pharmaceutical calculations and pharmacy principles

1. Lecture 6
Laith Al-Asadi

2. Reducing and enlargement
formula
 Pharmacists may have to reduce or enlarge formulas
for pharmaceutical preparations in the course of their
professional practice or manufacturing activities.
 Official (United States Pharmacopeia—National
Formulary) formulas generally are based on the
preparation of 1000 mL or 1000 g.
 Other formulas, as those found in the literature, may
be based on the preparation of a dosage unit (e.g., 5
mL, 1 capsule) or another quantity (e.g., 100 mL).

3. Reducing and enlargement
formula
 Industrial formulas may be scaled up to quantities of
ingredients sufficient to prepare hundreds of
thousands of dosage units in a production batch.
 In each of these instances, a pharmacist may calculate
the quantities of each ingredient required for a smaller
or greater quantity by reducing or enlarging the
specified formula, while maintaining the correct
proportion of one ingredient to the other.

4. Reducing and enlargement formula
 Calculations to reduce or enlarge formulas may be performed by
a two-step process:
The first step: determine the factor that defines the multiple or the
decimal fraction of the amount of formula to be prepared by the
following equation:
Factor =
Quantity of formula desired
Quantity of formula given
 When the factor is greater than 1 represents the multiple of the
formula
 When factor less than 1 indicates the fraction of the formula to
be prepared.

5. Reducing and enlargement formula
 The second step.
Multiply the quantity of each ingredient in the formula
by the factor to determine the amount of each ingredient
required in the reduced or enlarged formula.

6. Example 1
 If a formula for 1000 mL contains 6 g of a drug, how
many grams of drug are needed to prepare 60mL of
the formula?
Step 1.
60 𝑚𝑙
1000 𝑚𝑙
= 0.06 (factor)
Step 2. 6 g × 0.06 = 0.36 g, answer.

7. Example 2
 From the following formula, calculate the quantity of
each ingredient required to make 240 mL of calamine
lotion.
Calamine 80 g
Zinc Oxide 80 g
Glycerin 20 g
Bentonite Magma 250 mL
 Calcium Hydroxide Topical Solution, to make 1000 mL

8. Solution
Step 1.
240 𝑚𝑙
1000 𝑚𝑙
= 0.24 (factor)
Using the factor 0.24, the quantity of each ingredient is
calculated as follows:
Calamine 80 g × 0.24 = 19.2 g
Zinc Oxide 80 g × 0.24 = 19.2 g
Glycerin 20 g × 0.24 = 4.8 mL
Bentonite Magma 250 g × 0.24 = 60 mL
Calcium Hydroxide Topical Solution, to make 240 mL,
answers

9. Example 3
From the following formula for artificial tears,1calculate
the quantity of each ingredient required to prepare a
dozen 30-mL containers.
Polyvinyl Alcohol 1.4 g
Povidone 0.6 g
Chlorobutanol 0.5 g
Sterile Sodium Chloride Solution, 9% ad 100 mL

10. Solution
30 mL × 12 = 360 mL
360 𝑚𝑙
100 𝑚𝑙
= 3.6 (factor)
Using the factor 3.6, the quantity of each ingredient is
calculated as follows:
Polyvinyl Alcohol 1.4 g × 3.6 = 5.04 g
Povidone 0.6 g × 3.6 = 2.16 g
Chlorobutanol 0.5 g × 3.6 = 1.8 g
Sterile Sodium Chloride Solution, 9% ad 360 mL, answers

11. Example 3
From the following formula for an estradiol vaginal
gel,2calculate the quantity of each ingredient
required to prepare 1 lb. of gel.
Estradiol 200 g
Polysorbate 80 1 g
Methylcellulose Gel, 2% 95 g

12. Solution
1 lb. = 454 g
Formula weight 200 g + 1 g + 95 g = 296 g
454 𝑔
296𝑔
= 1.534 (factor)
Using the factor 1.534, the quantity of each ingredient is
calculated as follows:
Estradiol 200 g × 1.534 = 306.8 g
Polysorbate 80 1 g × 1.534 = 1.534 g
Methylcellulose Gel, 2% 95 g × 1.534 = 145.73 g, answers

13. Example 4
From the following formula for a dexamethasone
ophthalmic ointment,3calculate the quantity of each
ingredient needed to prepare 7.5 g of ointment.
Dexamethasone Sodium Phosphate 55 mg
Lanolin, Anhydrous 5 g
Mineral Oil 10 g
White Petrolatum ad 100 g

14. Solution
7.5 𝑔
100𝑔
= 0.075 (factor)
Using the factor 0.075, the quantity of each ingredient is
calculated as follows:
Dexamethasone Sodium Phosphate 55 mg × 0.075 = 4.125
mg
Lanolin, Anhydrous 5 g × 0.075 = 0.375 g
Mineral Oil 10 g × 0.075 = 0.75 g
White Petrolatum ad 7.5 g, answers.

15. Formulas That Specify Proportional
Parts
 On a rare occasion, a pharmacist may encounter an old
formula that indicates the ingredients in ‘‘parts’’ rather
than in measures of weight or volume.
 The parts indicate the relative proportion of each of
the ingredients in the formula by either weight or
volume, but not both.
 A formula for solid or semisolid ingredients, therefore,
may be considered in terms of grams, whereas a
formula of liquids may be considered in terms of
milliliters.

16. Example
 From the following formula, calculate the quantity of
each ingredient required to make 1000 g of the
ointment.
Coal Tar 5 parts
Zinc Oxide 10 parts
Hydrophilic Ointment 50 parts
Total number of parts (by weight) 65
1000 g will contain 65 parts

17. Solution
Total number of parts (by weight) 65
1000 g will contain 65 parts
65 𝑝𝑎𝑡𝑟𝑠
5 𝑝𝑎𝑟𝑡𝑠
=
1000 𝑔
𝑥
x = 76.92 g of Coal Tar,
The same steps for zinc oxide and hydrophilic ointment

18. Practice problems 1
 From the following formula for 40 sertraline capsules,
calculate the factor that would be used if a pharmacist
wished to prepare 250 capsules.
Sertraline Hydrochloride 300 mg
Silica Gel Sodium 6 g
Calcium Citrate 4 g

19. Practice problems 2
 19. From the following formula for an oral electrolyte
solution, calculate the amount of each ingredient
required to prepare 240 mL of the solution.
 Sodium 45 mEq
 Potassium 20 mEq
 Chloride 35 mEq
 Citrate 30 mEq
 Dextrose 25 g
 Water ad 1000 mL