Pharmacy Math Formulas for the PTCB Exam

Updated November 2026 · Facts checked against the sources listed at the end

PTCB's 2026 content outline lists formulas, calculations, ratios, proportions, conversions and Roman numerals under Order Entry and Processing, and marks calculation-based knowledge in several other areas too. These are the formulas you need, each with a worked example. When you have read one, practice it: our math drills generate a new problem every time.

Conversions to memorize

Temperature: °F = (°C × 9/5) + 32 and °C = (°F − 32) × 5/9. Example: 2°C = 35.6°F and 8°C = 46.4°F.

Days supply

Days supply = quantity dispensed ÷ (units per dose × doses per day)

Example: #90 tablets, sig 1 tab po tid. Tablets per day = 1 × 3 = 3. Days supply = 90 ÷ 3 = 30 days.

Liquids work the same way in mL: 150 mL, sig 5 mL po tid → 15 mL per day → 150 ÷ 15 = 10 days. If the result has a fraction, round down: the patient runs out on the last partial day.

Dose volume from a concentration

Volume = dose ÷ concentration

Example: amoxicillin 125 mg/5 mL, dose 250 mg. Concentration = 125 ÷ 5 = 25 mg/mL. Volume = 250 ÷ 25 = 10 mL.

Tablets per dose

Tablets = dose ÷ tablet strength. Example: 75 mg ordered, 25 mg tablets → 75 ÷ 25 = 3 tablets.

Weight-based dosing (mg/kg)

Dose = weight in kg × mg/kg. Convert pounds first: kg = lb ÷ 2.2.

Example: a 44 lb child, 10 mg/kg/day divided every 12 hours. Weight = 44 ÷ 2.2 = 20 kg. Daily dose = 20 × 10 = 200 mg. Every 12 hours means 2 doses, so 100 mg per dose.

Percent strength (w/v)

X% w/v = X grams per 100 mL. Grams in a volume = % × mL ÷ 100.

Example: 500 mL of 5% dextrose = 5 × 500 ÷ 100 = 25 g of dextrose. 1,000 mL of 0.9% sodium chloride = 9 g of sodium chloride.

Ratio strength

1:X (w/v) = 1 g in X mL. Example: 1:1,000 = 1 g in 1,000 mL = 1,000 mg in 1,000 mL = 1 mg/mL. 1:10,000 = 0.1 mg/mL.

Dilutions: C1 × V1 = C2 × V2

Example: how much 70% stock do you need to make 500 mL of 10%? V1 = (10 × 500) ÷ 70 = 71.4 mL of stock, plus 428.6 mL of diluent.

Alligation

Use it to mix a higher and a lower strength into one in between. Parts of the higher strength = desired − lower; parts of the lower strength = higher − desired.

Example: make 300 mL of 20% from 50% and 5%. Parts of 50% = 20 − 5 = 15. Parts of 5% = 50 − 20 = 30. Total parts = 45. 50%: 300 × 15 ÷ 45 = 100 mL. 5%: 300 × 30 ÷ 45 = 200 mL. Check: 50 g + 10 g = 60 g in 300 mL = 20%.

IV flow rate

mL/hr = total volume ÷ hours. Example: 1,000 mL over 8 hours = 125 mL/hr.

gtt/min = (volume in mL × drop factor) ÷ time in minutes. Example: 1,000 mL over 8 hours with a 15 gtt/mL set = (1,000 × 15) ÷ 480 = 31.25 → 31 gtt/min.

Roman numerals

I = 1, V = 5, X = 10, L = 50, C = 100. A smaller numeral before a larger one is subtracted. Examples: XIV = 14, XLV = 45, XC = 90. “Disp #XXX” means dispense 30.