Days' supply (tablets)
Rx: 2 tablets by mouth three times daily (TID). Quantity dispensed: #90. What is the days' supply?
- Tablets per day = 2 × 3 = 6.
- Days' supply = 90 ÷ 6 = 15 days.
Answer: 15 days
PTCB Math Practice: Pharmacy Calculations
Pick a calculation type and work through unlimited new problems. Every answer is checked instantly and explained step by step, so you learn the method rather than memorising numbers.
What math is on the PTCB exam?
PTCB calculations sit mostly in the Medications and Order Entry and Processing domains: converting between units, working out doses and volumes, days' supply, percent and ratio strengths, dilutions and alligations, and IV flow rates. You get an on-screen calculator, so the skill being tested is setting the problem up correctly.
Pharmacy calculation types
- Days' supply (tablets) — Quantity ÷ (tablets per dose × doses per day).
- Days' supply (liquids) — Volume ÷ (mL per dose × doses per day).
- Days' supply (eye drops) — Bottle size × drops per mL ÷ drops used per day, rounded down.
- Dose by weight — Convert lb to kg, multiply by mg/kg/day, divide into doses.
- Liquid dose volume — Dose needed ÷ concentration gives the volume to measure.
- Percent strength — % w/v = grams per 100 mL.
- Dilutions (C1V1 = C2V2) — How much stock to dilute to a weaker strength.
- Alligation — Mixing a stronger and a weaker product to hit a target strength.
- IV flow rates — mL per hour and drops per minute.
- Conversions — lb/kg, mg/g/mcg, household measures, temperature.
On the live page every category generates unlimited new problems with instant checking and a step-by-step solution.
Worked PTCB math examples
Days' supply (liquids)
Rx: Take 1 tablespoonful (15 mL) by mouth twice daily (BID). Dispense 420 mL. What is the days' supply?
- mL per day = 15 mL × 2 = 30 mL.
- Days' supply = 420 mL ÷ 30 mL/day = 14 days.
Answer: 14 days
Days' supply (eye drops)
Rx: Instill 2 drops in both eyes (OU) three times daily (TID). Dispense one 2.5 mL bottle. Assume 20 drops per mL. What is the days' supply (round down)?
- Total drops = 2.5 mL × 20 drops/mL = 50 drops.
- Drops per day = 2 × 2 eyes × 3 = 12.
- 50 ÷ 12 = 4.17, rounded down to 4 days (you can't dispense a partial day).
Answer: 4 days
Dose by weight
A child weighs 33 lb. The dose is 40 mg/kg/day divided every 6 hours. How many mg per dose?
- Weight in kg = 33 lb ÷ 2.2 = 15 kg.
- Daily dose = 15 kg × 40 mg/kg/day = 600 mg/day.
- Every 6 hours = 4 doses a day, so 600 ÷ 4 = 150 mg per dose.
Answer: 150 mg per dose
Liquid dose volume
A suspension contains 250 mg/5 mL. The prescribed dose is 500 mg. How many mL should the patient take?
- Concentration = 250 mg ÷ 5 mL = 50 mg/mL.
- Volume = 500 mg ÷ 50 mg/mL = 10 mL.
Answer: 10 mL
Percent strength
How many grams of sodium chloride in normal saline (0.9%) are in 100 mL?
- 0.9% w/v means 0.9 g per 100 mL.
- 0.9 g × (100 mL ÷ 100 mL) = 0.9 g.
Answer: 0.9 g
Dilutions (C1V1 = C2V2)
How many mL of a 20% stock solution are needed to make 200 mL of a 1% solution?
- Use C1 × V1 = C2 × V2.
- 20% × V1 = 1% × 200 mL.
- V1 = (1 × 200) ÷ 20 = 10 mL of stock; add 190 mL of diluent to reach 200 mL.
Answer: 10 mL of stock (plus 190 mL diluent)
Alligation
How many grams of 10% cream must be mixed with plain base (0%) to make 500 g of 2.5% cream?
- Parts of 10% = target − weaker = 2.5 − 0 = 2.5.
- Parts of weaker = stronger − target = 10 − 2.5 = 7.5.
- Total parts = 10, so 10% needed = 500 g × 2.5/10 = 125 g.
Answer: 125 g of 10% (and 375 g of plain base (0%))
IV flow rates
Infuse 500 mL over 10 hours using tubing with a drop factor of 60 gtt/mL. What is the flow rate in drops per minute (nearest whole drop)?
- Minutes = 10 h × 60 = 600 min.
- gtt/min = (500 mL × 60 gtt/mL) ÷ 600 min = 50.
- Rounded to the nearest whole drop: 50 gtt/min. (The pump rate would be 50 mL/hr.)
Answer: 50 gtt/min
Conversions
A bottle holds 2 fl oz. How many mL is that (use the pharmacy convention)?
- Pharmacy calculations round 1 fl oz to 30 mL (it's 29.57 mL exactly).
- 2 × 30 = 60 mL.
Answer: 60 mL
Pharmacy math formula sheet
| Days' supply | quantity ÷ (units per dose × doses per day) | Round down to whole days. |
| Eye drops | mL × 20 gtt/mL ÷ drops per day | 20 drops per mL unless told otherwise. |
| Weight conversion | kg = lb ÷ 2.2 | Convert before using mg/kg doses. |
| Dose by weight | kg × mg/kg/day ÷ doses per day | q12h = 2 doses, q8h = 3, q6h = 4. |
| Liquid dose | mL = dose (mg) ÷ concentration (mg/mL) | Turn mg/5 mL into mg/mL first. |
| Percent w/v | % = grams per 100 mL | D5W = 5 g/100 mL; NS = 0.9 g/100 mL. |
| Ratio strength | 1:1,000 = 1 g per 1,000 mL = 1 mg/mL | Epinephrine 1:1,000 is 1 mg/mL. |
| Dilution | C1 × V1 = C2 × V2 | Diluent = final volume − stock volume. |
| Alligation | parts strong = target − weak; parts weak = strong − target | Amount = total × parts ÷ total parts. |
| IV drops per minute | (volume mL × drop factor gtt/mL) ÷ minutes | Round to the nearest whole drop. |
| IV mL per hour | volume mL ÷ hours | What you set on a pump. |
| Household measures | 1 tsp = 5 mL · 1 tbsp = 15 mL · 1 fl oz = 30 mL | Pharmacy convention for fl oz. |
| Metric | 1 g = 1,000 mg · 1 mg = 1,000 mcg · 1 L = 1,000 mL | Move the decimal three places. |
| Temperature | °F = °C × 9/5 + 32 · °C = (°F − 32) × 5/9 | Fridge 2–8°C = 36–46°F. |
PTCB math: frequently asked questions
What math is on the PTCB exam?
PTCB calculations sit mostly in the Medications and Order Entry and Processing domains: converting between units, working out doses and volumes, days' supply, percent and ratio strengths, dilutions and alligations, and IV flow rates. You get an on-screen calculator, so the skill being tested is setting the problem up correctly.
Can I use a calculator on the PTCB exam?
Yes. The exam provides an on-screen calculator. Practise with a basic calculator so the method, not the arithmetic, is what you focus on.
How do you calculate days' supply for eye drops?
Multiply the bottle size in mL by 20 drops per mL (unless told otherwise), divide by the drops used per day, and round down. A 5 mL bottle used one drop in both eyes twice daily lasts 100 ÷ 4 = 25 days.
What is alligation used for?
Alligation tells you how much of a stronger and a weaker product to mix to reach a strength in between — for example, mixing 20% and 5% creams to make a 10% cream.
Do I round up or down?
Round days' supply down (a patient can't use a partial day's dose as a full day). For drops per minute, round to the nearest whole drop. Doses follow the rounding the question states.
More PTCB practice
- Free PTCB practice test — 1,500+ questions with answers