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Pharmaceutical calculations

Pallavi Kurra, profile picture
Pallavi Kurra

The document provides an overview of pharmaceutical calculations essential for pharmacists, including measurement systems, density calculations, and methods for preparing isotonic solutions. It details the imperial and metric systems, conversion tables, and calculations involved in preparing alcohol solutions using various methods, including the alligation method. Additionally, the document emphasizes the importance of understanding weights and measures in pharmacy practice.

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PHARMACEUTICAL CALCULATIONS UNDER THE ESTEEMED GUIDANCE OF 42 5 Presented By B.LAKSHMI DURGA 11AB1R0082 Mrs.PALLAVI.K M.Pharm 0011 0010 1010 1101 0001 0100 Assistant 1011 Professor 1 VIGNAN PHARMACY COLLEGE Approved by PCI,AICTE,New Delhi. Affiliated to JNTU,Kakinada. Vadlamudi-522213,Guntur,A.P 1
CONTENTS 1 0011 42 5 0010 1010 1101 0001 0100 1011 Percentage calculations Alcoholic dilutions Alligation method  Proof spirit calculations  Isotonic solutions  Posology  Temperature measurements  Dialysis Clearance  Pharmacokinetics VIGNAN PHARMACY COLLEGE 2
PHARMACEUTICAL CALCULATIONS 1 0011 Pharmacokinetic calculations 42 5 0010 1010 1101 0001 0100 1011 VIGNAN PHARMACY COLLEGE 3
INTRODUCTION  To have a complete understanding of various types of calculations, which are involved in dispensing, it is desirable that the pharmacist should have a thorough knowledge regarding weights and measures which are used in calculations. 1 0011 42 5 0010 1010 1101 0001 0100 1011  There are two systems of weights and measures. 1.The Imperial system 2.The Metric system 4
IMPERIAL SYSTEM 1 0011 42 5 0010 1010 1101 0001 0100 1011 • Imperial system is an old system of weight and measures. Imperial system Avoirdupois system Apothecaries system VIGNAN PHARMACY COLLEGE 5
Avoirdupois system : • In this system the pound is the standard unit for 1 0011 42 5 0010 1010 1101 0001 0100 1011 weighing and all measures of mass are derived from the Imperial standard pound (lb). Apothecaries system : • This system is also known as Troy system. • The grain is the standard unit in this system and all other weights are derived from it. VIGNAN PHARMACY COLLEGE 6
CONVERSION TABLE-1 FROM APOTHECARIES TO AVOIRDUPOIS 1 0011 1 Lb 16 oz (avoir) 1 Lb 7000 grains 1 oz (avoir) 7000/16 = 437.5 grains 20 grains (gr) 1 scruple (̶) ) 60 grains 1 drachm 480 grains 1 ounce (apothe) 42 5 0010 1010 1101 0001 0100 1011 12 ounces 1 pound (Lb) (apothe) 5760 grains 1 pound (apothe) VIGNAN PHARMACY COLLEGE 7
Measurement of capacity in imperial system : • The standard units for capacity is same for both the avoirdupois and the apothecaries systems. • The gallon is the standard unit and other measures of capacity 1 0011 42 5 0010 1010 1101 0001 0100 1011 are derived from it. 8 1gallon (c) = 160 fluid ounces 1/4th of gallon = 1 Quart 1/8th of gallon = 1 pint(O) 1/160th of gallon = 1 flounce 1 quart = 40 flounces 1 pint = 20 flounces 1 flounce = 480 minims 1 fl drachm = 60 minims CONVERSION TABLE-2
METRIC SYSTEM 1 0011 42 5 0010 1010 1101 0001 0100 1011 • Metric system is used in the Indian pharmacopeia for the measurement of weights and capacity. • It was implemented in India from 1st April , 1964 in pharmacy profession. Measurement of weight in metric system : • A kilogram is the standard unit for measurement of weight and all other measures are derived from it. VIGNAN PHARMACY COLLEGE 9
0010 1010 1101 0001 01010k 1i0lo1g1 ram = 1000gms 0011 1 hectogram = 100 gms 1 42 5 1 decagram = 10 gms 1 decigram = 0.1 gms 1 centigram = 0.01 gms 1 milligram = 0.001 gms 1 microgram = 0.000,001 gms 10 CONVERSION TABLE - 3 FROM HIGHER TO LOWER
Measurement of capacity in Metric System 1 0011 42 5 0010 1010 1101 0001 0100 1011 A litre is the standard unit for measurement of capacity and all measures of capacity are derived from it. 1 litre ( lt ) = 1000 milliliters (ml) VIGNAN PHARMACY COLLEGE 11
Conversion Tables 1 0011 42 5 0010 1010 1101 0001 0100 1011  The pharmacopeia of India uses only the metric system in formulae, But the prescription are still written in the imperial system by many old time physicians. So a conversion tables is used by the pharmacists. VIGNAN PHARMACY COLLEGE 12
Metric system Imperial system 1 kilogram (kg) = 2.2 lb ( pound ) 1 0011 42 5 0010 1010 1101 0001 0100 1011 13 • Weight measures • Capacity measures 30g = 1 ounce 450g = 1 pound ( avoir ) 1g = 15 grains 60mg = 1 grain 1000 ml = 1Quart 500 ml = 1 pint 30 ml = 1 fluid ounce 4 ml = 1 fluid drachm 1 ml = 15 minims 0.06 ml = 1 minim
Conversion table for Domestic Measures Domestic Measure Metric system Imperial system 1 drop 0.06 ml 1 minim 0011 1 tea spoonful 4.00 ml 1 fluid drachm 1 desert spoonful 8.00 ml 2 fluid drachm 1 42 5 0010 1010 1101 0001 0100 1011 1 tablespoonful 15.00 ml 4 fluid drachm 2 tablespoonful 30.00 ml 1 fluid ounce 1 wine glassful 60.00 ml 2 fluid ounce 1 tumblerful 240.00 ml 8 fluid ounce VIGNAN PHARMACY COLLEGE 14
CALCULATIONS BASED ON DENSITY :  Density is defined as the mass of a substance per unit volume. 1 0011 42 5 0010 1010 1101 0001 0100 1011  It has the units of mass over volume.  Specific gravity is defined as the ratio of the mass of a substance in air to that of an equal volume of water.  In the metric system both density and specific gravity are numerically equal. WEIGHT = VOLUME * DENSITY VIGNAN PHARMACY COLLEGE 15
Example problems for calculations based on density 1. Calculate the volume of 2kg of glycerin. The density of glycerin is 1.25g/ml. 1 0011 42 5 0010 1010 1101 0001 0100 1011 = 1600 ml VIGNAN PHARMACY COLLEGE 16 VOLUME = = =
0010 1010 2. Calcula 1te1 0t1h 0e0 w01e 0ig10h0t 1o0f1 1200ml of alcohol whose 1 0011 42 5 density is 0.816 g/ml WEIGHT = VOLUME X DENSITY = 200 ml x 0.816 g/ml = 163.2g VIGNAN PHARMACY COLLEGE 17
1 0011 42 5 0010 1010 1101 0001 0100 1011 VIGNAN PHARMACY COLLEGE 18
Example problem For Alcoholic Dilutions  Calculate the amount of 95% alcohol required to prepare 400ml of 45% alcohol 1 0011 42 5 0010 1010 1101 0001 0100 1011 volume required = 400ml percentage of alcohol required = 45 percentage of alcohol used = 95 Volume of strong alcohol = to be used = = = 184.47 ml 19
0011 Alligation method 1 42 5 0010 1010 1101 0001 0100 1011 VIGNAN PHARMACY COLLEGE 20
ALLIGATION METHOD 1 0011 42 5 0010 1010 1101 0001 0100 1011  When the calculation involves mixing of two similar preparations of different strenghts , to produce a preparation of intermediate strength , the alligation method is used. VIGNAN PHARMACY COLLEGE 21
Stronger Percentage Weaker percentage 1 0011 42 5 0010 1010 1101 0001 0100 1011 Required Percentage VIGNAN PHARMACY COLLEGE 22 Required percentage – Weaker Percentage Stronger percentage – Required Percentage
Example problems For Alligation method 1. Calculate the volume of 95% alcohol required to prepare 600ml of 70% alcohol. 1 0011 42 5 0010 1010 1101 0001 0100 1011 Volume required = 600 ml Percentage of alcohol required = 70 Percentage of alcohol used = 95 70 0 95 70 -0=70 95-70=25 VIGNAN PHARMACY COLLEGE 23
(Problem Contd…..) • 70 parts of 95 %alcohol and 25 parts of water will produce the 1 0011 42 5 0010 1010 1101 0001 0100 1011 required %alcohol. Quantity of 95% alcohol required = = 422.10ml Quantity of water required = =157.90ml VIGNAN PHARMACY COLLEGE 24
2. How much quantity of 60%,50%,30% and 20% alcohol should be mixed to get 40% alcohol. 1 0011 42 5 0010 1010 1101 0001 0100 1011 40 VIGNAN PHARMACY COLLEGE 25 60 20 50 30 40-20=20 parts of 60% 40-30=10 parts of 50% 50-40=10 parts of 30% 60-40=20 parts of 20%
( Problem contd……) • Quantity required = 20parts of 60%+10 parts of 50%+ 1 0011 42 5 0010 1010 1101 0001 0100 1011 10 parts of 30%+20 parts of 20% alcohol are mixed together, the resulting solution will produce 60% alcohol. Calculation can be checked by the following method: = (20 X 60+10 X 50+10 X 30 +20 X 20) =1200+500+300+400 =2400 20+10+10+20=60 i.e., 60 X 40 = 2400 26
PROOFSPIRIT 1 0011 42 5 0010 1010 1101 0001 0100 1011 CALCULATIONS VIGNAN PHARMACY COLLEGE 27
Introduction Proof spirit calculations 1 0011 42 5 0010 1010 1101 0001 0100 1011 • The strength of alcohol is calculated in proof degrees.The Indian standards of 100% proof spirit is equal to 57%v/v of ethyl alcohol. i.e., 100% p.s = 57%v/v ethyl alcohol • If the value is more than 57% then it is said to be as over proof spirit. • If the value is less than 57% then it is said to be as under proof spirit. 28
(Introduction contd….) • In India , the exercise duty is calculated in terms of rupees per 1 0011 42 5 0010 1010 1101 0001 0100 1011 liter of proof alcohol. So, any percentage volume in volume of alcohol can be converted into proof strength and vice versa by using the following method. i. Multiply the percentage strength of alcohol by 1.753 and deduct 100 from the product. ii. If the result is positive , it is known as over proof iii. If the result is negative , it is known as under proof. VIGNAN PHARMACY COLLEGE 29
• 1.753 is obtained as follows: 57.1 volume of ethyl alcohol = 100 ml of proof spirit. 1 0011 42 5 0010 1010 1101 0001 0100 1011 1 volume of ethyl alcohol = 100 / 57.1 = 1.753 volume of proof spirit Example problems for Proof Spirit calculations Calculate the strength of 30 0 O.P and 400 U.P 300 OVER PROOF = 100 + 30 = 130 400 Under proof = 100 – 40 = 60 VIGNAN PHARMACY COLLEGE 30
(Problem Contd….) Alcohol strength = = = 74.15%v/v 1 0011 42 5 0010 1010 1101 0001 0100 1011 Alcohol strength = = = 34.23%v/v Check :  If strength is 74.15%v/v 74.15 x 1.753 – 100 =129.9 – 100 = +29.90 or 300 O.P If strength is 34.23 %v/v 34.23 x 1.753 – 100 = 60.00 – 100 = - 400 U.P
2.What is the proof strength of 95% v/v alcohol. 1 0011 42 5 0010 1010 1101 0001 0100 1011 By applying the formula: percentage strength of alcohol x 1.753 – 100 = 95 x 1.753 – 100 = 166.53 – 100 = +66.530 O.P VIGNAN PHARMACY COLLEGE 32
3. How many proof gallons are contained in 5 gallon of 70% v/v alcohol Applying the formula: Value in proof = % strength of alcohol x 1.753 – 100 1 0011 42 5 0010 1010 1101 0001 0100 1011 = 70 x 1.753 – 100 = 122.71 – 100 = 22.710 o.p 100 gallons of 70% v/v alcohol =122.71 units of p.s 1 gallon of 70% v/v alcohol = 122.71/100 = 1.2271 5 gallons of 70% alcohol = 1.2271 x 5 = 6.1355 gallons of p.s 5 gallons of 70% v/v alcohol are equivalent to 6.1355 33 gallons of p.s
1 0011 42 5 0010 1010 1101 0001 0100 1011 ISOTONIC SOLUTIONS VIGNAN PHARMACY COLLEGE 34
Isotonic solutions 0010 1010  1101 0001 0100 1011 Isotonic solutions are which have same osmotic pressure or 1 0011 42 5 equal solute concentrations.  0.9% sodium chloride solution is considered to passes the same osmotic pressure and hence it is a standard solution which is isotonic with blood plasma.  Any concentration above this (0.9%) is considered as hypertonic and below this (0.9%) is considered as hypotonic. VIGNAN PHARMACY COLLEGE 35
ADJUSTMENT OF ISOTONICITY: FP depression /Cryoscopic 1 0011 42 5 0010 1010 1101 0001 0100 1011 36 method ISOTONIC ADJUSTMENT Nacl Equivalent method White Vinscent method Molecular Concentration method
I. Freezing point method/ Cryoscopic method %w/v of adjusting substance needed = 1 0011 42 5 0010 1010 1101 0001 0100 1011 Where PSM = percentage strength of medicament a = Freezing point of the unadjusted solution b = Freezing point of a 1% w/v solution of a adjusting substance VIGNAN PHARMACY COLLEGE 37
Example Problem for Freezing point method  Using cryoscopic method. How will you prepare 1% solution of boric acid ,iso osmotic with blood plasma. 1 0011 42 5 0010 1010 1101 0001 0100 1011 [Hint : The freezing point of 1%w/v solution of boric acid is 0.2880 c The freezing point of 1%w/v solution of sodium chloride is 0.5760 c] Percentage of w/v of sodium chloride required = = = 0.402% w/v 1gm of boric acid is needed for 0.402gm of Nacl to become isotonic. . 38
2. Nacl Equivalent method: Quantity of Nacl required to adjust tonicity = 0.9 – ( PSM x E ) Where 1 0011 42 5 0010 1010 1101 0001 0100 1011 PSM = Percentage strength of medicament. E = Nacl equivalent (quantity of Nacl i.e., equivalent to 1gm of drug) 3. White Vincet method : V = W x E x 111.1 Where V = volume of isotonic solution in ml that can be prepared by dissolving drug in water W = weight of the drug. E = Nacl equivalent . 39
4 . Molar (or) Molecular concentration : %W/V of adjusting substance required = Where 1 0011 42 5 0010 1010 1101 0001 0100 1011 M = gram molecular weight. N = no.of ions into which the substance is ionised. Problem: • How to prepare an iso osmotic solution using dextrose. [Hint: mol.wgt of dextrose = 180 [dextrose is non ionising substance] W = 0.03 M W = 0.03 x 180 = 5.4 g/100ml VIGNAN PHARMACY COLLEGE 40
POSOLOGY 1 0011 42 5 0010 1010 1101 0001 0100 1011 VIGNAN PHARMACY COLLEGE 41
POSOLOGY 0011 0010 1010 1101 0001 0100 1011 Posology refers to the calculation of doses for children. 1. Proportion to Age :- (a) Young’s formula: 1 42 5 Dose for a child = The above formula is used for calculating the doses for children 12 years of age. VIGNAN PHARMACY COLLEGE 42
• Example problem for young’s formula What will be the dose for a child of 5 years if the adult dose of a drug is 400 mg. 1 0011 42 5 0010 1010 1101 0001 0100 1011 Dose of the child = = = 117 mg (approximately) VIGNAN PHARMACY COLLEGE 43
(b) Dilling’s formula: Dose of a child = 1 0011 42 5 0010 1010 1101 0001 0100 1011 The above formula is used for calculating the doses of a children in between 4 to 20 years of age. Example problem:  What will be the dose for a child of 10 years if the adult dose of a drug is 600mg Dose of a child = = 300 mg 44
(c) Freid’s formula: Dose for a child = 1 0011 42 5 0010 1010 1101 0001 0100 1011 The above formula is applicable only for infants. Example problem:  What is the dose for an 8months old infant if the average adult dose of a drug is 250mg Dose for the child = = 13.3mg VIGNAN PHARMACY COLLEGE 45
(2) Calculations based on body weight: Catzel rule: 1 0011 42 5 0010 1010 1101 0001 0100 1011 Dose for the child = The average body surface area for an adult =1.73m2 Hence Dose for the child = VIGNAN PHARMACY COLLEGE 46
Example problem for calculations based on body weight  Calculate the dose for a child that has a body surface area of 0.57m2 , when the adult dose of a drug is 50mg. 1 0011 42 5 0010 1010 1101 0001 0100 1011 Child dose = = = 1.65 mg VIGNAN PHARMACY COLLEGE 47
Calculations based on body weight: 1 0011 42 5 0010 1010 Clarke’ s1 1r0u1 l0e0:0-1 0100 1011 • Dose = • Dose = Rule is applicable only when child dose is less than 150 lb or 70kg. VIGNAN PHARMACY COLLEGE 48
• Example problem for calculations based on body weight The dose of a drug is 5mg/kg body weight. How much of drug required for a boy of 12 years weighing 21kg. 1 0011 42 5 0010 1010 1101 0001 0100 1011 Dose = =1.5mg (3) Calculations based on body surface area: Most accurate method commonly used in onchology department Mosteller rule: BSA ( M2 ) = 49
Example problem for calculations based on body surface area 1 0011 42 5 0010 1010 1101 0001 0100 1011  Calculate the BSA of a boy of height 165 cm and weighing 65kg. BSA = = = 1.726 VIGNAN PHARMACY COLLEGE 50
1 0011 42 5 0010 1010 1101 0001 0100 1011 VIGNAN PHARMACY COLLEGE 51 TEMPERATURE MEASUREMENTS
TEMPERATURE MEASUREMENTS 0010 1010 • The tem p1e1r0a1t u0r0e01i s01g0e0n 1e0r1a1lly measured in pharmacy by using 0011 either Fahrenheit or Centigrade thermometers. 1 • The relationship of Centigrade (C) and Fahrenheit (F) degrees 42 5 is 90 (C) = 50 (F) – 160 Where 0 C is the number of degrees Centigrade. 0 F is the number of degrees Fahrenheit. VIGNAN PHARMACY COLLEGE 52
Example problem for converting Fahrenheit to Centigrade Convert 1200 F into 0 C 1 0011 42 5 0010 1010 1101 0001 0100 1011 90 (C) = 50 (F) -160 = 5(120) – 160 = 600 –160 = 440 0 C = 440/9 = 48.90 C VIGNAN PHARMACY COLLEGE 53
Example problem for converting Centigrade to Fahrenheit Convert 300 c into 0F 1 0011 42 5 0010 1010 1101 0001 0100 1011 50 F = 90 C + 160 = 9(30) + 160 = 270 + 160 = 430 0 F = = 860 F VIGNAN PHARMACY COLLEGE 54
1 0011 42 5 0010 1010 1101 0001 0100 1011 DIALYSIS CLEARANCE VIGNAN PHARMACY COLLEGE 55
• Dialysis clearance is also called as Dialysance. • It is used to express the ability of machine to clear the drug from 1 0011 42 5 0010 1010 1101 0001 0100 1011 blood. Cld = Q(Cin – Cout ) / Cin Where Cld = dialysis or dialysis clearance. Q = blood flow rate to dialyzer. Cin = concentration of drug in blood entering the dialyzer Cout= concentration of drug in blood leaving the dialyzer. VIGNAN PHARMACY COLLEGE 56 DIALYSIS CLEARANCE
1 0011 42 5 0010 1010 1101 0001 0100 1011 . 57 Semipermeable membrane Blood dialysate Diagrammatic representation of a haemodialyser . The blood and the dialysate flow counter-currently.
Example problem for Dialysis Clearance  Calculate the dialysis clearance if the blood flow rate to the dialyzer 50ml/min and concentration of drug entering and leaving the dialyzer is 100 and 200microgram/ml respectively. 1 0011 42 5 0010 1010 1101 0001 0100 1011 Dialysis Clearance = Q[C in – Cout ] / Cin = = = 40ml/min 58
1 0011 42 5 0010 1010 1101 0001 0100 1011 PHARMACOKINETICS VIGNAN PHARMACY COLLEGE 59
• Pharmacokinetics is the mathematical analysis of process of 1 0011 42 5 0010 1010 1101 0001 0100 1011 ADME. • The velocity with a reaction or a process occurs is called as its rate. • The manner in which the concentration of drug influences the rate of reaction or process is called as the order of reaction or order of a process. • consider the following equation Drug A Drug B • PHARMACOKINETICS 60
Rate of reaction can be expressed as follows dc/dt = -k.cn 1 0011 42 5 0010 1010 1101 0001 0100 1011 Where k = rate constant n= order of reaction • If n = 0 , it is a zero order process • If n=1 , it is a first order process VIGNAN PHARMACY COLLEGE 61
Conversion of various order of reactions 1 0011 42 5 0010 1010 1101 0001 0100 1011 Basic Equation Final Concentration T1/2 Zero order dc/dt = -k.c0 C = C0 – kt T1/2 = 0.5c0 /k First order dt/ct = -k.c1 log C = log T1/2 = 0.693/k Second order dc/dt = -k.c2 T1/2 = 1/c0 k VIGNAN PHARMACY COLLEGE 62
Example problem for pharmacokinetic calculations  A penicillin solution has a half-life of 21days.How long 1 0011 42 5 0010 1010 1101 0001 0100 1011 will take it for the potency to drop to 80% of the initial potency. t1/2 = 0.693/k 21 = 0.693/k k = 0.693/21 = 0.033 VIGNAN PHARMACY COLLEGE 63
t1/2 = 1 0011 42 5 0010 1010 1101 0001 0100 1011 = = 69.78 * log(1.25) = 69.78 * 0.096 = 6.6988 ~ 7days VIGNAN PHARMACY COLLEGE 64
CONCLUSION 1 0011 42 5 0010 1010 1101 0001 0100 1011 • Pharmaceutical calculations is a predominant area which plays keyrole in various areas of pharmacy like  Conversion of one measurement system to anthor.  Dose calculations for dispensing prescriptions.  Dilution of alcohols.  Filling of capsules etc…. • Pharmaceutical calculations also play a crucial role in diagnosis , Treatment and prevention of ailments. VIGNAN PHARMACY COLLEGE 65
REFERENCES Remington - science and practice of pharmacy. Patrick J Sinko – Martins physical pharmacy and phamaceutical sciences. 42 5 0011 0010 1010 1101 0001 0100 1011 1 M.E.Aulton - Pharmaceutics,The science of dosage form design. Haward c Ansel / Mitchell J stoklosa Lippincott – Pharmaceutical Calculations. Leon Shargel , Alan Mutnic , Paulf Souney , Larry N Swa – Comprehensive Pharmacy Review. 66
REFERENCES 0011  0010 1010 1101 0001 0100 1011 R.M.Mehta – Dispensing Pharmacy. Pg.no:77-103  B.M.Brahmankar Sunil B.Jaiswal – Pharmaceutics and 1 42 5 pharmacokinetics. Pg.no: 211-213,239-243.  R.M.Mehta – Pharmaceutics-II. Pg.no:14-38,65.  CVS.Subrahmanyam – Essentials of Physical Pharmacy. pg.no:29,195-198 VIGNAN PHARMACY COLLEGE 67
ACKNOWLEDGEMENT 1 0011 42 5 0010 1010 1101 0001 0100 1011  I Sincerely thank my guide Mrs.K.Pallavi garu for her constant guidance and support.  I’m very thankful to our beloved principal sir Dr.P.Srinivas Babu garu and also the seminar committee. VIGNAN PHARMACY COLLEGE 68
1 0011 42 5 0010 1010 1101 0001 0100 1011

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Pharmaceutical calculations

  • 1. PHARMACEUTICAL CALCULATIONS UNDER THE ESTEEMED GUIDANCE OF 42 5 Presented By B.LAKSHMI DURGA 11AB1R0082 Mrs.PALLAVI.K M.Pharm 0011 0010 1010 1101 0001 0100 Assistant 1011 Professor 1 VIGNAN PHARMACY COLLEGE Approved by PCI,AICTE,New Delhi. Affiliated to JNTU,Kakinada. Vadlamudi-522213,Guntur,A.P 1
  • 2. CONTENTS 1 0011 42 5 0010 1010 1101 0001 0100 1011 Percentage calculations Alcoholic dilutions Alligation method  Proof spirit calculations  Isotonic solutions  Posology  Temperature measurements  Dialysis Clearance  Pharmacokinetics VIGNAN PHARMACY COLLEGE 2
  • 3. PHARMACEUTICAL CALCULATIONS 1 0011 Pharmacokinetic calculations 42 5 0010 1010 1101 0001 0100 1011 VIGNAN PHARMACY COLLEGE 3
  • 4. INTRODUCTION  To have a complete understanding of various types of calculations, which are involved in dispensing, it is desirable that the pharmacist should have a thorough knowledge regarding weights and measures which are used in calculations. 1 0011 42 5 0010 1010 1101 0001 0100 1011  There are two systems of weights and measures. 1.The Imperial system 2.The Metric system 4
  • 5. IMPERIAL SYSTEM 1 0011 42 5 0010 1010 1101 0001 0100 1011 • Imperial system is an old system of weight and measures. Imperial system Avoirdupois system Apothecaries system VIGNAN PHARMACY COLLEGE 5
  • 6. Avoirdupois system : • In this system the pound is the standard unit for 1 0011 42 5 0010 1010 1101 0001 0100 1011 weighing and all measures of mass are derived from the Imperial standard pound (lb). Apothecaries system : • This system is also known as Troy system. • The grain is the standard unit in this system and all other weights are derived from it. VIGNAN PHARMACY COLLEGE 6
  • 7. CONVERSION TABLE-1 FROM APOTHECARIES TO AVOIRDUPOIS 1 0011 1 Lb 16 oz (avoir) 1 Lb 7000 grains 1 oz (avoir) 7000/16 = 437.5 grains 20 grains (gr) 1 scruple (̶) ) 60 grains 1 drachm 480 grains 1 ounce (apothe) 42 5 0010 1010 1101 0001 0100 1011 12 ounces 1 pound (Lb) (apothe) 5760 grains 1 pound (apothe) VIGNAN PHARMACY COLLEGE 7
  • 8. Measurement of capacity in imperial system : • The standard units for capacity is same for both the avoirdupois and the apothecaries systems. • The gallon is the standard unit and other measures of capacity 1 0011 42 5 0010 1010 1101 0001 0100 1011 are derived from it. 8 1gallon (c) = 160 fluid ounces 1/4th of gallon = 1 Quart 1/8th of gallon = 1 pint(O) 1/160th of gallon = 1 flounce 1 quart = 40 flounces 1 pint = 20 flounces 1 flounce = 480 minims 1 fl drachm = 60 minims CONVERSION TABLE-2
  • 9. METRIC SYSTEM 1 0011 42 5 0010 1010 1101 0001 0100 1011 • Metric system is used in the Indian pharmacopeia for the measurement of weights and capacity. • It was implemented in India from 1st April , 1964 in pharmacy profession. Measurement of weight in metric system : • A kilogram is the standard unit for measurement of weight and all other measures are derived from it. VIGNAN PHARMACY COLLEGE 9
  • 10. 0010 1010 1101 0001 01010k 1i0lo1g1 ram = 1000gms 0011 1 hectogram = 100 gms 1 42 5 1 decagram = 10 gms 1 decigram = 0.1 gms 1 centigram = 0.01 gms 1 milligram = 0.001 gms 1 microgram = 0.000,001 gms 10 CONVERSION TABLE - 3 FROM HIGHER TO LOWER
  • 11. Measurement of capacity in Metric System 1 0011 42 5 0010 1010 1101 0001 0100 1011 A litre is the standard unit for measurement of capacity and all measures of capacity are derived from it. 1 litre ( lt ) = 1000 milliliters (ml) VIGNAN PHARMACY COLLEGE 11
  • 12. Conversion Tables 1 0011 42 5 0010 1010 1101 0001 0100 1011  The pharmacopeia of India uses only the metric system in formulae, But the prescription are still written in the imperial system by many old time physicians. So a conversion tables is used by the pharmacists. VIGNAN PHARMACY COLLEGE 12
  • 13. Metric system Imperial system 1 kilogram (kg) = 2.2 lb ( pound ) 1 0011 42 5 0010 1010 1101 0001 0100 1011 13 • Weight measures • Capacity measures 30g = 1 ounce 450g = 1 pound ( avoir ) 1g = 15 grains 60mg = 1 grain 1000 ml = 1Quart 500 ml = 1 pint 30 ml = 1 fluid ounce 4 ml = 1 fluid drachm 1 ml = 15 minims 0.06 ml = 1 minim
  • 14. Conversion table for Domestic Measures Domestic Measure Metric system Imperial system 1 drop 0.06 ml 1 minim 0011 1 tea spoonful 4.00 ml 1 fluid drachm 1 desert spoonful 8.00 ml 2 fluid drachm 1 42 5 0010 1010 1101 0001 0100 1011 1 tablespoonful 15.00 ml 4 fluid drachm 2 tablespoonful 30.00 ml 1 fluid ounce 1 wine glassful 60.00 ml 2 fluid ounce 1 tumblerful 240.00 ml 8 fluid ounce VIGNAN PHARMACY COLLEGE 14
  • 15. CALCULATIONS BASED ON DENSITY :  Density is defined as the mass of a substance per unit volume. 1 0011 42 5 0010 1010 1101 0001 0100 1011  It has the units of mass over volume.  Specific gravity is defined as the ratio of the mass of a substance in air to that of an equal volume of water.  In the metric system both density and specific gravity are numerically equal. WEIGHT = VOLUME * DENSITY VIGNAN PHARMACY COLLEGE 15
  • 16. Example problems for calculations based on density 1. Calculate the volume of 2kg of glycerin. The density of glycerin is 1.25g/ml. 1 0011 42 5 0010 1010 1101 0001 0100 1011 = 1600 ml VIGNAN PHARMACY COLLEGE 16 VOLUME = = =
  • 17. 0010 1010 2. Calcula 1te1 0t1h 0e0 w01e 0ig10h0t 1o0f1 1200ml of alcohol whose 1 0011 42 5 density is 0.816 g/ml WEIGHT = VOLUME X DENSITY = 200 ml x 0.816 g/ml = 163.2g VIGNAN PHARMACY COLLEGE 17
  • 18. 1 0011 42 5 0010 1010 1101 0001 0100 1011 VIGNAN PHARMACY COLLEGE 18
  • 19. Example problem For Alcoholic Dilutions  Calculate the amount of 95% alcohol required to prepare 400ml of 45% alcohol 1 0011 42 5 0010 1010 1101 0001 0100 1011 volume required = 400ml percentage of alcohol required = 45 percentage of alcohol used = 95 Volume of strong alcohol = to be used = = = 184.47 ml 19
  • 20. 0011 Alligation method 1 42 5 0010 1010 1101 0001 0100 1011 VIGNAN PHARMACY COLLEGE 20
  • 21. ALLIGATION METHOD 1 0011 42 5 0010 1010 1101 0001 0100 1011  When the calculation involves mixing of two similar preparations of different strenghts , to produce a preparation of intermediate strength , the alligation method is used. VIGNAN PHARMACY COLLEGE 21
  • 22. Stronger Percentage Weaker percentage 1 0011 42 5 0010 1010 1101 0001 0100 1011 Required Percentage VIGNAN PHARMACY COLLEGE 22 Required percentage – Weaker Percentage Stronger percentage – Required Percentage
  • 23. Example problems For Alligation method 1. Calculate the volume of 95% alcohol required to prepare 600ml of 70% alcohol. 1 0011 42 5 0010 1010 1101 0001 0100 1011 Volume required = 600 ml Percentage of alcohol required = 70 Percentage of alcohol used = 95 70 0 95 70 -0=70 95-70=25 VIGNAN PHARMACY COLLEGE 23
  • 24. (Problem Contd…..) • 70 parts of 95 %alcohol and 25 parts of water will produce the 1 0011 42 5 0010 1010 1101 0001 0100 1011 required %alcohol. Quantity of 95% alcohol required = = 422.10ml Quantity of water required = =157.90ml VIGNAN PHARMACY COLLEGE 24
  • 25. 2. How much quantity of 60%,50%,30% and 20% alcohol should be mixed to get 40% alcohol. 1 0011 42 5 0010 1010 1101 0001 0100 1011 40 VIGNAN PHARMACY COLLEGE 25 60 20 50 30 40-20=20 parts of 60% 40-30=10 parts of 50% 50-40=10 parts of 30% 60-40=20 parts of 20%
  • 26. ( Problem contd……) • Quantity required = 20parts of 60%+10 parts of 50%+ 1 0011 42 5 0010 1010 1101 0001 0100 1011 10 parts of 30%+20 parts of 20% alcohol are mixed together, the resulting solution will produce 60% alcohol. Calculation can be checked by the following method: = (20 X 60+10 X 50+10 X 30 +20 X 20) =1200+500+300+400 =2400 20+10+10+20=60 i.e., 60 X 40 = 2400 26
  • 27. PROOFSPIRIT 1 0011 42 5 0010 1010 1101 0001 0100 1011 CALCULATIONS VIGNAN PHARMACY COLLEGE 27
  • 28. Introduction Proof spirit calculations 1 0011 42 5 0010 1010 1101 0001 0100 1011 • The strength of alcohol is calculated in proof degrees.The Indian standards of 100% proof spirit is equal to 57%v/v of ethyl alcohol. i.e., 100% p.s = 57%v/v ethyl alcohol • If the value is more than 57% then it is said to be as over proof spirit. • If the value is less than 57% then it is said to be as under proof spirit. 28
  • 29. (Introduction contd….) • In India , the exercise duty is calculated in terms of rupees per 1 0011 42 5 0010 1010 1101 0001 0100 1011 liter of proof alcohol. So, any percentage volume in volume of alcohol can be converted into proof strength and vice versa by using the following method. i. Multiply the percentage strength of alcohol by 1.753 and deduct 100 from the product. ii. If the result is positive , it is known as over proof iii. If the result is negative , it is known as under proof. VIGNAN PHARMACY COLLEGE 29
  • 30. • 1.753 is obtained as follows: 57.1 volume of ethyl alcohol = 100 ml of proof spirit. 1 0011 42 5 0010 1010 1101 0001 0100 1011 1 volume of ethyl alcohol = 100 / 57.1 = 1.753 volume of proof spirit Example problems for Proof Spirit calculations Calculate the strength of 30 0 O.P and 400 U.P 300 OVER PROOF = 100 + 30 = 130 400 Under proof = 100 – 40 = 60 VIGNAN PHARMACY COLLEGE 30
  • 31. (Problem Contd….) Alcohol strength = = = 74.15%v/v 1 0011 42 5 0010 1010 1101 0001 0100 1011 Alcohol strength = = = 34.23%v/v Check :  If strength is 74.15%v/v 74.15 x 1.753 – 100 =129.9 – 100 = +29.90 or 300 O.P If strength is 34.23 %v/v 34.23 x 1.753 – 100 = 60.00 – 100 = - 400 U.P
  • 32. 2.What is the proof strength of 95% v/v alcohol. 1 0011 42 5 0010 1010 1101 0001 0100 1011 By applying the formula: percentage strength of alcohol x 1.753 – 100 = 95 x 1.753 – 100 = 166.53 – 100 = +66.530 O.P VIGNAN PHARMACY COLLEGE 32
  • 33. 3. How many proof gallons are contained in 5 gallon of 70% v/v alcohol Applying the formula: Value in proof = % strength of alcohol x 1.753 – 100 1 0011 42 5 0010 1010 1101 0001 0100 1011 = 70 x 1.753 – 100 = 122.71 – 100 = 22.710 o.p 100 gallons of 70% v/v alcohol =122.71 units of p.s 1 gallon of 70% v/v alcohol = 122.71/100 = 1.2271 5 gallons of 70% alcohol = 1.2271 x 5 = 6.1355 gallons of p.s 5 gallons of 70% v/v alcohol are equivalent to 6.1355 33 gallons of p.s
  • 34. 1 0011 42 5 0010 1010 1101 0001 0100 1011 ISOTONIC SOLUTIONS VIGNAN PHARMACY COLLEGE 34
  • 35. Isotonic solutions 0010 1010  1101 0001 0100 1011 Isotonic solutions are which have same osmotic pressure or 1 0011 42 5 equal solute concentrations.  0.9% sodium chloride solution is considered to passes the same osmotic pressure and hence it is a standard solution which is isotonic with blood plasma.  Any concentration above this (0.9%) is considered as hypertonic and below this (0.9%) is considered as hypotonic. VIGNAN PHARMACY COLLEGE 35
  • 36. ADJUSTMENT OF ISOTONICITY: FP depression /Cryoscopic 1 0011 42 5 0010 1010 1101 0001 0100 1011 36 method ISOTONIC ADJUSTMENT Nacl Equivalent method White Vinscent method Molecular Concentration method
  • 37. I. Freezing point method/ Cryoscopic method %w/v of adjusting substance needed = 1 0011 42 5 0010 1010 1101 0001 0100 1011 Where PSM = percentage strength of medicament a = Freezing point of the unadjusted solution b = Freezing point of a 1% w/v solution of a adjusting substance VIGNAN PHARMACY COLLEGE 37
  • 38. Example Problem for Freezing point method  Using cryoscopic method. How will you prepare 1% solution of boric acid ,iso osmotic with blood plasma. 1 0011 42 5 0010 1010 1101 0001 0100 1011 [Hint : The freezing point of 1%w/v solution of boric acid is 0.2880 c The freezing point of 1%w/v solution of sodium chloride is 0.5760 c] Percentage of w/v of sodium chloride required = = = 0.402% w/v 1gm of boric acid is needed for 0.402gm of Nacl to become isotonic. . 38
  • 39. 2. Nacl Equivalent method: Quantity of Nacl required to adjust tonicity = 0.9 – ( PSM x E ) Where 1 0011 42 5 0010 1010 1101 0001 0100 1011 PSM = Percentage strength of medicament. E = Nacl equivalent (quantity of Nacl i.e., equivalent to 1gm of drug) 3. White Vincet method : V = W x E x 111.1 Where V = volume of isotonic solution in ml that can be prepared by dissolving drug in water W = weight of the drug. E = Nacl equivalent . 39
  • 40. 4 . Molar (or) Molecular concentration : %W/V of adjusting substance required = Where 1 0011 42 5 0010 1010 1101 0001 0100 1011 M = gram molecular weight. N = no.of ions into which the substance is ionised. Problem: • How to prepare an iso osmotic solution using dextrose. [Hint: mol.wgt of dextrose = 180 [dextrose is non ionising substance] W = 0.03 M W = 0.03 x 180 = 5.4 g/100ml VIGNAN PHARMACY COLLEGE 40
  • 41. POSOLOGY 1 0011 42 5 0010 1010 1101 0001 0100 1011 VIGNAN PHARMACY COLLEGE 41
  • 42. POSOLOGY 0011 0010 1010 1101 0001 0100 1011 Posology refers to the calculation of doses for children. 1. Proportion to Age :- (a) Young’s formula: 1 42 5 Dose for a child = The above formula is used for calculating the doses for children 12 years of age. VIGNAN PHARMACY COLLEGE 42
  • 43. • Example problem for young’s formula What will be the dose for a child of 5 years if the adult dose of a drug is 400 mg. 1 0011 42 5 0010 1010 1101 0001 0100 1011 Dose of the child = = = 117 mg (approximately) VIGNAN PHARMACY COLLEGE 43
  • 44. (b) Dilling’s formula: Dose of a child = 1 0011 42 5 0010 1010 1101 0001 0100 1011 The above formula is used for calculating the doses of a children in between 4 to 20 years of age. Example problem:  What will be the dose for a child of 10 years if the adult dose of a drug is 600mg Dose of a child = = 300 mg 44
  • 45. (c) Freid’s formula: Dose for a child = 1 0011 42 5 0010 1010 1101 0001 0100 1011 The above formula is applicable only for infants. Example problem:  What is the dose for an 8months old infant if the average adult dose of a drug is 250mg Dose for the child = = 13.3mg VIGNAN PHARMACY COLLEGE 45
  • 46. (2) Calculations based on body weight: Catzel rule: 1 0011 42 5 0010 1010 1101 0001 0100 1011 Dose for the child = The average body surface area for an adult =1.73m2 Hence Dose for the child = VIGNAN PHARMACY COLLEGE 46
  • 47. Example problem for calculations based on body weight  Calculate the dose for a child that has a body surface area of 0.57m2 , when the adult dose of a drug is 50mg. 1 0011 42 5 0010 1010 1101 0001 0100 1011 Child dose = = = 1.65 mg VIGNAN PHARMACY COLLEGE 47
  • 48. Calculations based on body weight: 1 0011 42 5 0010 1010 Clarke’ s1 1r0u1 l0e0:0-1 0100 1011 • Dose = • Dose = Rule is applicable only when child dose is less than 150 lb or 70kg. VIGNAN PHARMACY COLLEGE 48
  • 49. • Example problem for calculations based on body weight The dose of a drug is 5mg/kg body weight. How much of drug required for a boy of 12 years weighing 21kg. 1 0011 42 5 0010 1010 1101 0001 0100 1011 Dose = =1.5mg (3) Calculations based on body surface area: Most accurate method commonly used in onchology department Mosteller rule: BSA ( M2 ) = 49
  • 50. Example problem for calculations based on body surface area 1 0011 42 5 0010 1010 1101 0001 0100 1011  Calculate the BSA of a boy of height 165 cm and weighing 65kg. BSA = = = 1.726 VIGNAN PHARMACY COLLEGE 50
  • 51. 1 0011 42 5 0010 1010 1101 0001 0100 1011 VIGNAN PHARMACY COLLEGE 51 TEMPERATURE MEASUREMENTS
  • 52. TEMPERATURE MEASUREMENTS 0010 1010 • The tem p1e1r0a1t u0r0e01i s01g0e0n 1e0r1a1lly measured in pharmacy by using 0011 either Fahrenheit or Centigrade thermometers. 1 • The relationship of Centigrade (C) and Fahrenheit (F) degrees 42 5 is 90 (C) = 50 (F) – 160 Where 0 C is the number of degrees Centigrade. 0 F is the number of degrees Fahrenheit. VIGNAN PHARMACY COLLEGE 52
  • 53. Example problem for converting Fahrenheit to Centigrade Convert 1200 F into 0 C 1 0011 42 5 0010 1010 1101 0001 0100 1011 90 (C) = 50 (F) -160 = 5(120) – 160 = 600 –160 = 440 0 C = 440/9 = 48.90 C VIGNAN PHARMACY COLLEGE 53
  • 54. Example problem for converting Centigrade to Fahrenheit Convert 300 c into 0F 1 0011 42 5 0010 1010 1101 0001 0100 1011 50 F = 90 C + 160 = 9(30) + 160 = 270 + 160 = 430 0 F = = 860 F VIGNAN PHARMACY COLLEGE 54
  • 55. 1 0011 42 5 0010 1010 1101 0001 0100 1011 DIALYSIS CLEARANCE VIGNAN PHARMACY COLLEGE 55
  • 56. • Dialysis clearance is also called as Dialysance. • It is used to express the ability of machine to clear the drug from 1 0011 42 5 0010 1010 1101 0001 0100 1011 blood. Cld = Q(Cin – Cout ) / Cin Where Cld = dialysis or dialysis clearance. Q = blood flow rate to dialyzer. Cin = concentration of drug in blood entering the dialyzer Cout= concentration of drug in blood leaving the dialyzer. VIGNAN PHARMACY COLLEGE 56 DIALYSIS CLEARANCE
  • 57. 1 0011 42 5 0010 1010 1101 0001 0100 1011 . 57 Semipermeable membrane Blood dialysate Diagrammatic representation of a haemodialyser . The blood and the dialysate flow counter-currently.
  • 58. Example problem for Dialysis Clearance  Calculate the dialysis clearance if the blood flow rate to the dialyzer 50ml/min and concentration of drug entering and leaving the dialyzer is 100 and 200microgram/ml respectively. 1 0011 42 5 0010 1010 1101 0001 0100 1011 Dialysis Clearance = Q[C in – Cout ] / Cin = = = 40ml/min 58
  • 59. 1 0011 42 5 0010 1010 1101 0001 0100 1011 PHARMACOKINETICS VIGNAN PHARMACY COLLEGE 59
  • 60. • Pharmacokinetics is the mathematical analysis of process of 1 0011 42 5 0010 1010 1101 0001 0100 1011 ADME. • The velocity with a reaction or a process occurs is called as its rate. • The manner in which the concentration of drug influences the rate of reaction or process is called as the order of reaction or order of a process. • consider the following equation Drug A Drug B • PHARMACOKINETICS 60
  • 61. Rate of reaction can be expressed as follows dc/dt = -k.cn 1 0011 42 5 0010 1010 1101 0001 0100 1011 Where k = rate constant n= order of reaction • If n = 0 , it is a zero order process • If n=1 , it is a first order process VIGNAN PHARMACY COLLEGE 61
  • 62. Conversion of various order of reactions 1 0011 42 5 0010 1010 1101 0001 0100 1011 Basic Equation Final Concentration T1/2 Zero order dc/dt = -k.c0 C = C0 – kt T1/2 = 0.5c0 /k First order dt/ct = -k.c1 log C = log T1/2 = 0.693/k Second order dc/dt = -k.c2 T1/2 = 1/c0 k VIGNAN PHARMACY COLLEGE 62
  • 63. Example problem for pharmacokinetic calculations  A penicillin solution has a half-life of 21days.How long 1 0011 42 5 0010 1010 1101 0001 0100 1011 will take it for the potency to drop to 80% of the initial potency. t1/2 = 0.693/k 21 = 0.693/k k = 0.693/21 = 0.033 VIGNAN PHARMACY COLLEGE 63
  • 64. t1/2 = 1 0011 42 5 0010 1010 1101 0001 0100 1011 = = 69.78 * log(1.25) = 69.78 * 0.096 = 6.6988 ~ 7days VIGNAN PHARMACY COLLEGE 64
  • 65. CONCLUSION 1 0011 42 5 0010 1010 1101 0001 0100 1011 • Pharmaceutical calculations is a predominant area which plays keyrole in various areas of pharmacy like  Conversion of one measurement system to anthor.  Dose calculations for dispensing prescriptions.  Dilution of alcohols.  Filling of capsules etc…. • Pharmaceutical calculations also play a crucial role in diagnosis , Treatment and prevention of ailments. VIGNAN PHARMACY COLLEGE 65
  • 66. REFERENCES Remington - science and practice of pharmacy. Patrick J Sinko – Martins physical pharmacy and phamaceutical sciences. 42 5 0011 0010 1010 1101 0001 0100 1011 1 M.E.Aulton - Pharmaceutics,The science of dosage form design. Haward c Ansel / Mitchell J stoklosa Lippincott – Pharmaceutical Calculations. Leon Shargel , Alan Mutnic , Paulf Souney , Larry N Swa – Comprehensive Pharmacy Review. 66
  • 67. REFERENCES 0011  0010 1010 1101 0001 0100 1011 R.M.Mehta – Dispensing Pharmacy. Pg.no:77-103  B.M.Brahmankar Sunil B.Jaiswal – Pharmaceutics and 1 42 5 pharmacokinetics. Pg.no: 211-213,239-243.  R.M.Mehta – Pharmaceutics-II. Pg.no:14-38,65.  CVS.Subrahmanyam – Essentials of Physical Pharmacy. pg.no:29,195-198 VIGNAN PHARMACY COLLEGE 67
  • 68. ACKNOWLEDGEMENT 1 0011 42 5 0010 1010 1101 0001 0100 1011  I Sincerely thank my guide Mrs.K.Pallavi garu for her constant guidance and support.  I’m very thankful to our beloved principal sir Dr.P.Srinivas Babu garu and also the seminar committee. VIGNAN PHARMACY COLLEGE 68
  • 69. 1 0011 42 5 0010 1010 1101 0001 0100 1011