Dosage calculations: practice problems with step-by-step solutions

1Why dosage calculations matter

A doctor prescribes a dose, for example 500 mg of a drug. The ward stocks that drug in a fixed strength, for example tablets of 250 mg or a liquid with 125 mg in 5 mL.

Your job is to turn the prescription into something you can actually give: a number of tablets or a volume of liquid.

Small slips here can harm a patient. A factor of 10 or 1000 is the most dangerous mistake. So the method is simple, and you check every answer.

Three numbers appear in almost every question:

• D, the dose that is desired (prescribed).
• H, the amount of drug you have in one tablet or in a certain volume.
• Q, the quantity that contains H: 1 tablet, or for example 5 mL.

2Units first

The ordered dose and the stock must be in the same unit before you calculate. These are the conversions you need most:

To go to a smaller unit, multiply by 1000. To go to a bigger unit, divide by 1000.

Example: 0.25 mg is 0.25 × 1000 = 250 mcg.

3Desired over have

Once the units match, one formula does the work:

For tablets, Q is 1 tablet. Example: 500 mg is ordered and the tablets contain 250 mg. Give (500/250) × 1 = 2 tablets.

For liquids, Q is the volume on the label. Example: 300 mg is ordered and the syrup has 250 mg in 5 mL. Give (300/250) × 5 = 6 mL.

Estimate before you calculate. 300 mg is a bit more than 250 mg, so you expect a bit more than 5 mL. 6 mL fits.

4Weight-based doses

Children and some drugs are dosed by body weight, for example 15 mg/kg/day: 15 mg for every kilogram the patient weighs, per day.

1. Make sure the weight is in kilograms. Divide pounds by 2.2.
2. Multiply the weight by the dose per kg. This gives the total dose (per day, if the order says per day).
3. If the daily dose is split, divide it by the number of doses.
4. If a liquid is given, use desired over have to turn the milligrams into millilitres.

Read the order carefully: “15 mg/kg” is one dose, but “15 mg/kg/day in 3 doses” has to be divided by 3.

5A worked example

Follow every step. Try to predict the next one before you open it.

6Common mistakes

• Mixing mg and mcg, or g and mg. This gives an answer 1000 times too big or too small.
• Using the weight in pounds as if it were kilograms.
• Forgetting to divide a daily dose into the separate doses.
• Turning desired over have upside down: it is D/H, not H/D.
• Rounding too early. Round only the final answer, as the question or the syringe requires.

7How exam questions look

• Easy: tablets and liquids. One unit conversion at most, then desired over have.
• Medium: weight-based doses. Weight × dose per kg, then divide by the number of doses.
• Hard: doses and concentrations together: a weight-based dose given as a volume of a liquid.

Always estimate first and check that the answer is reasonable. A dose of 30 tablets or 0.01 mL is almost certainly wrong.