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PTCB guide · updated 2026-09-29

Pharmacy math for the PTCB exam

Nine of the 22 knowledge areas in the 2026 PTCE outline are marked as calculation-based, led by area 4.1: formulas, ratios, conversions and Sig codes for days supply, quantity, dose, concentration and dilution. Most PTCE math comes down to a handful of conversions and three or four formulas, used carefully.

Where the math is on the exam

The outline marks these areas with an asterisk for calculation-based knowledge: 1.4 strengths and doses, 1.7 drug stability, 2.2 controlled substance prescriptions, 2.4 restricted drug programs, 3.3 issues needing pharmacist intervention, 3.5 prescription error types, 4.1 formulas and conversions, 4.2 administration equipment and supplies, and 4.3 lot numbers, expiration dates and NDC numbers.

So math is spread across the exam. A beyond-use date after reconstitution, a pseudoephedrine quantity limit, or a dose that does not match the patient weight can all be calculation questions.

Conversions to know cold

ConversionValue
1 kg2.2 lb
1 g1,000 mg
1 mg1,000 mcg
1 L1,000 mL
1 teaspoon (tsp)5 mL
1 tablespoon (tbsp)15 mL
1 fluid ounceabout 30 mL (29.57 mL)
Celsius from FahrenheitC = (F - 32) x 5/9

Days supply

Days supply = quantity dispensed / quantity used per day.

Example: metformin 500 mg, 1 tablet twice daily, quantity 60. The patient uses 2 tablets a day, so 60 / 2 = 30 days.

Example with insulin: a 10 mL vial of U-100 insulin holds 1,000 units. At 25 units twice daily the patient uses 50 units a day, so 1,000 / 50 = 20 days.

Weight-based doses

Convert pounds to kilograms first, then multiply by the dose per kilogram.

Example: a child weighs 22 lb and the dose is 5 mg/kg. 22 / 2.2 = 10 kg, and 10 x 5 = 50 mg per dose.

Concentrations and ratio strength

Percent weight in volume (w/v) means grams per 100 mL. Dextrose 5% contains 5 g per 100 mL, so a 1,000 mL bag contains 50 g.

Ratio strength works the same way. Epinephrine 1:1,000 means 1 g in 1,000 mL, which is 1 mg per mL.

Dilutions and alligation

For a simple dilution use C1 x V1 = C2 x V2. To make 200 mL of 10% from a 50% stock: 50 x V1 = 10 x 200, so V1 = 40 mL of stock plus 160 mL of diluent.

Alligation handles mixing two strengths. To make 300 mL of 10% from 20% and 5%: take the differences across the grid. 20% gets 10 - 5 = 5 parts, 5% gets 20 - 10 = 10 parts, 15 parts in all. Each part is 300 / 15 = 20 mL, so use 100 mL of 20% and 200 mL of 5%. Check: 20 g + 10 g = 30 g in 300 mL, which is 10%.

Flow rates, Sig codes and Roman numerals

  • mL per hour = total volume / hours. 1,000 mL over 8 hours = 125 mL/h.
  • Drops per minute = mL/h x drop factor / 60. At 125 mL/h with a 15 gtt/mL set: 125 x 15 / 60 = 31.25, about 31 gtt/min.
  • Common Sig codes: b.i.d. twice daily, t.i.d. three times daily, q.i.d. four times daily, h.s. at bedtime, a.c. before meals, p.c. after meals, p.r.n. as needed, p.o. by mouth.
  • Roman numerals: ss = 1/2, iv = 4, ix = 9, xl = 40, LX = 60. "Disp #LX" means dispense 60.

Habits that prevent wrong answers

  • Write the units at every step. Most wrong answers are unit errors, not arithmetic errors.
  • Estimate first. If a pediatric dose comes out larger than an adult dose, recheck.
  • Watch leading and trailing zeros: 0.5 mg, never .5 mg; 5 mg, never 5.0 mg.
  • Round only at the end, and only as the question directs.

Sample PTCB questions with answers

1. A prescription reads: Amoxicillin 250 mg/5 mL oral suspension. Sig: 500 mg PO t.i.d. Dispense: 150 mL. How many days will this prescription last?

  1. 5 days
  2. 10 days
  3. 15 days
  4. 3 days
Show answer

A. 5 days Each 500 mg dose requires 10 mL (500 mg ÷ 250 mg/5 mL = 10 mL per dose). t.i.d. = three times daily, so 10 mL × 3 = 30 mL/day. Days supply = 150 mL ÷ 30 mL/day = 5 days. Option B (10 days) would require only 15 mL per dose or b.i.d. dosing. Option C (15 days) would result from once-daily dosing. Option D (3 days) results from incorrectly using 50 mL per day.

2. A prescription is written with the sig: 'ii tabs PO b.i.d. pc.' Which of the following correctly translates this direction?

  1. Two tablets by mouth twice daily after meals
  2. Two tablets by mouth three times daily before meals
  3. One tablet by mouth twice daily with meals
  4. Two tablets by mouth twice daily before meals
Show answer

A. Two tablets by mouth twice daily after meals 'ii' is the Roman numeral for 2. 'PO' means by mouth (per os). 'b.i.d.' means twice daily (bis in die). 'pc' means after meals (post cibum). Option B confuses b.i.d. (twice daily) with t.i.d. (three times daily) and pc (after meals) with ac (before meals). Option C misreads Roman numeral 'ii' as 1. Option D correctly reads the dose and frequency but misidentifies 'pc' as before meals; 'ac' is the abbreviation for before meals.

3. A child weighs 44 lbs. The recommended dose of ibuprofen is 10 mg/kg per dose. The available suspension is 100 mg/5 mL. How many mL should be administered per dose?

  1. 5 mL
  2. 8 mL
  3. 10 mL
  4. 20 mL
Show answer

C. 10 mL Step 1 — convert weight: 44 lbs ÷ 2.2 lb/kg = 20 kg. Step 2 — calculate dose: 20 kg × 10 mg/kg = 200 mg. Step 3 — convert to volume: 200 mg × (5 mL ÷ 100 mg) = 10 mL. Option A (5 mL = 100 mg) delivers half the correct dose. Option B likely results from an arithmetic error; option D (20 mL) doubles the correct volume, which would deliver 400 mg.

4. A pharmacy technician needs to prepare 500 mL of a 35% isopropyl alcohol solution using a 70% isopropyl alcohol stock solution. How many mL of the stock solution are required?

  1. 125 mL
  2. 175 mL
  3. 250 mL
  4. 350 mL
Show answer

C. 250 mL Apply the dilution equation C₁V₁ = C₂V₂: (70%)(V₁) = (35%)(500 mL). V₁ = (35 × 500) ÷ 70 = 17,500 ÷ 70 = 250 mL. The remaining 250 mL is purified water (qs to 500 mL). Option A (125 mL) halves the correct answer. Option D (350 mL) results from inverting the concentration ratio. Option B has no basis in this formula.

5. A prescription reads 'Disp: XXIV caps.' How many capsules should be dispensed?

  1. 14
  2. 19
  3. 24
  4. 26
Show answer

C. 24 In Roman numerals, X = 10, so XX = 20. IV uses subtractive notation: I (1) placed before V (5) equals 5 − 1 = 4. Therefore XXIV = 20 + 4 = 24. Option A (14) results from reading XX as a single X (10). Option B (19) confuses IV (4) with IX (9), giving XX + IX = 29 — or misreads as XIV + V. Option D (26) adds rather than subtracts the I, treating IV as VI.

Frequently asked questions

Is there a calculator on the PTCB exam?

Yes, the testing software includes an on-screen calculator.

How many math questions are on the PTCE?

PTCB does not publish a count. Nine of the 22 knowledge areas are marked as partly or fully calculation-based, so expect math throughout the exam.

Try the free PTCB practice test

Questions tagged to the official outline, with an explanation for every answer. 15 free a day, no sign-up.

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Sources: PTCE Content Outline v1.4 (effective Jan 6, 2026) · PTCB: Certified Pharmacy Technician (CPhT). Independent study material. Not affiliated with or endorsed by PTCB.

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