Pharmaceutical Calculation

Introduction

I once half-jokingly told my colleague that calculation is one of the most important skills for pharmacists.

  • We often need to calculate how many medication supplies a patient needs over a period of time.

Nonetheless, there are many circumstances where more advanced pharmaceutical calculation may be needed.



Percentage and Conversion

The strength of many formulations is often expressed as a percentage, such as atropine 1% eye drop, benzoyl peroxide 5% gel, hydrocortisone 1% cream, permethrin 5% lotion, potassium chloride 10% injection, selenium sulphide 2.5% shampoo and more.

  • In other words, this is a universally accepted expression.

The word "percentage" expresses the number of units of something relative to 100 units.

  • 1% w/w = 1 g of a solid in 100 g of product
  • 1% w/v = 1 g of a solid in 100 ml of product, which is also equivalent to 10 mg/ml.
  • 1% v/v = 1 ml of a liquid in 100 ml of product
  • 1% v/w = 1 ml of a liquid in 100 g of product

When a pharmaceutical formula is expressed as a percentage without specifying the units of weight or measure:

  • Liquids (irrespective of density) are measured by volume, and solids by weight.
  • It is important to take note the units used in the expression above (g and ml, NOT mg and L).

NOTE: Both dextrose 5% and normal saline (sodium chloride 0.9%) are isotonic to our body.



Dilution of Liquid Formulations

What volume of ethanol 95% is needed to prepare a 1000 ml of ethanol 20% using ethanol 95% and distilled water?

Given that the total ethanol in the stock solution is equal to the total ethanol in the final solution

Concentration1 * Volume1 = Concentration2 * Volume2
95% * Volume of ethanol 95% needed = 20% * 1000 ml
Volume of ethanol 95% needed = 20% * 1000 ml / 95 = 210.5 ml

Distilled water should then be added to the 210.5 ml of ethanol 95% until the volume reaches 1000 ml.

NOTE: Although in theory, the volume of distilled water would be 789.5 ml (from 1000 ml - 210.5 ml), the final volume of a mixture of two liquids might be smaller than the sum of the individual volumes due to the displacement of molecules.



Extemporaneous Preparations

Based on the formula of isoniazid 10 mg/ml suspension,

  • Isoniazid 100 mg, 10 tablets
  • X-temp, qs to 100 ml
  • Expiry: 90 days at room temperature

Calculate the quantity of isoniazid 100 mg and diluent required for

  • Prescription: Syr Isoniazid 80 mg OD for 2/52

Total isoniazid required for 2 weeks = 80 mg * 14 = 1120 mg

Volume of isoniazid 10 mg/ml suspension
= Total dose / Concentration of syrup
= 1120 mg / 10 mg/ml
=112 ml

Minimum number of isoniazid 100 mg to be used
= 1120 mg / 100 mg
= 11.2 tablets (approximately 12 tablets, which will have 1200 mg)

Approximate amount of diluent required
= Total dose / Concentration of syrup
= 1200 mg / 10 mg/ml
= 120 ml (~extra by 8 ml)

NOTE: Depending on personal preference, some pharmacists prefer to prepare more extra volume of isoniazid suspension to compensate the wastage occurred when transferring or administering the suspension.



Summary

Pharmacy calculations are essential for pharmacists to accurate prepare and dispense medications.

  • Even small errors in calculations can have a significant impact on the medication that a patient receives.



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