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Pharmacists may have to reduce or enlarge formulas for pharmaceutical preparations in the course of their professional practice or manufacturing activities. Official 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., 5mL, 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. 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.

This type of calculation is performed when the amount of prescribed or ordered medicines deviate from the official quantities of a formula in a reference book. To obtain the required amounts of each ingredient, the figures of the official formula are multiplied by a factor which is determined by the following formula

**Formula**

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.

**Examples (Reducing)**

Compound Benzoic acid ointment PCx

Benzoic acid 60g

Salicylic acid 30g

Emulsifying ointment 910g

Mitte: 20g

**Step 1**

Desired = 20g

Amount in the official formula (Formula given) | factor | New amount of each ingredients |

Benzoic acid 60g | | |

Salicylic acid 30g | | |

Emulsifying ointment 910g | | |

**Solution**

Quantity of formula desired: 20g

Quantity of formula given: 60g + 30g + 910g = 1000g

**Step 2**

The figures of the official are multiplied by a factor in order to obtain new amount of each ingredients for the preparation of the product

**Example (Enlarging)**

From the following formula for artificial tears, calculate 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

**Step 1**

**Desired: **30 ml * 12 (multiplied by 12 because we are asked to prepare a dozen) = 360 ml

**Formula given**: 100ml

**Step 2**

**Formula 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.

**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

**Solution**

Total parts in the official: 5 + 10 + 50 = 65 parts by weight

Desired amount: 1000g will contain 65 parts

**Calculations**

If 1000g contains 65 parts, how many grams are in each ingredient?

Refer:

Pharmaceutical Calculations;13th Edition: Howard C. Ansel, PhD Professor and Dean Emeritus College of Pharmacy University of Georgia Athens, Georgia