Pharmacy Compounding Calculations: PTCE Math Guide
Master the math behind compounding including percentage strength, weight-in-weight, ratio strength, and powder volume calculations for the PTCE exam.
Compounding Math Fundamentals
Compounding calculations require precision. A miscalculation can produce a preparation that is too strong, too weak, or potentially harmful. The PTCE includes compounding-related math in the order entry and processing domain. Let us work through the key calculation types.
Percentage Strength
Percentage strength describes the concentration of a preparation:
- % w/v - Grams of drug per 100 mL of preparation. A 2% w/v solution contains 2 g per 100 mL.
- % w/w - Grams of drug per 100 g of preparation. A 5% w/w ointment contains 5 g of drug per 100 g of ointment.
- % v/v - Milliliters of drug per 100 mL of preparation.
Example: Percentage Strength
How many grams of hydrocortisone are needed to prepare 60 g of a 2.5% w/w cream? Answer: 60 g x 0.025 = 1.5 g of hydrocortisone.
Ratio Strength
Ratio strength expresses concentration as a ratio (e.g., 1:1000 means 1 g per 1000 mL for solutions or 1 g per 1000 g for solids). To convert ratio strength to percentage: 1:1000 = 1/1000 = 0.001 = 0.1%.
Powder Volume Calculations
When reconstituting a dry powder, the powder itself takes up volume (the powder volume). The formula is:
Powder Volume = Final Volume - Diluent Volume
Example: A vial contains 1 g of cefazolin. Adding 2.5 mL of diluent produces a final volume of 3 mL. Powder volume = 3 mL - 2.5 mL = 0.5 mL. The concentration is 1 g / 3 mL = 333 mg/mL.
Enlarging and Reducing Formulas
When a master formula needs to be scaled up or down, multiply or divide each ingredient by the same factor. Example: A formula makes 100 capsules. You need 30 capsules. Multiply each ingredient quantity by 30/100 = 0.3.
Least Weighable Quantity
Every balance has a minimum weighable quantity based on its sensitivity. If the amount needed is below this, use the aliquot method: weigh a larger amount mixed with an inert diluent, then measure out the proportion containing the desired drug amount.
Practice compounding math with PTCB calculation drills to build speed and confidence.
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