the body as this speeds
approaches close to speed of light, it increases with velocity and tends to infinity when the velocity
approaches the speed of light.
Relativistic mass = rest mass / squared root [one minus (velocity / speed of light) squared]
The equation is:
mr = m0 / sqrt (1 – v2
/ c2
)
Where:
mr: relativistic mass
m0: rest mass (invariant mass)
v: velocity
c: speed of light
Relativistic Momentum Formula
The relativistic momentum refers to the maximum momentum that a body can acquire limited by speed
light c which is the absolute speed limit in the universe.
Relativistic momentum = rest mass * velocity / squared root [one minus (velocity / speed of light)
squared]
The equation is:
p = mv / sqrt (1 – v2 / c2)
Where:
m: rest mass (invariant mass)
v: velocity of the body
c: speed of light
Equations of motion Formula
Equations of motion or kinematic equations are the set of formulas describing the motion of a particle
or the center of mass of a rigid body that is moving to a constant acceleration. They describe the
behavior of the particle as it moves and as a function of time. The essence of all the equations is in the
position of the particle, that is derived for the second law of Newton. From this all other motion
characteristic can be derive.
position = initial position + (initial velocity)*time +1/2*(constant acceleration)*(time)2
The equation is:

r = r0 + v0 t + ½ a t2
Where:
r: position
r0: initial position
v0: initial velocity
a: acceleration
t: time
Half-Life Formula
It is the time requires to decay in half. Half-life is the time required for the amount of something to fall
to half its initial value. The mathematical representation of Half life is given by,
(Half life time) = (Napierian logarithm of 2)/(disintegration constant)
The equation is:
t1/2 = ln(2)/λ
Where:
λ : disintegration constant of the system
t1/2: Half life time
Rydberg Formula
If the state of an electron in a hydrogen atom is slightly perturbed, then the electron can make a
transition to another stationary. The transition will emit a photon with a certain wavelength. If the
electron state is characterized by the quantum number n the wavelength is given by the Rydberg
formula.
(1/wavelength of the emitted photon) = (Rydberg constant)(1/(integer 1)2
- 1/(integer 2)2
)
The equation is:
1/λ = R(1/(n1)2 -1/(n2)2)
with n1 < n2
Where:
R: Rydberg's constant (R=1.097 * 107 m(−1))
λ: Wavelength of the emitted photon
n1: integer 1
n2: integer 2
Schrodinger Equation Formula

The Schrodinger equation plays the role of Newton's laws and the conservation of energy in classical
mechanics. It is a wave equation in terms of the a called wavefunction which predicts analytically and
precisely the probability of an outcome. The detailed outcome is not strictly determined, but the
Schrodinger equation will predict the distribution of results.
(Planck's constant)2
/2(mass) Second derivative of the wavefunction = energy wavefunction
The equation is:
-ℏ2
/2m ∂2
/∂x2
Ψ = E Ψ
Where:
ℏ: Planck's constant
m: mass of the particle
ψ: Wavefunction
Uncertainty Principle Formula
It states that the position and momentum of a particle cannot be simultaneously measured with
arbitrarily high precision. There exists a minimum value for the product of the uncertainties of these
two measurements. There is also a minimum for the product of the uncertainties of the energy and
time. It arises from the wave properties inherent in the quantum mechanical description of nature. The
uncertainty is inherent in nature.
(Position uncertainty) * (momentum uncertainty) ≥ (Planck's constant) /2
(Energy uncertainty) * (time uncertainty) ≥ (Planck's constant) /2
The equations are:
Δx Δp ≤ ℏ/2
ΔE Δt ≤ ℏ/2
Where:
ℏ: Planck's constant
Δx: Position uncertainty
Δp: Momentum uncertainty
ΔE: Energy uncertainty
Δt: Time uncertainty
Archimedes Principle Formula
The Archimedes principle states that the upward buoyancy force exerted on a body partially or
completely immersed in a fluid is equal to the weight of the fluid that the body displaces and acts in an
upward direction in the center of the mass of the displaced fluid. The Archimedes principle is a
fundamental law of physics for fluid mechanics. It was formulated by Archimedes of Syracuse.

push = density of fluid * gravity acceleration * volume of object.
The equation is:
p=ρf*g*V
we have,
p = push
ρf = density of fluid.
g = gravity acceleration.
V = volume of object.
Critical angle Formula
The critical angle in optics refers to the angle of incidence, beyond which the total internal reflection of
light occurs. The trajectory of a ray of light that strikes a medium that has a lower refractive index
deviates from the normal trajectory. As a result, the angle of exit of the ray is greater than the angle of
incidence. This reflection is called internal reflection. Whenever light travels from a medium with a
higher refractive index (n1) to a medium with a lower refractive index (n2), the angle of refraction is
greater than the angle of incidence. As a result of the difference in the refractive index, the ray bends
towards the surface. So the critical angle is defined as the angle of incidence that provides a 90
degree angle of refraction. Note that the critical angle is an angle of incidence value. For the water-air
limit, the critical angle is 48.6 degrees. For the boundary between glass and crown water, the critical
angle is 61.0 degrees. The actual value of the critical angle depends on the combination of materials
present on each side of the boundary.
Let's consider two different media, half i (incident half) and half r (refractive half). The critical angle is
that of θi which gives a value of 90 degrees. If this information is substituted in the Snell's Law
equation, a generic equation can be obtained to predict the critical angle.
The critical angle = the inverse function of the sine (refraction index / incident index).
The equation is:
θcrit = sin-1(nr/ni)
We have:
θcrit = The critical angle.
nr = refraction index.
ni = incident index.
Cross product Formula
The vector product or cross product is a binary operation between two vectors in a three-dimensional
space. The result is a vector perpendicular to the vectors that multiply, and therefore normal to the

plane that contains them. Due to its ability to obtain a vector perpendicular to two other vectors, whose
direction varies according to the angle formed between these two vectors, this operation is often
applied to solve mathematical, physical or engineering problems.
vector a X vector b = module of the vector a * module of the vector b * sine of the angle
between vectors a and b * normal of the plane formed by vectors a and b.
The equation is:
,
we have,
vector a.
vector b.
module of the vector a.
module of the vector b.
= angle between vectors a and b.
= * the normal of the plane formed by vectors a and b.
Another way to calculate the vector product in Cartesian space R3 isthrough the determinant of the
following matrix.
| I j k |
| ax ay az |
| bx by bz |
And the determinant is:
= (ay*bz - az*by)i + (az*bx - ax*bz)j + (ax*by - ay*bx)k
Friction loss Formula
In fluids, friction loss is the loss of pressure or height that occurs in the flow of the pipe or conduit due
to the effect of the viscosity of the fluid near the pipe surface. In mechanical systems such as internal
combustion engines, the term refers to the power lost by overcoming friction between two moving
surfaces.
friction loss = friction loss coefficient * ( flow rate / 100) 2
* hose length /100.
FL = C* (Q/100)2 *L/100.
We have:
FL = friction loss.
C = friction loss coefficient.
Q = flow rate.
L = hose length.

Linear acceleration Formula
Before defining the linear or tangential acceleration it is necessary to first clarify that it is a term related
to the circular movement; it describes a circular path around an axis on which it rotates maintaining a
constant radius. When the speed of this movement is also maintained in time, what is known as
uniform circular movement takes place. When a circular movement is made, the moving body has an
angular velocity, since it rotates constantly with a certain inclination. The elements that compose its
definition are the rotation angle for each time unit. Tangential velocity is the velocity presented by the
body at a given moment in time, taking into account its direction and sense, as well as the radius by
which it is traveling in a particular fraction of its trajectory. Tangential acceleration is the magnitude
that links the variation of speed with time.
tangential acceleration = angular velocity / time * circle radius.
The equation is:
We have:
at = tangential acceleration.
= angular velocity
= time.
r = circle radius.
Orbital speed Formula
In gravitationally linked systems, the orbital speed of a body or astronomical object is the speed at
which it orbits around the barycenter or, if the object is much less massive than the largest body in the
system, its relative velocity to that larger body. The speed in the latter case may be relative to the
surface of the largest body or relative to its center of mass.
The term can be used to refer to the mean orbital speed, the mean velocity in an entire orbit, or its
instantaneous speed at a given point in its orbit. The maximum orbital velocity (instantaneous) occurs
in the periapsis, while the minimum speed for objects in closed orbits occurs in the apogee. In ideal
two-body systems, objects in open orbits continue to slow down forever as their distance to the centre
of gravity increases.
orbital speed = square root (gravitational constant * mass of the attractive body / radius of the
orbit)
The equation is:
,

We have:
orbital speed.
G = the gravitational constant.
M = mass of the attractive body.
r = radius of the orbit.
Sound intensity Formula
The intensity of sound is defined as the sound power per unit area. The usual context is the
measurement of the intensity of sound in the air where the listener is. It also depends on the surface of
the sound source. The increase in the amplitude of the source and that of the vibrating surface causes
the kinetic energy of the mass of air in contact with it to increase simultaneously; this kinetic energy
increases, in effect, with the mass of air that is put into vibration and with its average speed (which is
proportional to the square of the amplitude). The intensity of perception of a sound by the ear also
depends on its distance from the sound source. Finally, the intensity also depends on the nature of the
elastic medium between the source and the ear. Non-elastic media, such as wool, felt, etc.,
considerably weaken the sounds. The intensity of the sound that is perceived subjectively is what is
called sonority and allows sounds to be arranged on a scale from the loudest to the weakest.
sound intensity = acoustic power / normal area to the direction of propagation.
The equation is:
I = P/A.
We have,
I = sound intensity.
P = acoustic power.
A = normal area to the direction of propagation.
The physiological intensity or sound sensation of a sound is measured in decibels (dB). For example,
the hearing threshold is 0 dB, the physiological intensity of a whisper corresponds to about 10 dB and
the noise of waves on the coast to about 40 dB. The scale of sound sensation is logarithmic, which
means that an increase of 10 dB corresponds to an intensity 10 times greater for example, the noise of
the waves on the coast is 1,000 times more intense than a whisper, which equals an increase of 30
dB.
Due to the extension of this audibility interval, to express sound intensities is used a scale whose
divisions are powers of ten and whose unit of measurement is the decibel (dB).
The conversion between intensity and decibels follows this equation:
The intensity in decibels = 10 * log10 (intensity/ intensity of zero decibels)
The equation is:

S = 10*log(I/I0)
s = intensity in decibels.
I = sound intensity.
I0 = sound intensity of zero decibels= 10-12
W/m-2
Speed of sound Formula
The speed of sound is the dynamic propagation of sound waves. The speed or dynamic of the
propagation of the sound wave depends on the characteristics of the medium in which the propagation
takes place and not on the characteristics of the wave or the force that generates it. Its propagation in
a medium can be used to study some properties of this transmission medium.
In gases the equation of the speed of sound is:
speed of sound = the square root of (the coefficient of adiabatic expansion * the pressure of
the gas / the density of the medium).
The equation is:
We have:
v = speed of sound.
= the coefficient of adiabatic expansion.
P = the pressure of the gas.
= the density of the medium.
Transformer Formula
The transformer is an electrical device that allows to increase or decrease the voltage in an alternating
current electrical circuit, maintaining the power. The power that enters the equipment, in the case of an
ideal transformer, is equal to that obtained at the output. Real machines have a small percentage of
losses. It is a device that converts the alternating electrical energy of a certain voltage level into
alternating energy of another voltage level, based on the phenomenon of electromagnetic induction. It
is made up of two coils of conductive material, wound on a closed nucleus of ferromagnetic material,
but electrically isolated from each other. The only connection between the coils is the common
magnetic flux established in the core. The coils are called primary and secondary according to the
input or output of the system in question, respectively.

The value of the power for an electric circuit is the value of the voltage by the value of the current
intensity. As in the case of a transformer, the value of the power in the primary is the same value for
the power in the secondary we have:
input voltage on the primary coil * input current on the primary coil = output voltage on the
secondary coil * output current on the secondary coil.
We can also work out the transformer output voltage if we know the input voltage and the number of
turns (coils) on the primary and secondary coils, using the equation below;
input voltage on the primary coil / output voltage on the secondary coil = number of turns of
wire on the primary coil / number of turns of wire on the secondary coil
we have:
Vp = input voltage on the primary coil.
Vs = input voltage on the secondary coil.
Ip = input current on the primary coil.
Is = input current on the secondary coil.
np = number of turns of wire on the primary coil.
ns = number of turns of wire on the secondaryad coil.
Voltage divider Formula
A voltage divider is a configuration of an electrical circuit that produces an output voltage that is a
fraction of its input voltage, dividing the source voltage between one or more impedances connected in
series.
Suppose you have a source voltage (input voltage), connected in series with n impedances. To know
the output voltage on the generic impedance, Ohm's law is used:
output voltage = (generic impedance / the sum from the first to the nth impedance of the
circuit) * input voltage.
We have:

Vout = output voltage.
Zi = generic impedance.
= the sum from the first to the nth impedance of the circuit.
Vin = input voltage.
Distance Traveled Formula
The distance travelled is the path taken by a body to get from an initial point to an end point in a given
period of time, at a certain velocity. If the velocity is constant:
Distance = time * velocity.
d = v*t.
We have:
d = distance.
v = velocity.
t = time.
Electrical Formula
Ohm's law
Ohm's law is a basic law of electrical circuits. It states that the potential difference V which is applied
at the ends of a conductor of resistance R is proportional to the current intensity I circulating through
the conductor.
Potential difference = Resistance of the conductor cable * Current intensity
V = R*I
We have:
V = Potential difference
R = Resistance of the conductor cable
I = Current intensity
Energy Density Formula
Energy density is defined as the amount of energy accumulated in a system per unit volume.
In the case of electrical energy
Electrical energy density = permittivity* Electric field squared/2

UE = εE2
/2
In the case of magnetic energy
Magnetic energy density = magnetic field squared/ 2* magnetic permeability
UB = B2
/2*μ
The general energy is:
U = UE + UB
We have:
U = energy density
UE = electrical energy density
UB = magnetic energy density
ε = permittivity
E = Electric field
B = Magnetic field
μ = magnetic permeability
Gravitational Acceleration Formula
The law of universal gravitation says that the intensity of the forces of attraction between two bodies
was proportional to their masses and to the distance between them. Gravity acceleration is the specific
gravitational force acting on one body in the gravitational field of the other, like the gravitational force
per unit mass of the body experiencing it.
Gravity acceleration= universal gravitational constant * planet mass / planet radius.
g = G*M/R2
We have:
g = gravity acceleration
G = universal gravitational constant
M = planet mass
R = planet radius.
Intensity Formula
The intensity of a wave measures the power passing through a surface unit perpendicular to the
direction of propagation of the wave.
Intensity = power/ surface perpendicular to the direction of propagation

I = P/S
We have:
I = Intensity
P = power
S = surface perpendicular to the direction of propagation
Resonant Frequency Formula
The resonant frequency is the characteristic frequency of a body or a system that reaches the
maximum degree of oscillation. In an electrical system, the resonant frequency is the frequency at
which the transfer function reaches its maximum. In other words, given an input, a maximum output is
obtained. The resonance is obtained when the capacitive impedance and the inductive impedance are
equal.
Resonant frequency = 1/ 2*pi* squere root (Inductance * Capacitance)
We have:
fr: resonant frequency
L: Inductance.
C: capacitance.
Temperature Formula
Temperature is a magnitude referred to a body's common notions of measurable heat. It is measured
on the scales of Celsius, Fahrenheit and Kelvin. The temperature change depends on the amount of
heat released or absorbed.
Temperature difference = amount of heat absorbed or released/ mass of the body* specific heat of
the body.
ΔT = Q/m*c.
ΔT: Temperature difference.
Q: Amount of heat absorbed or released
m: mass of the body
c: specific heat of the body
Thermal Expansion Formula

Thermal expansion is the increase in length suffered by a body due to an increase in temperature
caused by an external medium.
Final length = initial length*(1+ coefficient of linear expansion * temperature difference)
Lf = L0(1+αL∆T)
We have:
Lf = Final length
L0 = Initial length
αL = Coefficient of linear expansion
∆T = Temperature difference.
Wave Formula
A wave is a disturbance on a medium (case of mechanical waves) or in vacuum (electromagnetic
waves) with a certain wavelength, velocity and frequency, where space is considered as a medium in
which such disturbances can occur and propagate through it.
velocity = frequency* wavelength
v = f * λ
We have:
v = velocity
f = frequency
λ = wavelength
Force of attraction Formula
The law of attraction between bodies with mass was described by Sir Isaac Newton which states that
objects are attracted to each other by the simple fact being massive. What causes this attraction is
gravitational force, which is why Newton called this law the Universal Law of Gravitation. The
interaction between two bodies of mass m1 and m2 is described in terms of an attractive force, whose
direction is the straight line passing through the center of the two bodies and inversely proportional to
the square of the distance separating the two bodies. This force explains, among many other things,
why the planets orbit.
Force of attraction = Gravitational constant* mass 1 * mass 2 / (distance between bodies) ^2
F = G*m1*m2/d2

We have:
F = force of attraction
G = 6.67*10-11
Nm2
/kg2
= gravitational constant
m1 = mass 1
m2 = mass 2
d = distance between bodies
Inductance Formula
When an electric current flow through a conductor, it creates a magnetic field around it. A changing
current creates a varying magnetic field, so that the magnetic flux is also varying inducing an
electromotive force. Inductance describes the tendency of an electrical conductor to oppose a change
in the electric current flowing through it. The change of current induces an inverse electromotive force.
The inductance forms part of the impedance of the circuit; that is, its existence implies a certain
resistance to the circulation of the current. The formula for magnetic inductance is defined as the
quotient between the magnetic flux in the element, and the electric current circulating through the
element.
Inductance = Magnetic flux* Number of coil turns / current intensity
L = ΦN/I
We have
L = Inductance
Φ = Magnetic flux
N = Number of coil turns
I = current intensity
Mass Formula
The mass is a fundamental property of a body, a measure of the amount of matter the body
possesses; a numerical measure of its inertia. All mechanical magnitudes can be defined in terms of
mass, length and time. The symbol for mass is m and its SI unit is kilogram.
To know the value of the mass of a body, we can use the second law of newton that establishes that
the magnitude of the force exerted on the body will depend on the mass times the acceleration of the
movement, independently of the type of force that this acting on the body.
mass = force / acceleration
m = F/a

We have:
m = mass
F = force
a = acceleration
Position Formula
A rectilinear movement is one whose trajectory follows a straight line. In addition, this movement is
performed at constant acceleration. On the straight line we place an origin x0, where there will be an
observer who will measure the position x of the mobile at the instant t. The position x of the mobile can
be related to time t by means of a polynomial function.
position = initial position+ initial velocity * time + 1/2 * acceleration * (time)^2
The equation is written:
x = x0 + v0t + a*t2/2
We have:
x = position
x0 = initial position
v0 = initial velocity
t = time
a = acceleration
Thermal Energy Formula
Is part of the internal energy of a thermodynamic system in equilibrium that is proportional to its
absolute temperature and is increased or decreased by energy transfer, usually in the form of heat or
work, through thermodynamic processes. At the microscopic level and within the framework of Kinetic
Theory, it is the total of the mean kinetic energy present as the result of the random movements of
atoms and molecules or thermal agitation, which disappear in the act.
Heat transferred = mass * specific heat capacity* (final temperature - initial temperature)
Q = m*cp(Tf-Ti)
We have:
Q = heat transferred
m = mass
cp = specific heat capacity
Tf = final temperature
Ti = initial temperature

Vector Projection Formula
A vector is a mathematical entity. It is represented by a line segment that has module (the length of
the segment), direction (the line where the segment is represented) and direction (the orientation of
the segment, from the origin to the end of the vector). A unit vector is a vector of module one, which is
given by the vector divided by its module.
The vector projection of a vector on a vector other than zero b (also known as vector component or
vector resolution of a in the direction of b) is the orthogonal projection of a on a straight line parallel to
b. The vector projection of a vector on a vector other than zero b (also known as vector component or
vector resolution of a in the direction of b) is the orthogonal projection of a on a straight line parallel to
b. It is a parallel vector a b, defined as the scalar projection of a on b in the direction of b.
Projection of the vector a on the vector b = product scale between vectors a and b /( vector module
b)^2
We have:
= Projection of the vector a on the vector b
= vector a
= vector b
= product scale between vectors a and b
= module of vector b
Weight Formula
Weight is the force exerted on a body by the action of the local gravitational field acting on the mass of
the body. The magnitude of the weight of an object, from the operational definition of weight, depends
only on the intensity of the local gravitational field and the mass of the body, in a strict sense.
That is why the weight of an object on earth is different from the weight of that same object on the
moon.
weight = mass * gravity
w = m*g

We have:
w = weight
m = mass
g = gravity
Work done by gravity Formula
If you apply a force on a moving object, we say that the force you are exerting performs a work. The
work will be proportional to the magnitude of the force exerted by the distance travelled. Gravitational
force is defined as the force that attracts a body to the earth or to any other physical body that has
mass. If the body moves under the action of the gravitational force, it also performs a work called
gravitational work. If a particular object is falling, the particle is forced to point in the direction of
gravity. The magnitude of the fall of the body depends on the mass, the gravitational constant and the
height from which it is falling.
work = mass* gravity* height
W = m*g*h
We have:
W = work done by gravity
m = mass
g = gravity
h = height
Period of a Pendulum Formula
Definition: A pendulum is a weight suspended from a pivot that swing with a regular movement. The
first scientist that tried to describe the physical phenomenon behind this movement was Galileo Galilei,
which in 1602, after he became interested from a chandelier in Pisa Cathedral. He discovered that this
movement could be useful to be used as a timekeeper because the time in which a pendulum
completes a whole movement from one side to the opposite side is independent on the mass of the
pendulum or the width of the swing.
Today, the bases of the movement of pendulum is the base for comprehension of quantum mechanics
phenomena such as the harmonic oscillator.
Formula: the period of a pendulum is defined as the time taken to complete a cycle (swing). It
depends on the length of the pendulum and the gravity of the place where it is been measured. It also

depends on the amplitude that is the maximum angle that a pendulum can swing form the point zero
or the vertical axis. The period is called T and the formula is:
Where L represents the length of the pendulum and g is the value of the acceleration of gravity.

Bibliography
 www.softschools.com
 www.wikipedia.org
 www.quora.com
Thank you to all who helped to create this book

Physics 200+ formulas and concepts

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