Pharmacy technician (PTCE, ExCPT)
Dosage calculations: four calculators with the formulas
Enter an order in mg per kg, the weight and the strength of the product: the dose and the volume appear at once. The other three calculators are further down.
Dose by body weight
Dose
200.0 mg
- Weight in kg
- 20.0
- Volume to give
- 4.00 mL
Pounds are divided by 2.2, the factor exam questions use. Practice arithmetic only, not a dosing tool.
Dosage calculations on the pharmacy technician exams fall into four families. Dose by body weight multiplies an order in mg per kg by the patient's weight in kilograms, after converting pounds at 2.2 per kilogram, then turns the dose into a volume with the strength of the product. Dilution uses the relation C1 × V1 = C2 × V2: the stock strength times the stock volume equals the final strength times the final volume, which gives how much stock to measure and how much diluent to add. Alligation finds how many parts of a stronger and a weaker product to mix to reach a strength in between; the parts are the differences between the strengths, read crosswise. IV flow rates turn a volume and a time into mL per hour, for a pump, or into drops per minute, using the drop factor printed on the tubing set. Each family has a calculator on this page with a worked example, and the formulas are the same ones the exams expect you to set up by hand.
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Dose by body weight
Dose (mg) = mg/kg × weight (kg); volume (mL) = dose ÷ strength (mg/mL). Example: an order of 15 mg/kg for a 22 kg child, with a liquid of 40 mg/mL, gives 330 mg, or 8.25 mL. When the order is per day and divided into several doses, divide the daily dose by the number of doses before converting to mL.
Dilutions: C1 × V1 = C2 × V2
To make 200 mL of 70% alcohol from a 95% stock: V1 = 70 × 200 ÷ 95 = 147.4 mL of stock, made up to 200 mL with 52.6 mL of water. The final strength must be lower than the stock; if a question asks for a stronger product from a weaker one, the answer is that it cannot be done by dilution.
Dilution with C1 × V1 = C2 × V2
Stock to use
178.6 mL
- Diluent to add
- 321.4 mL
- Final volume
- 500 mL
V1 = C2 × V2 ÷ C1; the diluent makes up the rest of the volume.
Alligation
Write the higher strength top left, the lower one bottom left, the wanted strength in the middle. Subtract crosswise: wanted minus lower gives the parts of the higher product, higher minus wanted gives the parts of the lower one. Example: 240 g of a 5% ointment from 10% and 2%. Parts of 10%: 5 − 2 = 3; parts of 2%: 10 − 5 = 5; total 8 parts. So 90 g of the 10% and 150 g of the 2%.
Alligation: mix two strengths
Higher strength to use
90.0 g
- Lower strength to use
- 150.0 g
- Parts
- 3.00 : 5.00
Parts of the higher = wanted minus lower; parts of the lower = higher minus wanted.
IV flow rates
mL per hour = volume ÷ hours. Drops per minute = volume × drop factor ÷ minutes. Example: 1,000 mL over 8 hours runs at 125 mL per hour; with a 15 drops per mL set, that is 31.3 drops per minute, which in practice is rounded to a whole drop. With a microdrip set of 60 drops per mL, drops per minute equal mL per hour: 100 mL over 30 minutes is 200 mL per hour and 200 drops per minute.
IV flow rate
Flow rate
125.0 mL/h
- Drops per minute
- 31.3
- Volume per minute
- 2.08 mL
mL per hour = volume ÷ hours; drops per minute = volume × drop factor ÷ minutes.
Checking an answer
- Units. Write the unit beside every number; the units that cancel should leave the unit asked for.
- Size. Estimate before computing: a child's dose in mL is rarely more than a few teaspoons, an IV rate over 500 mL per hour is unusual outside a bolus.
- Rounding. Round once, at the end, to what can be measured.
The PTCE outline lists these calculations under order entry and processing, the ExCPT test plan under the dispensing process. Unit factors follow NIST Handbook 44. The pharmacy math page covers conversions and percent strength, the days supply page the most frequent calculation of all.
All examples are exam arithmetic, not dosing guidance: real doses are ordered by a prescriber and verified by a pharmacist.