Drug Calculations: free practice, theory and problems

1. Units and conversion

What is it about?

Almost every error in drug calculations comes from the wrong unit, not from difficult maths. You must move confidently between grams, milligrams and micrograms, between litres and millilitres, and know what a percentage means for a solution.

Concepts and formulas

• 1 g = 1000 mg, 1 mg = 1000 µg (micrograms). One step down: multiply by 1000. One step up: divide by 1000.
• 1 L = 1000 mL, 1 dL = 100 mL.
• Strength is often given as mg/mL: how many mg of active substance there is in each mL.
• Percent in a solution means grams per 100 mL: 5% glucose = 5 g glucose per 100 mL = 50 mg/mL.
• Per mille (‰) means grams per 1000 mL: 9‰ = 9 g per litre = 9 mg/mL.
• Amount = strength × volume. Volume = amount / strength.

How to solve the problems

1. Write down what you have (strength) and what you must give (dose).
2. Make the units equal before calculating (for example everything in mg).
3. Calculate, and check that the answer is reasonable: 40 tablets or 0.001 mL is almost always wrong.

Example

How many mg of glucose are there in 500 mL of glucose 5%?

1. 5% = 5 g per 100 mL.
2. 500 mL is 5 times 100 mL, so 25 g.
3. 25 g = 25,000 mg.

Common mistakes

• Mixing up mg and µg. A factor of 1000 can be life-threatening.
• Thinking 5% means 5 mg/mL. It means 50 mg/mL.
• Forgetting to check whether the answer is reasonable.

Practise units and conversion in the app →

2. Tablets, oral solutions and dose per kg

What is it about?

The most common calculation on a ward: the doctor has prescribed a dose, and you must work out how many tablets or how many mL of oral solution the patient should have. For children and for some drugs, the dose is calculated from body weight.

Concepts and formulas

• Number of tablets = prescribed dose / strength per tablet.
• Volume of oral solution (mL) = prescribed dose / strength (mg/mL).
• Dose per kg: daily dose = mg/kg/day × weight. If the daily dose is split into several doses, the single dose = daily dose / number of doses.
• Daily dose = single dose × number of doses per day.

How to solve the problems

1. Find the prescribed dose and the strength, in the same unit.
2. Divide the dose by the strength.
3. For weight-based dosing: work out the daily dose first, then divide by the number of doses.
4. Check that the answer is reasonable. Split tablets should be halves (use the score line), and large deviations from the usual dose must always be raised.

Example

A child weighing 18 kg is to have 30 mg/kg/day divided into 3 doses. Oral solution 50 mg/mL. How many mL per dose?

1. Daily dose: 30 · 18 = 540 mg.
2. Per dose: 540 / 3 = 180 mg.
3. Volume: 180 / 50 = 3.6 mL.

Common mistakes

• Using the daily dose as a single dose (three times too much).
• Using the strength in the wrong unit (g instead of mg).
• Flipping the fraction: strength/dose instead of dose/strength.

Practise tablets, oral solutions and dose per kg in the app →

3. Infusions and drip rate

What is it about?

Intravenous fluids and drugs are often given as an infusion over time. With an infusion pump you set mL per hour. Without a pump (gravity) you count drops per minute, and then you must know how many drops the giving set delivers per mL.

Concepts and formulas

• Infusion rate: mL/h = volume (mL) / time (hours).
• Drip rate: drops/min = volume (mL) · drop factor (drops/mL) / time (minutes).
• Standard giving set: 20 drops/mL. Micro-drip set: 60 drops/mL (then drops/min = mL/h).
• Time: hours = volume / (mL/h).

How to solve the problems

1. Convert the time to the right unit: hours for mL/h, minutes for drops/min.
2. Insert into the formula.
3. Drops are rounded to the nearest whole drop. Pumps can be set with decimals.

Example

1000 mL of saline is to run over 8 hours with a set of 20 drops/mL. What is the drip rate?

1. Time: 8 h = 480 min.
2. Drops/min = 1000 · 20 / 480 ≈ 41.7.
3. About 42 drops per minute. (With a pump: 1000 / 8 = 125 mL/h.)

Common mistakes

• Using hours where the formula needs minutes.
• Forgetting the drop factor.
• Calculating mL/h when the problem asks for drops/min, or the other way round.

Practise infusions and drip rate in the app →

4. Dilution and solutions

What is it about?

Some drugs must be diluted before they are given, and sometimes you must draw up a specific dose from an ampoule. The basic rule is that the amount of active substance is the same before and after dilution, just spread over more fluid.

Concepts and formulas

• Amount of active substance = concentration · volume.
• Dilution: $C_1 V_1 = C_2 V_2$. Concentration times volume before dilution equals concentration times volume after.
• Fluid to add = $V_2 - V_1$.
• From an ampoule: volume to draw up = dose / concentration in the ampoule.

How to solve the problems

1. Find which three of the four quantities in $C_1V_1 = C_2V_2$ you know.
2. Solve for the fourth.
3. If the problem asks how much to add, subtract the starting volume.

Example

You have 10 mL of a 50 mg/mL solution and must dilute it to 10 mg/mL. How much fluid must be added?

1. $V_2 = C_1V_1 / C_2 = 50 \cdot 10 / 10 = 50$ mL.
2. Add 50 − 10 = 40 mL.

Common mistakes

• Answering with the final volume when the problem asks how much to add.
• Mixing percent and mg/mL without converting (1% = 10 mg/mL).

Practise dilution and solutions in the app →

5. Insulin, units and mixed problems

What is it about?

Some drugs are dosed in international units (IU) instead of mg, for example insulin and heparin. The calculation is the same: dose divided by strength.

Concepts and formulas

• Insulin is almost always 100 IU/mL. 10 IU is then 0.1 mL.
• Volume = dose (IU) / strength (IU/mL).
• Heparin comes in several strengths, for example 5000 IU/mL. Always read the strength on the ampoule.
• IU cannot be converted to mg without more information, because it depends on the drug.
• Mixed problems: use the same method as before. Write down what you have, what you need, and check the units.

Example

The patient is to have 16 IU of insulin, 100 IU/mL. Volume = 16/100 = 0.16 mL.

Common mistakes

• Handwriting "U". It can be read as 0 or 4, so write "units" or "IU".
• Using an ordinary syringe for insulin. Use an insulin syringe or pen.

Practise insulin, units and mixed problems in the app →