Learn Pharmacy calculations from scratch
Before this: Dosage calculations
1What pharmacy calculations cover
Pharmacists, pharmacy technicians and nurses often meet strengths that are not written as mg per tablet. A local anaesthetic is labelled “2%”, an old-style label reads “1:1000”, and an antibiotic arrives as a powder that you dissolve yourself.
This topic has three parts:
- Percentage and ratio strength: how much drug is in a solution.
- Reconstitution: dissolving a powder and working out the concentration you get.
- Alligation: mixing two strengths to make a third.
Every calculation comes back to the same question: how much drug is in how much liquid?
2Percentage and ratio strength
For a solid dissolved in a liquid, percentage strength is weight in volume (% w/v): grams of drug per 100 mL of solution.
1% w/v = 1 g per 100 mL = 10 mg per mL
So 2% lidocaine contains 2 g in 100 mL, which is 20 mg in every mL. To find the amount in a volume:
grams = % × mL / 100
Ratio strength 1:X means 1 g in X mL. So 1:1000 is 1 g in 1000 mL, which is 1 mg per mL. To turn a ratio into a percentage, divide 100 by X: 1:400 is 100/400 = 0.25%.
For ointments and creams, strength is weight in weight (% w/w): grams of drug per 100 g of product.
Self-check How many mg of lidocaine are in 10 mL of a 2% w/v solution?
- 0.2 mg
- 20 mg
- 200 mg
- 2000 mg
Answer: 200 mg. 2% is 2 g in 100 mL, so 20 mg per mL, and 10 mL contains 200 mg. 20 mg is only one mL. 0.2 mg comes from writing 0.2 g as if it were mg.
3Reconstitution
Some drugs are supplied as a dry powder in a vial. You add a liquid, the diluent (often sterile water), to dissolve it. This is reconstitution.
The powder itself takes up space once it is dissolved. This is the powder volume. The final volume is therefore larger than the diluent you added:
final volume = diluent + powder volume
concentration = drug in vial / final volume
Example: a vial holds 1000 mg. The label says to add 9.6 mL, and the powder adds 0.4 mL. The final volume is 10 mL, so the concentration is 1000/10 = 100 mg/mL. A dose of 500 mg is 5 mL.
Some labels list several diluent volumes, each with the strength it gives. Read the line that matches the diluent you used.
Self-check A vial with 500 mg of powder is reconstituted with 4.8 mL. The powder volume is 0.2 mL. What is the concentration?
- 0.01 mg/mL
- 100 mg/mL
- 104 mg/mL
- 2500 mg/mL
Answer: 100 mg/mL. Final volume 4.8 + 0.2 = 5 mL, so 500/5 = 100 mg/mL. Dividing by the diluent alone (500/4.8 = 104) forgets the powder volume.
4Alligation
Alligation finds how much of a higher strength H and a lower strength L to mix to get a target strength T in between. Water or a plain ointment base counts as 0%.
Write the parts crosswise: each strength gets the difference between the target and the other strength.
parts of H = T − L parts of L = H − T
Add the parts, then share the total amount in that ratio.
Example: make 100 mL of 3% from a 30% stock and water. Parts of 30%: 3 − 0 = 3. Parts of water: 30 − 3 = 27. Total 30 parts. Stock: 100 × 3/30 = 10 mL. Water: 100 × 27/30 = 90 mL.
5A worked example
Follow every step. Try to predict the next one before you open it. All values are made up for practice.
Worked exampleYou must prepare 1000 mL of 20% dextrose by mixing 50% and 10% dextrose. How many mL of each do you need?
1H = 50%, L = 10% and the target T = 20%. The target lies between H and L, so the mix is possible.
2parts of 50% = T − L = 20 − 10 = 10
parts of 10% = H − T = 50 − 20 = 30
Total: 40 parts.
350%: 1000 × 10/40 = 250 mL
10%: 1000 × 30/40 = 750 mL
4Dextrose from the 50%: 250 × 0.50 = 125 g. From the 10%: 750 × 0.10 = 75 g. Total 200 g in 1000 mL, which is 20 g per 100 mL: 20%.
Answer Mix 250 mL of 50% dextrose with 750 mL of 10% dextrose.
6Common mistakes
- Mixing up g and mg: 1% is 10 mg/mL, not 1 mg/mL.
- Reading 1:1000 as 1 mg in 1000 mL. It is 1 g in 1000 mL.
- Dividing by the diluent instead of the final volume after reconstitution.
- In alligation, giving each strength its own difference instead of crossing: the higher strength gets T − L.
- Forgetting that water or plain base is 0%.
Self-check You need 100 mL of 10% solution, made from a 40% stock and water. How much stock do you use?
- 10 mL
- 25 mL
- 40 mL
- 75 mL
Answer: 25 mL. Parts of 40%: 10 − 0 = 10. Parts of water: 40 − 10 = 30. Stock: 100 × 10/40 = 25 mL, with 75 mL of water. 75 mL comes from not crossing the parts.
7How exam questions look
- Easy: percentage and ratio strength. Find the mg or g in a volume, a percentage from grams and volume, or turn a ratio into a percentage.
- Medium: reconstitution and concentrations. Add the powder volume, find the mg/mL, and the volume to draw up for a dose. Some labels give several strengths in a table.
- Hard: alligation. Dilute a stock with water, mix two solutions, or add a weaker ointment or plain base to reach a target strength.
All values in these questions are made up for practice and are not clinical guidance. In real practice, always use the product information and local procedures.
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