PTCB Math Practice Guide
Every pharmacy calculation type tested on the PTCB exam — explained simply, with a worked example and practice problems. Each section links straight to the matching PharmaCalc Pro calculator so you can verify your work in seconds.
Weight-Based Dosage
Most adult and pediatric medication orders are written as mg per kg per day. The technician must verify the prescribed dose against patient weight and the available concentration.
Dose (mg) = Weight (kg) × Dose (mg/kg). Volume (mL) = Dose (mg) ÷ Concentration (mg/mL).Worked example
Order: amoxicillin 40 mg/kg/day divided BID for a 22-kg child. Suspension is 250 mg/5 mL. How many mL per dose?
- Daily dose: 22 kg × 40 mg/kg = 880 mg/day.
- Per dose (BID): 880 ÷ 2 = 440 mg/dose.
- Concentration: 250 mg / 5 mL = 50 mg/mL.
- Volume per dose: 440 mg ÷ 50 mg/mL = 8.8 mL.
Answer: 8.8 mL BID
Practice problems
- Cefdinir 14 mg/kg/day BID, child weighs 18 kg, 125 mg/5 mL — mL per dose?
- Vancomycin 15 mg/kg IV q12h, patient 85 kg, vial 1 g / 20 mL — mL per dose?
Days' Supply
Days' supply is the most-tested PTCB calculation. Insurance billing and refill rules depend on getting it right — especially for inhalers, insulin, and drops.
Days' Supply = Quantity dispensed ÷ Daily use.Worked example
Lisinopril 10 mg, 1 tab PO daily, dispensed #90. Days' supply?
- Daily use: 1 tab/day.
- 90 tabs ÷ 1 tab/day = 90 days.
Answer: 90 days
Practice problems
- Albuterol HFA 8.5 g (200 puffs), 2 puffs QID — days' supply?
- Latanoprost 2.5 mL bottle, 1 gtt each eye QHS (20 gtts/mL) — days' supply?
Alligation
Alligation is used in compounding to mix two strengths of the same drug to obtain a desired intermediate strength.
Tic-tac-toe: place high % top-left, low % bottom-left, desired % center. Subtract diagonally to get parts.Worked example
Compound 100 g of 5% hydrocortisone ointment from 2.5% and 10% stocks. How much of each?
- 10% − 5% = 5 parts of the 2.5% stock.
- 5% − 2.5% = 2.5 parts of the 10% stock.
- Total parts: 5 + 2.5 = 7.5 parts = 100 g, so 1 part = 13.33 g.
- 2.5% stock: 5 × 13.33 = 66.67 g. 10% stock: 2.5 × 13.33 = 33.33 g.
Answer: 66.67 g of 2.5% + 33.33 g of 10%
Practice problems
- Make 500 mL of 40% dextrose from 70% and 5% — how much of each?
- Make 60 g of 1% hydrocortisone from 2.5% and a base (0%) — how much of each?
IV Drip Rate
IV drip rate is dispensed in drops per minute (gtt/min). The drop factor is printed on the tubing (10, 15, 20, or 60 gtt/mL).
gtt/min = (Volume mL × Drop factor gtt/mL) ÷ Time min.Worked example
1000 mL NS over 8 hours with a 15 gtt/mL set. Rate in gtt/min?
- Time: 8 h × 60 min/h = 480 min.
- gtt/min = (1000 × 15) ÷ 480 = 15000 ÷ 480 = 31.25.
Answer: 31 gtt/min
Practice problems
- 500 mL D5W over 4 h with 20 gtt/mL tubing — gtt/min?
- 250 mL piggyback over 30 min with 60 gtt/mL microdrip — gtt/min?
Body Surface Area (BSA)
BSA dosing is used for oncology and many high-risk drugs because it tracks metabolic rate better than weight alone.
Mosteller: BSA (m²) = √((Height cm × Weight kg) ÷ 3600).Worked example
Patient is 170 cm and 75 kg. BSA?
- Numerator: 170 × 75 = 12750.
- Divide: 12750 ÷ 3600 = 3.5417.
- Square root: √3.5417 ≈ 1.88 m².
Answer: 1.88 m²
Practice problems
- Patient is 160 cm, 60 kg — BSA?
- Patient is 185 cm, 95 kg — BSA?
Creatinine Clearance (CrCl)
CrCl drives renal dose adjustments for vancomycin, DOACs, gabapentin, and many other drugs. Use the Cockcroft–Gault equation.
CrCl = ((140 − age) × weight kg) ÷ (72 × SCr mg/dL) × 0.85 if female.Worked example
70-year-old female, 60 kg, SCr 1.2 mg/dL. CrCl?
- Numerator: (140 − 70) × 60 = 70 × 60 = 4200.
- Denominator: 72 × 1.2 = 86.4.
- Pre-sex: 4200 ÷ 86.4 = 48.6.
- Female adjust: 48.6 × 0.85 ≈ 41.3 mL/min.
Answer: 41 mL/min
Practice problems
- 55-year-old male, 80 kg, SCr 1.0 — CrCl?
- 82-year-old female, 52 kg, SCr 1.4 — CrCl?
Morphine Milligram Equivalents (MME)
MME standardizes opioid dosing to gauge overdose risk. CDC flags 50 MME/day for caution and 90 MME/day as high-risk.
Daily MME = Σ (Dose mg/day × CDC conversion factor).Worked example
Patient takes oxycodone 10 mg q6h. Daily MME?
- Daily oxycodone: 10 mg × 4 doses = 40 mg/day.
- Conversion factor (oxycodone): 1.5.
- MME: 40 × 1.5 = 60 MME/day (above the 50 caution threshold).
Answer: 60 MME/day
Practice problems
- Hydrocodone 5 mg q4h ATC — daily MME?
- Fentanyl patch 50 mcg/h — daily MME?
Study tips for PTCB math
- Memorize the four drop factors (10, 15, 20, 60 gtt/mL) and the CDC opioid conversion factors.
- Always write units beside every number — most errors are unit errors, not arithmetic.
- Round only at the end. Carry 4 decimals through intermediate steps.
- For alligation, draw the tic-tac-toe grid every time until it's automatic.
- Verify your worked answers against the matching PharmaCalc Pro calculator.