1. Pharmaceutical Calculations: Reducing and Enlarging Formulas
Danielle DelVillano, Pharm.D.

2. Objectives
Perform calculations to reduce or enlarge formulas for pharmaceutical preparations stated in metric quantities
Perform calculations to reduce or enlarge formulas for pharmaceutical preparations stated in proportional parts

3. Determining the “Factor”
To go from a larger to smaller quantity, or vice versa, determine the “factor” by which to reduce or enlarge the formula
Ex. USP recipe is for 1000 mL but you only wish to make 100 mL of solution
Quantity of the formula desired = Factor
Quantity of the formula given
Then multiply the quantity of each ingredient in the formula given by the factor to determine the amount of each ingredient needed to prepare the desired compund

4. Example 1
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?
60 mL (quantity desired) = (factor)
1000 mL (quantity given)
6 g x = g of drug needed

5. Problem 1: Solve by using factor
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 solutionn, to make 1000 mL

6. Problem 1: Solve by using factor
240 mL (quantity desired) = 0.24 (factor) 1000 mL (quantity required) Calamine: 80 g x 0.24 = 19.2 g Zinc Oxide: 80 g x 0.24 = 19.2 g Glycerin: 20 g x 0.24 = 4.8 g Bentonite: 250 mL x 0.24 = 60 mL Calcium hydroxide: to make 240 mL

7. Problem 1: Solve by Using Dimensional Analysis
Calamine 80 g x 240 mL = 19.2 g 1000 mL Zinc Oxide 80 g x 240 mL = 19.2 g Glycerin 20 mL x 240 mL = 4.8 mL Bentonite 250 mL x 240 mL = 60 mL Calcium hydroxide to make 240 mL

8. Problem 2
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

9. Problem 2: Solve Using a Factor
Estradiol g
Polysorbate 80 – 1 g
Methylcellulose Gel, 2% - 95 g

10. Problem 2: Solve Using Dimensional Analysis
Estradiol g
Polysorbate 80 – 1 g
Methylcellulose Gel, 2% - 95 g

11. Problem 3: Proportional 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
Hydrophillic Ointment 50 parts

12. Problem 3: Proportional Parts
Total number of parts: = 65 parts So 1000g will contain 65 parts Coal Tar 5 parts = x g 65 parts 1000 g x = g Zinc Oxide 10 parts = x g y = g Hydrophillic Ointment 50 parts = x g z = g

13. Additional Problems

14. Chapter 16 Problem 5
Calculate the quantity of each ingredient needed to prepare 15 mL of the following ophthalmic solution:
Eryromycin lactobionate mg
Dexamethasone sodium phosphate mg
Glycerin mL
Sterile Water for Injection, a.d mL
Erythromycin – 75 mg
Dexamethasone – 15 mg
Glycerin – mL
Sterile water qs ad 15 mL

15. Chapter 16 Problem 5

16. Chapter 16 Problem 10
According to the literature, when the product Amevive (alefacept) is reconstituted with sterile water for injection it contains the following in each 0.5 mL
Alefacept mg
Sucrose mg
Glycine mg
Sodium citrate, dihydrate mg
Citric acid, monohydrate mg

17. Chapter 16 Problem 10 continuted
How much alefacept would be needed to manufacture a 5000 batch of vials for reconstitution?
A) 12.5 mg
B) g
C) 37.5 g
D) 45 g
D) 45 g

18. Chapter 16 Problem 10

19. Chapter 16 Problem 11
The formula for a ciprofloxacin otic drop is given in the literature as follows:
Ciprofloxacin g
Propylene glycol mL
Glycerin qs ad mL
How many grams of ciprofloxacin would be required to prepare mL bottles of the ear drop?
30 g

20. Chapter 16 Problem 11

21. Questions

22. Reference
Ansel, H. C. (2009) Phamaceutical Calculations (13th Ed.). Philadelphia:Lippincott Williams & Wilkins, and Wolters Kluwer Publishers