Pharmacy Math Conversions
Updated
Conversions are the plumbing behind every other pharmacy calculation. Miss one and the whole problem tips over, so it pays to know the factors cold. This guide covers the metric system, household measures, temperature, and the Roman numerals prescribers still use. Lock them in on the PTCB math practice test after the examples.
Metric conversions
The metric system moves in steps of 1000. Each step up or down the ladder shifts the decimal three places.
- 1 kg = 1000 g
- 1 g = 1000 mg
- 1 mg = 1000 mcg
- 1 L = 1000 mL
Moving along the metric ladder
A pharmacist asks you to repackage 2.5 L of suspension. How many mL is that? And how many mg is 0.5 g?
- Step 1. Litres to millilitres: 1 L = 1000 mL, so 2.5 L × 1000 = 2500 mL.
- Step 2. Grams to milligrams: 1 g = 1000 mg, so 0.5 g × 1000 = 500 mg.
- Step 3. Both moves go to a smaller unit, so the number gets bigger.
Answer: 2500 mL, and 500 mg
The trap: Multiplying by 100 instead of 1000. Each metric step is three decimal places, not two.
Household to metric
Patients speak in teaspoons and pounds, so you convert to metric to calculate. These are the factors to memorize:
| Household | Metric |
|---|---|
| 1 teaspoonful (tsp) | 5 mL |
| 1 tablespoonful (tbsp) | 15 mL (3 tsp) |
| 1 fluid ounce (fl oz) | 30 mL (2 tbsp) |
| 1 pound (lb) | 454 g |
| 1 kilogram (kg) | 2.2 lb |
| 1 inch | 2.54 cm |
Weight and volume together
A patient weighs 176 lb and is prescribed 15 mL of a suspension per dose. Give the weight in kg and the dose in teaspoonfuls.
- Step 1. Weight: pounds to kilograms means dividing by 2.2, because 1 kg = 2.2 lb. 176 ÷ 2.2 = 80 kg.
- Step 2. Dose: 1 teaspoonful = 5 mL, so divide the volume by 5. 15 ÷ 5 = 3 teaspoonfuls.
Answer: 80 kg, and 3 teaspoonfuls per dose
The trap: Multiplying by 2.2 when going from pounds to kilograms. Pounds to kilograms divides; kilograms to pounds multiplies.
Temperature
Refrigerated storage and body temperature both come up, so keep the two-way formula ready.
°C = (°F - 32) × 5/9
°F = (°C × 9/5) + 32
Fahrenheit to Celsius
Convert normal body temperature, 98.6°F, to Celsius.
- Step 1. Subtract 32 first: 98.6 - 32 = 66.6.
- Step 2. Multiply by 5/9: 66.6 × 5 = 333, then 333 ÷ 9 = 37.
Answer: 37°C
The trap: Multiplying before subtracting. Always subtract 32 first, then multiply by 5/9.
Roman numerals
Prescribers still write quantities in lowercase Roman numerals. Read them left to right, adding as you go, but subtracting when a smaller numeral sits before a larger one.
| Symbol | Value |
|---|---|
| ss | one half |
| i | 1 |
| v | 5 |
| x | 10 |
| l | 50 |
| c | 100 |
| d | 500 |
| m | 1000 |
Reading a prescription quantity
A prescription reads Disp. #xxiv, Sig: tab i po qid. How many tablets are dispensed?
- Step 1. Read xxiv left to right: xx is 20, and iv is 4 (i before v means 5 - 1).
- Step 2. Add the parts: 20 + 4 = 24.
Answer: 24 tablets
The trap: Reading iv as 6 by adding instead of 4 by subtracting. A smaller numeral before a larger one is subtracted.
The most common mistake
The error that sinks the most points is decimal placement. A metric step is three places, not two, so 1 g is 1000 mg, not 100 mg. The same care applies to direction: converting to a smaller unit always makes the number bigger. If your answer shrank when it should have grown, you divided when you should have multiplied.
Try it
- Convert 500 mcg to milligrams.
- Convert 104°F to Celsius.
- Write the quantity 15 as a Roman numeral for a prescription.
Show answers
- 1 mg = 1000 mcg, so 500 ÷ 1000 = 0.5 mg.
- (104 - 32) × 5/9 = 72 × 5 ÷ 9 = 360 ÷ 9 = 40°C.
- 15 is xv (x is 10, v is 5, added together).
Frequently asked questions
What conversions do I need to know for the PTCB?
The metric ladder (kg, g, mg, mcg, L, mL), household to metric (tsp = 5 mL, tbsp = 15 mL, fl oz = 30 mL, lb = 454 g, kg = 2.2 lb, inch = 2.54 cm), the Fahrenheit to Celsius formula, and the Roman numerals used to write prescription quantities.
How do you convert pounds to kilograms?
Divide the weight in pounds by 2.2, because 1 kg = 2.2 lb. A 176 lb patient is 176 ÷ 2.2 = 80 kg. To go from kilograms back to pounds you multiply by 2.2 instead.
How many mL are in a teaspoon and a tablespoon?
In pharmacy calculations 1 teaspoonful is 5 mL and 1 tablespoonful is 15 mL, so a tablespoon is three teaspoons. One fluid ounce is 30 mL, which is two tablespoons.
What is the Fahrenheit to Celsius formula?
Celsius = (Fahrenheit - 32) × 5/9. Subtract 32 first, then multiply by 5/9. To reverse it, Fahrenheit = (Celsius × 9/5) + 32.
How are Roman numerals used on prescriptions?
Prescribers write quantities in lowercase Roman numerals: i is 1, v is 5, x is 10, l is 50, c is 100. A smaller numeral before a larger one is subtracted (iv is 4, ix is 9), and ss stands for one half. So Disp. #xxx means dispense 30.
Practise this
Conversions feed straight into IV flow rate and days supply problems, so clean unit handling here pays off everywhere. Drill them on the pharmacy math practice test, then return to the pharmacy math hub. Keep the pharmacy abbreviations reference handy for the sig shorthand.
PTCB Quiz Prep is an independent study resource, not affiliated with the Pharmacy Technician Certification Board. Conversion factors shown are the standard pharmacy conventions used for calculations.