Pharmacy Calculations

## Introduction

Formulations are recipes that can be found in pharmaceutical literature, such as the Martindale. Formulations list both the active ingredient and the excipients (additional ingredients) needed to generate the medicine. As such, formulations form one of the many backbones of pharmacy calculations. You’ll find that formulations are quite straightforward, at least when compared to other topics in pharmaceutical calculations.

Nonetheless, if you are embarking on your pharmacy career as an undergraduate, you need to start somewhere. Below, we review five examples of formulations and how best you should approach each problem. Some questions below may reference British or European formulation standards, but the underlying principles behind each answer remain the same – regardless of geography.

Section 1

## Reducing formulae

### Example 1

A pharmacist has been handed a prescription that asks for 200mL of chalk mixture, pediatric BP. The formula is listed as follows:

 Chalk 20g Tragacanth powder 2g Concentrated cinnamon water 4mL Syrup 100mL Double strength chloroform water 500mL Water for preparation to 1000mL

The recipe we have prepares for 1,000mL, but the prescription asks for 200mL.

As a result, we must divide each ingredient in the formula by 5 – meaning the formula is now prepared to 200mL rather than 1,000mL.

When reducing formula – always double check you got the correct ratio. By rushing, you carry the risk of applying the incorrect divisor and undermining the end result. When taking a pharmacy calculation exam, always take your time. Most likely, you will have time at the end of the exam to review your answers. It’s best, though, to secure the correct answer from the outset – approaching the question with a methodical, non-rushed approach that delivers the result you set out to achieve.

Section 2

## Increasing formulae

### Example 2

Find the formulation needed to produce 600mL of aromatic magnesium carbonate mixture BP:

 Light magnesium carbonate 300mg Sodium bicarbonate 500mg Aromatic cardamom tincture 0.3mL Double strength chloroform water 5mL Water to 10mL

The formulation prepared 10mL, but the question asks us to prepare 600mL of medicine. As before, we find the relevant factor. In this case, the difference is 60 – that is to say, we need to create 60 times the listed formulation to make 600mL of medicine.
For example:

• 300mg becomes 18g of light magnesium carbonate.
• Water to 10mL becomes water to 600mL of medicine.

By modifying the proposed recipe, we can create medicines of different amounts and volumes.

Section 3

## Formulae involving parts

Sometimes product formula are expressed as parts rather than as quantities. The total amount of product is the sum of the parts of the ingredients. From this, a formula can be adduced – a formula that can be used to calculate the amount of ingredient needed in a specific amount of product.

### Example 3

Consider the standard for industrial methylated spirits (IMS) BP – which states that ingredients should be in the ratio 95 parts spirit to 5 parts wood naphtha. In IMS, both ingredients are liquids so the parts must be v/v. How much of each ingredient is needed to produce 300L?

First, we need to add the parts – (95 + 5 = 100) – and relate this to the 300L required. The multiplication difference here is 3 (300L divided by 100 parts – we now have a relationship between both:

• 95 parts + 5 parts = 100 parts
• 300L/100 Parts = 3L per part
• 5 parts = 15L
• 95 parts = 285L

We need 15L of wood naphtha and 285L of spirit to produce 300L of (IMS) BP.

### Example 4

Find the quantity of ingredients needed to produce 50g of product using the following formula:

 Calamine (parts) 2 Yellow soft paraffin (parts) 38

The total ointment itself contains 40 parts.

• 2/40 x 50g = 2.5g of calamine
• Therefore, 50g – 2.5g = 47.5g of yellow soft paraffin

Once we understand how many parts there are what the final ingredient total needs to be, it becomes a matter of basic multiplication.

Section 4

## Formulae Involving Percentages

A formula can be expressed as a percentage – commonly seen in ointments and creams, for example. The percentage of ingredients can be used to produce a formula and, from there, the ingredients in a known amount of product can be calculated.

### Example 5

Using the following formula, calculate the amount of each ingredient needed to produce 75g.

• Sulfur – 6%
• Salicylic acid – 4%
• White soft paraffin to 100%

First, we need to recognize that 75g is the equivalent of “to 100%”. 6 percent of 75g is 4.5g.

By the same method, there is 3g of salicyclic and, by subtraction both values from 75g, there must be 92.5 grams of white soft paraffin

## Conclusion

Formulations are by no means the most challenging topic in pharmacy calculations. As an undergraduate though, you must start somewhere. These five examples go some way toward building the knowledge-base you need to tackle formulation questions. This guide is not intended to be exhaustive, but the underlying principles remain the same.

Modifying formulations to meet a prescriptive need is a basic, yet fundamental skill that the aspiring pharmacist must have.