Pharmacy technician (PTCE, ExCPT)
Pharmacy math for technician exams
Type an amount and choose two units: the converter gives the result with the factors used. Below, the four kinds of pharmacy arithmetic, each with a worked example.
Pharmacy unit converter
2.0000 tsp =
10.00 mL
- 1 tsp
- 5 mL
- 1 tbsp
- 15 mL
- 1 fl oz
- 30 mL
Household measures as federal labeling rules round them (21 CFR 101.9); 1 grain is taken as 64.79891 mg and 1 lb as 0.45359237 kg.
Pharmacy math on the technician exams rests on four skills: converting units, setting up a proportion, reading a strength written as a percent or a ratio, and applying them to a prescription. Conversions come first, because almost every calculation starts with one. The metric system is exact: 1 g is 1,000 mg and 1 mg is 1,000 mcg. Household measures are not, so the exams use the values that federal labeling rules set for them: a teaspoon is 5 mL, a tablespoon 15 mL, a fluid ounce 30 mL and a cup 240 mL. For weight, a kilogram is 2.2 pounds in most exam questions, while the exact factor is 0.45359237 kg per pound. A proportion turns one known ratio into the unknown one; percent strength is grams of drug in 100 mL or 100 g; ratio strength writes the same idea as 1 part in so many. The converter above handles the units; the rest of the page shows each skill on a short worked example.
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| Study target: 4 of 5 (80%), not the official passing score |
Practice questions written by Radif Partners from the public outline; not questions from the real exam. Progress stays in this browser.
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Conversions to know by heart
| Unit | Equals | Basis |
|---|---|---|
| 1 kg | 1,000 g | Metric, exact |
| 1 g | 1,000 mg | Metric, exact |
| 1 mg | 1,000 mcg | Metric, exact |
| 1 L | 1,000 mL | Metric, exact |
| 1 teaspoon | 5 mL | Labeling rule |
| 1 tablespoon | 15 mL | Labeling rule |
| 1 fluid ounce | 30 mL | Labeling rule |
| 1 cup | 240 mL | Labeling rule |
| 1 kg | 2.2 lb | Rounded factor |
| 1 grain | 64.80 mg | Exact; labels often round to 65 |
Three quick examples with the converter: 1.5 tablespoons is 23 mL; 5 grains is 324.0 mg; 0.25 mg is 250 mcg. To go from a larger unit to a smaller one, multiply; from smaller to larger, divide.
Ratio and proportion
Most pharmacy problems are a proportion: a known pair of quantities, and a second pair with one unknown. Write both with the same units in the same places, then cross-multiply. Example: an oral suspension has 250 mg in 5 mL, and the order is 400 mg. Set 250 mg / 5 mL = 400 mg / x mL; x = 400 × 5 ÷ 250 = 8 mL. Checking the size helps: 400 mg is a bit more than 250 mg, so the volume must be a bit more than 5 mL.
Dose by body weight
When an order is in mg per kg, convert the weight to kilograms first. Example: 5 mg/kg for a child of 66 lb, with a liquid of 25 mg/mL. The child weighs 66 ÷ 2.2 = 30 kg, so the dose is 150 mg, which is 6.0 mL of the liquid. The dosage calculations page has a calculator for this.
Percent strength and ratio strength
| Written as | Means | Example |
|---|---|---|
| % w/v | g of drug in 100 mL | 0.9% sodium chloride: 0.9 g in 100 mL, so 9 g per liter |
| % w/w | g of drug in 100 g | 1% hydrocortisone cream: 1 g in 100 g, so 0.3 g in a 30 g tube |
| % v/v | mL in 100 mL | 70% isopropyl alcohol: 70 mL in 100 mL |
| Ratio 1:x | 1 g in x mL (or 1 g in x g) | 1:1,000 is 1 g in 1,000 mL, so 1 mg per mL and 0.1% |
To convert a ratio strength to a percent, divide 100 by the second number: 1:1,000 is 100 ÷ 1,000 = 0.1%. To go the other way, divide 100 by the percent: 0.1% is 1:1,000.
Where the rest of the math lives
Days supply, the most frequent calculation in a pharmacy, has its own page with four calculators: tablets, liquids, insulin and eye drops. Dilutions, alligation and IV flow rates are on the dosage calculations page. The PTCE outline places calculations in order entry and processing; the ExCPT test plan in the dispensing process.
The examples are exam arithmetic. Real doses are set by the prescriber and checked by the pharmacist.