1. Reducing and Enlarging Formulas
Yewande Dayo
Student Pharmacist

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

3. Reducing and Enlarging Formulas
Official USP-NF formulas are generally based on preparing mL or 1000g of product.
Some formulas are based on the preparation of a dosage unit (e.g. 1 capsule) or other quantity (e.g. 100 mL).
Industrial formulas may be scaled up to quantities of ingredients necessary to make hundreds of thousands of dosage units in a production batch.
Thus, quite frequently, Pharmacists have to reduce or enlarge formulas in their course of practice
This may be calculating the quantities of each ingredient required for a smaller or greater quantity while maintaining the correct proportion of one ingredient to the other.
It is important to maintain the proportion of one ingredient to the other

4. Reducing or enlarging formulas can be done by a two- step process:
Determine the factor that defines the multiple or the fraction of the amount of formula to be prepared Factor = Quantity of formula desired/ quantity of formula given
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
A factor greater than 1 represents the multiple of the formula, and a factor less than 1 indicates the fraction of the formula

5. 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/1000 mL = 0.06 (factor)
6 g x 0.06 = 0.36 g, answer

6. Example 2 RX Zinc oxide 50 g Pine tar 120 g Petrolatum 284 g
How much pine tar would be required to prepare 1 kg of the ointment?
Factor = 1000 g/454 g = 2.2
Amount of pine tar required = 120 x 2.2 = 264 g

7. Example 3 RX Zinc oxide 50 g Pine tar 120 g Petrolatum q.s. ad. 284 g
How much pine tar would be required to prepare 1 kg of the ointment?
Factor = 1000/284 = 3.5
Amount of pine tar required = 3.5 x 120 = 420 g

8. Example 4
From the following formula, calculate the quantity of each ingredient required to make 240 mL of calamine lotion.
Calamine g
Zinc oxide g
Glycerin 20g
Bentonite magma mL
Ca(OH)2 solution to make mL
Calamine: 19.2 g, Zinc Oxide: 19.2 g, Glycerin: 4.8 mL, bentonite magma: 60 mL, calcium hydroxide qs to make 240 mL

9. Example 5
From the following formula for artificial tears, calculate the quantity of each ingredient required to prepare a dozen 30 mL container
Polyvinyl Alcohol g
Povidone g
Chlorobutanol g
Sterile Sodium Chloride Solution, 9% ad 100 mL
Polyvinyl: 5.04 g, Povidone: 2.16 g, Chlorobutanol: 1.8 g, 9% NS ad 360 mL

10. Formulas That Specify Proportional Parts
Rarely, a pharmacist may encounter an old formula with ingredients in “parts” rather than measures of weight and volume
The “parts” indicate a relative proportion of each ingredient in weight or volume

11. Example 6 RX Coal Tar 5 parts Zinc Oxide 10 parts
Hydrophilic Ointment 50 parts
Calculate the quantity of each ingredient to make 1000g of the ointment.
Total parts by weight = 65
Thus, 1000 g will contain 65 parts!!!
Coal tar: g, Zinc Oxide: g, hydrophilic ointment: g, make sure it adds up to 1000g