Pharmacy Calculations and Compounding
Setup is the skill
Calculation items are scored on the final number, so what is really tested is the setup: canceling units, choosing the right denominator, and rounding only at the end. Writing units beside every number tells you immediately when a ratio is inverted.
Concepts you must own
- Dimensional analysis and ratio/proportion for doses, concentrations, and dilutions; pound-to-kilogram conversion (÷ 2.2); 1 g = 1000 mg = 1,000,000 mcg.
- Percent concentrations: %w/v is grams per 100 mL, %w/w is grams per 100 g, %v/v is mL per 100 mL. Ratio strengths convert directly: 1:1000 = 1 g per 1000 mL = 0.1%.
- IV flow: mL/hr from total volume and hours; drops/min = (volume in mL × drop factor) ÷ time in minutes.
- Body-size dosing: mg/kg/day versus mg/kg/dose, ideal body weight, adjusted body weight, body surface area via Mosteller √(height cm × weight kg ÷ 3600), and pediatric maximum caps.
- Compounding math: alligation, the reducing/increasing formula for ointments, displacement volume for reconstitution, and the aliquot method for potent powders.
- Renal function: Cockcroft-Gault creatinine clearance = [(140 − age) × weight] ÷ (72 × SCr), multiplied by 0.85 for females.
Traps
An order for 30 mg/kg/day divided every 8 hours is not 30 mg/kg every 8 hours. Drop factors differ by set (10, 15, 20, or 60 gtt/mL). A ratio strength misread as a percentage produces a tenfold error. Always confirm whether the requested answer is per dose or per day, and whether the calculated dose exceeds a maximum.
Worked example
Infuse 1 L over 8 hours with a 15 gtt/mL set. Drops/min = (1000 mL × 15 gtt/mL) ÷ 480 min = 31.25, rounded to 31 gtt/min. The same order expressed as mL/hr is 125 mL/hr. Both are correct; the stem decides which one is asked.