This is the third in our seven-part series on pharmaceutical calculations, this time dealing comprehensively with formulations.

Medicine Bottle

Formulations in pharmacy are, in effect, recipes that can be found in pharmaceutical literature such as the Martindale. Such formulae have listed quantities of drug and excipients which may need to be altered prior to formulating the medicine – depending on how much volume is required. In this section, we will take a look at some basic calculations of formulations. This section is simple and straightforward, but it would be remiss of PharmaFactz not to include even a basic overview of such a necessary concept.

Section 1 – Formulae Reducing

Example 1

You’ve been handed a prescription from your assistant which asks for 200mL of Chalk Mixture, Paediatric 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 problem we have is that the recipe prepares for 1,000mL but the prescription asks for 200mL. Therefore, we need to divide each of the values in the formula by 5 [20g -> 5g; 4mL -> 0.8mL and so forth]

When reducing formula always re-check at the end to ensure you got the correct ratio as rushing could cause even a simple error which would destroy the preparation being requested.

Section 2 – Increasing the Formulae

Example 2

Calculate the quantities required to produce 600mL of Aromatic Magnesium Carbonate Mixture BP using the formula:

Light Magnesium Carbonate 300mg
Sodium Bicarbonate 500mg
Aromatic Cardamom Tincture 0.3mL
Double Strength Chloroform Water 5mL
Water to 10mL

We need to create 600mL but the formula only allows us to make 10mL, so as before, we find the multiplication difference which is 60 (600/10). We then multiply all the values here by 60 [300 -> 18,000; 500 ->30,000 etc.]

Section 3 – Formulae Involving Parts

Sometimes the formula for a product is expressed as parts rather than as quantities. The total amount of product will be the sum of the parts of the ingredients. From this, a formula can be produced and used to calculate the amounts of the ingredients in a required 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 the ingredients are liquids so the parts are volume in volume. How much of each ingredient is required to produce 300L?

All we need to here is add the parts to make 100 (95 + 5) and relate this to the 300L required. The multiplication difference here is 3 so all we need do is multiply 95 and 5 by 3 to discover the amounts in L required.

95 parts + 5 parts = 100 parts
300L/100 Parts = 3L/Part
5 Parts = 15L
95 Parts = 285L

So we need 15L of Wood Naphtha and 285L of Spirit to make 300L of (IMS) BP.

Example 4

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

Calamine (Parts) 2
Yellow Soft Paraffin (Parts) 38

Thus, the total ointment itself will contain 40 parts.

2/40 x 50g = 2.5g of Calamine
Therefore 50g – 2.5g = 47.5g of Yellow Soft Paraffin.

Straightforward at worst!

Example 5

You have been given a preparation which consists of the following ingredients:

  • Calamine
  • White Soft Paraffin

The record shows that 5,000mg of Calamine was used which was filled to 11 parts by the White Soft Paraffin. How much White Soft Paraffin in grams was used in the preparation?

This is another relatively straightforward question but the key to the answer lies in the phrase ‘to 11 parts’. This could easily be skimmed and the quantity would wrongly assumed to be 11 grams but it is of course 6 grams.

Section 4 – Formulae Involving Percentages

A formula can be expressed as a percentage most commonly done in ointments and creams. The percentages of the ingredients can be used to produce a formula and the ingredients in a known amount of product can be calculated.

Example 6

Using the following formula, calculate the amount of ingredients required to make 75g.

Sulfur – 6%
Salicylic Acid – 4%
White Soft Paraffin to 100%

Basic arithmetic dictates that we merely get 6% and 4% of 75g respectively.

Answer: Sulfur (4.5g) and Salicylic Acid (3g) – White Soft Paraffin 92.5g.

The next section in our seven-part series on pharmaceutical calculations deals withDosage Calculations.

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