Pharmaceutics I Calculations Amr Fayed

Calculations

Systems of Measurement

The knowledge and applications of pharmaceutical and clinical calculations are essential
for the practice of pharmacy and related health professions.

Roman Numerals

In the usage of Roman numerals, the following set of rules apply:

I=1 II=2 III=3

X=10 XX=20 XXX=30

Examples:
VII =5+1+1=7
XVI=10+5+1=16
Examples:
IV=5-1=4
IX=10-1=9

2. The three systems of measurements and their interconversions:

1. Metric system.
2. Apothecary and Avoirdupois systems (the common systems).
3. Household system.

The Metric System

To add, subtract, multiply or divide different metric units, first convert all the units to the
same denomination.

For example, to subtract 54 mg from 0.28 g, solve as

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280 mg – 54 mg = 226 mg.

Example:

Add 1.25 g, 35 mg, and 80μg, and express the result in milligrams.

Solving

1.25 g = 1250 mg, and 80 μg = 0.08 mg

Therefore, 1250 + 35 + 0.08 = 1285.08 mg

Answer: 1285.08 mg.

APOTHECARIESˈ SYSTEM
Unlike the metric system which has units for weight, volume and length, the apothecary’s
system has units for weight and volume only. This is an old system and its use is rapidly
declining. However, some physicians still prescribe using this system.

 The basic unit for weight is grain (gr) and that of volume is minim (m).

Example:
A pharmacist had 1 gallon of alcohol. At different times he dispensed f-oz iv, Oii, f-oz viii
and ƒ Ӡ iv. What volume of alcohol was left?
Answer
f-oz iv = 4 f-oz
o ii = 2 x 16 f-oz = 32 f-oz
f-oz viii = 8 f-oz
1
ƒ Ӡ iv = 𝑓. 𝑜𝑧
2

Pharmacist dispensed= 4+32+8+0.5= 44.5 Fl OZ

G = 128 f-oz

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Convert F З iiss to Convert 2.5 L to How many grams are

milliliters? fluidounces? represented by 850 grains?
1 f З --------------------- 4 ml 1 f-oz ---------------- 30 ml 1 gr ------------------0.065 gm
F З iiss = 2.5 f З ------- x ml X ------------- 2.5 L x 1000 850 gr --------------------- x
X= 2.5 x 4 = 10 ml X= 1 x 2.5 x 1000 / 30 = X = 850 x 0.065 = 55.25 gm
83.33 f-oz

THE AVOIRDUPOIS SYSTEM

1 ounce (oz) = 437.5 grains 1 pound (Ib) = 7000 grains
2.2 Pound (Ib) = 1 Kg
Example 1: 1 kg 2.2 Ib
Convert 15 Kg to avoirdupois pounds? 15 kg X
X = 15 x 2.2 = 33 Ib

THE HOUSEHOLD SYSTEM

If a preparation contains 5 mg of a drug in 500 5 mg = 500 ml
ml, how many grams are contained in each X = 15 ml
tablespoonful dose? X = 0.15 gm x 1000 = 150 g

If a cough syrup contains 0.24 gm of codeine 0.24 gm x 1000 = 240 mg = 120 ml

in 120 ml, how many milligrams are contained X mg = 5 ml
in each teaspoonful dose? X= 5 x 240 / 120 = 10 mg

A physician prescribes tetracycline suspension 2 x 5 ml x 4x 4 + 1 x 5 ml x 4 x 2 =

for a patient to be taken in doses of two 200 ml
teaspoonful four times a day for 4 days, and
then one teaspoonful four times a day for 2
days. How many milliliters of the suspension

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should be dispensed to provide the quantity for

the prescribed dosage regimen?

Calculation of doses for children:

Example: (Young’s Rule)
The doctor orders an adult dose of Lasix 20 mg PO.
Calculate the dose for a child who is 5 years old using Youngerˈs Rule.
Answer:
𝟓 𝒚𝒆𝒂𝒓𝒔 5
= x 20mg = x 20 mg = 5.9 mg
𝟓 𝒚𝒆𝒂𝒓𝒔+𝟏𝟐 𝒚𝒆𝒂𝒓𝒔 17

Example: (Clarkˈs Rule)

The doctor orders an adult dose of Decadron (Dexamethasone) 4 mg/day. Calculate
the dose for a child the weighs 16 Ibs using Clarkˈs Rule.
Answer
𝟏𝟔𝟎 𝑰𝒃𝒔 𝒙 𝟒 𝒎𝒈 𝟔𝟒 𝒎𝒈
= = = 0.43 mg/ day
𝟏𝟓𝟎 𝑰𝒃𝒔 𝟏𝟓𝟎
To calculate the dose of drug for children based on body surface area:
Approximate dose for child =
𝐁𝐒𝐀 𝐨𝐟 𝐜𝐡𝐢𝐥𝐝 (𝐦𝟐)
Adult dose x
𝟏.𝟕𝟑 𝒎𝟐 (𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝒂𝒅𝒖𝒍𝒕 𝑩𝑺𝑨)

If the adult dose of drug is 100 mg, what would be the dose for a child with a body
surface area of 0.7 m2?
Approximate dose for child =
𝐁𝐒𝐀 𝐨𝐟 𝐜𝐡𝐢𝐥𝐝 (𝐦𝟐)
Adult dose x
𝟏.𝟕𝟑 𝒎𝟐 (𝒂𝒗𝒆𝒓𝒂𝒈𝒆 𝒂𝒅𝒖𝒍𝒕 𝑩𝑺𝑨)

Dose for child = 100 x 0.7 / 1.73 =40.5 mg

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Temperature Measurements:
The relationship of centigrade (C) and Fahrenheit (F) degrees is
9 (C) = 5 (F) – 160
Example problem for converting Fahrenheit to Centigrade:
Convert 120 F into C
9 (C) = 5 (F) – 160
C = 5(120) – 160 = 600 -160 = 440
C = 440/9 = 48.9 C
Reducing and enlarging formulas

Example 1:
R/ benzoin 100 g
Aloe 20 g
Storax 80 g
Tolu Balsam 40 g
Alcohol to make 1000 ml 𝐓𝐨𝐭𝐚𝐥 𝐚𝐦𝐨𝐮𝐧𝐭 𝐬𝐩𝐞𝐜𝐢𝐟𝐢𝐞𝐝 𝐢𝐧 𝐟𝐨𝐫𝐦𝐮𝐥𝐚
Prepare 1 gallon of compound benzoin tincture. 𝐓𝐨𝐭𝐚𝐥 𝐚𝐦𝐨𝐮𝐧𝐭 𝐝𝐞𝐬𝐢𝐫𝐞𝐝
Answer:
1 gallon = 3785ml
𝟑𝟕𝟖𝟓𝐦𝐥
Factor = = 3.785
𝟏𝟎𝟎𝟎𝐦𝐥

Benzoin = 100× 3.785= 378.5g

Aloe = 20× 3.785= 75.7g
Storax = 80× 3.785= 302.8g
Tolu Balsam = 40× 3.785= 151.4g
Alc. To make 3785ml

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Example 2: Example 3:
R/ Coal Tar 50 g R/ Belladonna extract 1g
Starch 250 g Ephedrine sulphate 1.6 g
Zinc oxide 150 g Phenobarbital 2g
Petrolatum 550 g Aspirin 32 g
Prepare 1 lb (avoir) of the ointment. The following formula for 100 capsules.
Calculate the quantity of each ingredient
required to make 24 capsules.
Answer:
𝟐𝟒
𝟒𝟓𝟒 Factor = = 0.24
𝟏𝟎𝟎
Factor = = 0.454
𝟏𝟎𝟎𝟎

Formulas that specify proportional parts

Example:
R/ Coal tar 5 parts Answer:
5
Zinc oxide 10 parts Coal tar = 1000 g × = 76.92g
65
10
Hydrophilic ointment 50 parts Zinc oxide = 1000 g × = 153.85g
65
50
Prepare 1000 g of the ointment. Hydrophilic ointment = 1000g × = 769.23g
65

Percentage and ratio strength calculations

1. Percentage
The number of grams of a constituent in 100 ml of solution
or liquid preparation.
Percent weight-in-
volume (W/V): - The term used for solutions or suspensions of solids in
liquids.

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The number of ml of a constituent in 100 ml of solution or

Percent volume-in- liquid preparation.
volume (V/V) - The term used for solutions of liquids in liquids.

The number of grams of a constituent in 100 g of solution or

Percent weight-in- mixture.
weight (W/W): - The term used for mixtures of solids and semisolids.

Examples Answer
1. How many grams of dextrose are 5% W/V means
required to prepare 4000 ml of a 5% 5 gm ------------- 100 ml
(W/V) solution?? X gm ------------ 4000 ml
X = 200 gm
A sunscreen lotion contains 5% (v/v) of Answer
menthyl salicylate. 5pt = 5× 16 f- OZ × 30 ml = 2400 ml
2. How many milliliters of menthyl 5ml --------- 100 ml lotion
salicylate should be used in X ml -------- 2400 ml
preparing 5 pt. of the lotion?? X= 120ml

3. If 1500 g of a solution contain 75g Answer

of a drug substance, what is the 75 g of drug --------- 1500 g
percentage strength (w/w) of the X g -------------------- 100 g
solution?? % = 5% w/w

4. What is the percentage strength Answer

(v/v) of solution of 800 g of liquid Volume = Weight / Specific Gravity.
Volume = 800 / 0.8 = 1000 ml

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with a specific gravity of 0.800 in 1000

% V/V= 𝑥 100 = 25%
4000
enough water to make 4000 ml?

Ratio strength
 Ratio strength means: 1 part of the active ingredient contained in a designated ‫محدد‬
number of parts of the total preparation.

For example, a 1: 500 solution of mercuric chloride in water means that 1 gram of
mercuric chloride is contained in 500 ml of the solution.

 For solids in liquids (w/v) = 1g of solute in1000 ml of solution.

 For liquids in liquids (v/v) = 1ml of constituent in1000 ml of solution.
 For solids in solids (w/w) = 1g of constituent in1000 ml of mixture.

Example:
How many grams of potassium permanganate should be used in preparing 500 ml
of a 1:2500 solution (w/v)?
1:2500 means 1g in 2500 ml of solution.
1g …………………. 2500 ml
X g ………………….500 ml
X= 500/2500 = 0.2 g.

Dilution and Concentration

Dilution and Concentration of liquids:

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Example 1: (quantity) x (concentration) (concentrated mixture) =

1- If 500 ml of a 15% (v/v) solution of (quantity) x (concentration) (diluted mixture)
methyl salicylate in alcohol are diluted 500 x 15 = 1500 x % of diluted solution
to 1500 ml, what will be the % = 5% (v/v)
percentage strength (v/v)?
Example 2: (quantity) x (concentration) (concentrated mixture) =
If a 50 ml of 1:20 (w/v) solution of (quantity) x (concentration) (diluted mixture)
aluminum acetate is diluted to 1000 50 ml x 5% = 1000 ml x??%
ml, what is the ratio strength (w/v)? Percent strength = 0.25%
Ratio strength ≈ 1:400 (w/v)
Example 3: 1 pint = 16 f-oz
If 4 f-oz of a 1:2000 (w/v) solution of 4 x 0.05% = 16 x ??%
cetylpyridinium chloride are diluted to Percent strength of the dilution = 0.0125%
1 pint, what will be the ratio strength Ratio strength ≈ 1:8000
(w/v) of the solution?
Example 4: Suppose that the volume before evaporation =
If a syrup containing 65% (w/v) of 100 ml
sugar is evaporated to 85% of its The volume after evaporation = 85 ml
volume, what percent (w/v) of sugar (quantity) x (concentration) (concentrated mixture) =
will it contain? (quantity) x (concentration) (diluted mixture)
85 ml x % of conc. syrup = 100 ml x 65%
X = 76.47% (w/v)

Alligation medial:
What is the percentage (v/v) of alcohol in a Answer
mixture of 3000 ml of 40% (v/v) alcohol, 40 X 3000ml = 120000

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1000 ml of 60% (v/v) alcohol, and 1000 ml 60 X 1000ml = 60000

of 70% (v/v) alcohol? 70 X 1000ml = 70000
Totals: 5000ml = 250000
250000
% (v/v) = = 50% (v/v)
5000

What is the percentage of iodine in a 10 pints = 10 x 16 f-oz x 30 = 4800ml

mixture of 3 liters of 7% (w/v) iodine 7 x 3000 ml = 21000
topical solution, 10 pints of 2% (w/v) 2 x 4800 ml = 9600
solution, and 2270ml of 3.5% (w/v) 3.5 x 2270 ml = 7945
solution? Totals: 10070 ml = 38545
38545
% (w/v) = 3.8%
10070

Alligation alternate
1- In what proportion should alcohols of 95% and 50% strengths be mixed to make
70% alcohol?
The no of parts of 95% alcohol = 20 parts.
The no of parts of 50% alcohol = 25 parts.
Relative amount = 20:25 = 4:5

Example:
In what proportion should 10% and 2% coal tar ointments be mixed to prepare a 5%
ointment?
10% 3 parts (of 10%)
5%
2% 5 parts (of 2%)
Proportion = 3:5
The mathematic validity of this relationship can be demonstrated as follows:
95 %

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70%
50%
So,
95 % X (20 parts)
70%
50% Y (25 parts)

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