1. University of Sulaimani Collage of Pharmacy 2nd Stage Pharmaceutical Orientation
Some Calculations Involving ‘‘Units,’’ ‘‘µg/mg,’’ and Other Measures of Potency
Lecture (2)
Shahen S. Mohammed
BSc Pharmacy
MSc Pharmaceutics

2. Potency
The potencies of some antibiotics, endocrine products, vitamins, products derived through biotechnology, and biologics (e.g., vaccines) are based on their activity and are expressed in terms of units (of activity), in micrograms per milligram (µg/mg).
Potency: amount of drug necessary to produce maximum effect is the potency of drug.

3. Units of Activity
The potency of many pharmaceutical products derived from biological sources is based on units of activity. Units of activity are determined against specific biologic standards and vary between products.
Generally, there is an established relationship between a product’s units of activity and a measurable quantity (e.g., units per milligram; units per milliliter). This relationship may be used in a ratio and proportion to determine either the number of units of activity or the weight or volume containing a specified number of units:

4. Units of activity (given) Weight or volume (given) = Units of activity (given or desired) Weight or volume (given or desired)

6. Example Calculations of Measures of Activity or Potency
Determinations of the activity or potency of a biologic material may be performed through the use of ratio and proportion or dimensional analysis.

7. Examples
How many milliliters of U-100 insulin should be used to obtain 40 units of insulin?
U-100 insulin contains 100 units/mL.

8. A physician prescribed 100 units of insulin to be added to 500 mL of D5W in treating a patient with severe diabetic acidosis. How many milliliters of insulin injection concentrate, U-500, should be used?

9. How many milliliters of a heparin sodium injection containing 200,000 units in 10 mL should be used to obtain 5,000 Heparin Sodium Units that are to be added to an intravenous dextrose solution?

10. If neomycin sulfate has a potency of 600 µg of neomycin per milligram, how many milligrams of neomycin sulfate would be equivalent in potency to 1 mg of neomycin?

11. A biologic contains 50 Lf Units of diphtheria toxoid in each 2
A biologic contains 50 Lf Units of diphtheria toxoid in each 2.5 mL of product. If a pediatric patient is to receive 10 Lf Units, how many milliliters of product should be administered?

12. Measles Virus Vaccine Live is prepared to contain 1000 TCID50 per 0
Measles Virus Vaccine Live is prepared to contain 1000 TCID50 per 0.5-mL dose. What is the TCID50 content of a 50-mL multiple dose vial of the vaccine?

14. Reducing and Enlarging Formulas
University of Sulaimani College of Pharmacy 2nd Stage Pharmaceutical Orientation
Reducing and Enlarging Formulas
Lecture (3)
Shahen S. Mohammed
BSc Pharmacy
MSc pharmaceutics

15. 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).
Industrial formulas may be scaled up to quantities of ingredients sufficient to prepare hundreds of thousands of dosage units in a production batch.

16. 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.

17. Calculations to reduce or enlarge formulas
Calculations to reduce or enlarge formulas may be performed by a two-step process:
Step 1. Using the following equation, determine the factor that defines the multiple or the decimal fraction of the amount of formula to be prepared:
Quantity of formula desired Quantity of formula given = Factor
A factor greater than 1 represents the multiple of the formula, and a factor less than 1 indicates the fraction of the formula to be prepared.

18. Step 2. 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.

19. Applying the equation and factor:
If a formula for 1000 mL contains 6 g of a drug, how many grams of drug are needed to prepare 60 mL of the formula?
Step 1.
60 mL mL = 0.06 (factor)
Step 2.
6 g × 0.06 = 0.36 g

20. Example Calculations of Reducing and Enlarging Formulas
1- From the following formula, calculate the quantity of each ingredient required to make 240 mL of calamine lotion.
Calamine g
Zinc Oxide g
Glycerin g
Bentonite Magma mL
Calcium Hydroxide Topical Solution, to make mL
240 mL 1000 mL = 0.24 (factor)

21. 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

22. 2- From the following formula for artificial tears, calculate the quantity of each ingredient required to prepare a dozen 30-mL containers.
Polyvinyl Alcohol g
Povidone g
Chlorobutanol g
Sterile Sodium Chloride Solution, 9% ad mL
30 mL × 12 = 360 mL
360 mL 100 mL = 3.6 (factor)

23. 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

24. Formula weight = 200 g + 1 g + 95 g = 296 g
3- From the following formula for an estradiol vaginal gel,calculate the quantity of each ingredient required to prepare 1 lb. of gel.
Estradiol g
Polysorbate g
Methylcellulose Gel, 2% g
1 lb. = 454 g
Formula weight = 200 g + 1 g + 95 g = 296 g
454 g 296 g = (factor)

25. Using the factor 1.534, the quantity of each ingredient is calculated as follows:
Estradiol = 200 g × = g
Polysorbate = 1 g × = g
Methylcellulose Gel, 2% = 95 g × = g

26. 4- From the following formula for a dexamethasone ophthalmic ointment, calculate the quantity of each ingredient needed to prepare 7.5 g of ointment.
Dexamethasone Sodium Phosphate mg
Lanolin, Anhydrous g
Mineral Oil g
White Petrolatum ad g
7.5 g 100 g = (factor)

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

28. 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.

29. Example Calculation of a Formula Expressed in Parts
From the following formula, calculate the quantity of each ingredient required to make 1000 g of the ointment.
Coal Tar parts
Zinc Oxide parts
Hydrophilic Ointment parts
Total number of parts (by weight) = 65
1000 g will contain parts
65 (parts) 5 (parts) = (g) x (g)
x = g of Coal Tar

30. 65 (parts) 10 (parts) = 1000 (g) y (g)
and
65 (parts) 10 (parts) = (g) y (g)
y = g of Zinc Oxide
65 (parts) 50 (parts) = (g) z (g)
z = g of hydrophilic ointment
(Check total: 1000 g)