Pharmacy Math Formulas for the PTCB
Updated
Pharmacy calculations are the most learnable questions on the whole PTCE, because the formulas never change. Master the fifteen below and you can answer almost every calculation the exam throws at you. Every formula on this page carries a worked example drawn from the kind of numbers you see on test day, so you can check your setup against a correct answer rather than a rule in the abstract.
Calculations live in the exam's Order Entry & Processing domain, which is 22.5% of the 2026 PTCE, so this is high-yield ground. When you are ready to test yourself, work through the PTCB math practice test and the deeper dive on how to calculate days supply. For the full plan, this sheet is one stop on our PTCB study guide.
Download 30 math practice problems (PDF)How to use this cheat sheet
The PTCE gives you an on-screen calculator, so nobody loses marks on the arithmetic: they lose them on the setup. Two habits fix that. First, write out what the question asks for and label every number with its unit (mg, mL, kg, gtt), then cancel units until only the target unit remains. Second, learn the three big traps built into these problems: mixing pounds with kilograms, inverting a ratio or proportion, and reporting the final volume when the question asked for the diluent to add. If your answer looks impossible (a patient dosed at 387 kg, or a bottle that lasts 300 days), you almost certainly inverted a step. Recognising the trap is worth more than memorising the formula, because the exam writes distractor answers precisely for the technician who skips a conversion.
The formula reference table
This is the asset to save. Each row pairs a formula with a worked example so you can see the numbers move. Read across: name, formula, example.
| Calculation | Formula | Worked example |
|---|---|---|
| Days supply | days supply = total quantity ÷ amount used per day | #60 tablets, 1 tablet twice daily: 60 ÷ 2 = 30 days. |
| Ratio and proportion | a/b = c/d, then cross multiply and solve for the unknown | 250 mg/5 mL = 400 mg/x: x = (400 × 5) ÷ 250 = 8 mL. |
| Percent strength (w/v) | grams of drug per 100 mL of solution | 0.9% sodium chloride in 1,000 mL: 0.9 g × (1,000 ÷ 100) = 9 g. |
| Percent strength (w/w) | grams of drug per 100 g of product | 2.5% cream in a 45 g tube: 0.025 × 45 = 1.125 g. |
| Percent strength (v/v) | millilitres of active liquid per 100 mL of solution | 70% alcohol in 480 mL: 0.70 × 480 = 336 mL. |
| Ratio strength | 1:x (w/v) means 1 g of drug in x mL of solution | 1:200 solution: 1,000 mg ÷ 200 mL = 5 mg/mL, so 15 mL holds 75 mg. |
| Alligation | parts of the high strength = desired - low; parts of the low strength = high - desired | 5% from 10% and 2%, total 120 g: high part = 5 - 2 = 3, low part = 10 - 5 = 5, total 8 parts, so 120 × (3 ÷ 8) = 45 g of the 10%. |
| Dilution | C1 × V1 = C2 × V2 | Make 250 mL of 2% from a 10% stock: (2 × 250) ÷ 10 = 50 mL of stock, then q.s. to 250 mL. |
| Weight-based dose | dose = dose per kg × weight in kg (convert lb to kg by dividing by 2.2) | 15 mg/kg/day for 44 lb: 44 ÷ 2.2 = 20 kg, then 20 × 15 = 300 mg/day. |
| IV flow rate | flow rate (mL/hr) = total volume (mL) ÷ time (hr) | 1,000 mL over 8 hr: 1,000 ÷ 8 = 125 mL/hr. |
| IV drip rate | drip rate (gtt/min) = (volume in mL × drop factor in gtt/mL) ÷ time in minutes | 1,000 mL over 12 hr at 15 gtt/mL: (1,000 × 15) ÷ 720 = 21 gtt/min (rounded). |
| Drops back to mL/hr | mL/hr = (gtt/min ÷ drop factor) × 60 | 30 gtt/min at 10 gtt/mL: (30 ÷ 10) × 60 = 180 mL/hr. |
| Milliequivalents (mEq) | mEq = (mg of drug × valence) ÷ molecular weight | 9,000 mg sodium chloride (MW 58.5, valence 1): 9,000 ÷ 58.5 ≈ 154 mEq. |
| Selling price (markup) | selling price = cost + (cost × markup rate) | $48 cost at 25% markup: 48 + (48 × 0.25) = $60. |
| Gross profit margin | margin % = (selling price - cost) ÷ selling price × 100 | $65 price, $39 cost: (65 - 39) ÷ 65 = 40%. |
Worked examples in full
Four formulas trip up more candidates than the rest. Here is each one solved step by step, with the distractor answer the exam plants for the technician who rushes.
Alligation: mixing two strengths
Compound 120 g of a 5% ointment from a 10% ointment and a 2% ointment. How many grams of the 10% are required?
- Step 1. Set up the alligation grid: 10% (high), 2% (low), 5% (desired).
- Step 2. Parts of the 10% = desired - low = 5 - 2 = 3. Parts of the 2% = high - desired = 10 - 5 = 5. Total = 8 parts.
- Step 3. Grams of 10% = 120 g × (3 ÷ 8) = 45 g. The remaining 75 g is the 2% ointment.
Answer: 45 g of the 10% ointment
The trap: Swapping the parts. The 3 parts belong to the strength nearer the desired value, so 75 g is the 2%, not the 10%.
Dilution: how much water to add
How many millilitres of sterile water must be ADDED to 120 mL of a 25% solution to reduce it to 10%?
- Step 1. Find the final volume with C1 × V1 = C2 × V2: 25 × 120 = 10 × V2, so V2 = 3,000 ÷ 10 = 300 mL.
- Step 2. The question asks for water added, not the final volume.
- Step 3. Subtract the starting volume: 300 mL - 120 mL = 180 mL.
Answer: 180 mL of water added
The trap: Reporting 300 mL, the final volume. C1V1 = C2V2 gives the total; the diluent added is that total minus what you started with.
IV drip rate with a drop factor
One litre of D5W is to infuse over 12 hours through a set calibrated at 15 gtt/mL. What is the rate in drops per minute?
- Step 1. Convert the units: 1 L = 1,000 mL, and 12 hr × 60 = 720 minutes.
- Step 2. Apply gtt/min = (volume in mL × drop factor) ÷ time in minutes: (1,000 × 15) ÷ 720.
- Step 3. 15,000 ÷ 720 = 20.83, which rounds to 21 gtt/min.
Answer: 21 gtt/min
The trap: Dividing by 12 hours instead of 720 minutes. Drip rate is per minute, so the time must be in minutes.
Weight-based dose into a volume
Order: vancomycin 20 mg/kg IV for a 187 lb patient. The solution is 50 mg/mL. How many millilitres are drawn up?
- Step 1. Convert weight to kilograms: 187 ÷ 2.2 = 85 kg.
- Step 2. Calculate the dose: 20 mg/kg × 85 kg = 1,700 mg.
- Step 3. Divide by the concentration: 1,700 mg ÷ 50 mg/mL = 34 mL.
Answer: 34 mL
The trap: Using pounds instead of kilograms gives 37.4 mL. Always convert to kilograms before applying a mg/kg dose.
Frequently asked questions
What math is on the PTCB exam?
Calculations sit in the Order Entry and Processing domain, 22.5% of the 2026 PTCE. Expect unit conversions, ratio and proportion, percent and ratio strength, alligation, dilution, days supply, weight-based dosing, milliequivalents, and IV flow rates. A calculator is provided on screen, so the marks are won on setup, not arithmetic.
What is the difference between w/v, w/w, and v/v?
Percent weight in volume (w/v) is grams of drug per 100 mL of solution, used for a solid dissolved in a liquid. Percent weight in weight (w/w) is grams per 100 g, used for creams and ointments. Percent volume in volume (v/v) is millilitres per 100 mL, used for a liquid mixed into a liquid such as alcohol solutions.
How do you convert pounds to kilograms for dosing?
Divide the weight in pounds by 2.2, because 1 kg = 2.2 lb. A 44 lb child is 20 kg. Skipping this step is the most common weight-based dosing error, because a dose in mg/kg must use kilograms, never pounds.
Do you round days supply up or down?
Round down to a whole day. A partial day is not a full day of therapy, so a result of 14.28 days is dispensed and billed as 14 days.
Keep studying
Formulas stick once you drill them under time pressure. Run the pharmacy math practice test and the order entry and processing quiz, then study the dedicated guide on calculating days supply. Keep the measurement conversions chart beside this one, since almost every calculation begins with a conversion, and follow the full 2026 PTCB study guide.
Official sources checked
PTCB Quiz Prep is an independent study resource, not affiliated with the Pharmacy Technician Certification Board. Formulas are standard pharmacy calculations; the 2.2 lb per kg and 20 drops per mL figures are the conventions used for exam calculations. See our editorial standards.