Percentage strengths, ratio strengths and dilutions
Strengths come written four ways, and a question may swap between them halfway through. Learn one conversion each way, then the dilution formula, and these questions get routine.
Not affiliated with the General Pharmaceutical Council. This guide is for revision only. It is not clinical or legal advice, and its worked examples use invented numbers. Check a current source before you rely on any point.
Four ways to write a strength
- % w/v means grams in 100 mL. 2.5% w/v is 2.5 g in 100 mL.
- % w/w means grams in 100 g. It is used for creams and ointments.
- % v/v means mL in 100 mL. It is used when a liquid is mixed with a liquid.
- Ratio strength, such as 1 in 10,000, means 1 g in 10,000 mL (for a liquid).
The fastest route to anything else is mg/mL. A % w/v figure times 10 gives mg/mL: 2.5% w/v is 25 mg/mL. A ratio of 1 in x is 100 ÷ x per cent.
Two strengths from real product information
The SmPC for sodium chloride 0.9% intravenous infusion gives the composition as 9 g of sodium chloride per litre. That is 0.9% w/v: 0.9 × 10 = 9 g in 1,000 mL.
The SmPC for adrenaline 1 mg/10 mL pre-filled syringe is titled with the ratio 1:10,000. It states 0.1 mg of adrenaline in each mL and 1 mg in the 10 mL syringe. Check it with the rule: 1 in 10,000 is 100 ÷ 10,000 = 0.01%, and 0.01 × 10 = 0.1 mg/mL. The ratio, the percentage and the mg/mL figures all say the same thing.
Example 1: ratio to percentage to mg/mL
Drug F is supplied as a 1 in 5,000 solution. Express this as a % w/v and in mg/mL.
100 ÷ 5,000 = 0.02% w/v. Multiply by 10: 0.2 mg/mL. Check the other way: 1 g in 5,000 mL is 1,000 mg ÷ 5,000 = 0.2 mg/mL.
Example 2: how much drug is in a volume
How much Drug G is in 150 mL of a 2.5% w/v solution?
2.5% w/v is 2.5 g per 100 mL. In 150 mL: 2.5 × 150 ÷ 100 = 3.75 g.
Example 3: a simple dilution
The formula is C1 × V1 = C2 × V2. The amount of drug stays the same before and after, so the strength times the volume matches on both sides. Use the same units for both strengths.
You need 50 mL of a 0.1% w/v solution of Drug H from a 2% w/v stock. How much stock do you use?
V1 = 0.1 × 50 ÷ 2 = 2.5 mL of stock. Make it up to 50 mL, so 47.5 mL of diluent. Read the question for whether it says "add 47.5 mL" or "make up to 50 mL". Those are different instructions, and the first is only right if the volumes simply add.
Example 4: diluting a cream
You have 30 g of a 2% w/w cream. How much cream base do you add to make a 0.5% w/w cream? What is the final weight?
The amount of drug in 30 g of 2% w/w cream is 0.6 g. At 0.5% w/w, 0.6 g needs a final weight of 0.6 ÷ 0.005 = 120 g. Base to add = 120 − 30 = 90 g. The same answer comes from C1 × W1 = C2 × W2: 2 × 30 ÷ 0.5 = 120.
Example 5: a percentage of a weight
How much Drug J is in a 60 g tube of 1.5% w/w ointment?
1.5 × 60 ÷ 100 = 0.9 g.
Example 6: a volume-in-volume dilution
You are asked to make 500 mL of 70% v/v alcohol from 95% v/v stock. How much stock?
V1 = 70 × 500 ÷ 95 = 368.4 mL, so 368 mL of stock made up to 500 mL with water. Read whether the question says "make up to 500 mL" or "add", because they are different instructions.
Where marks go
- Mixing up % w/v (per 100 mL) with % w/w (per 100 g).
- Putting the wrong strength in the wrong place in C1V1 = C2V2. The stock is the stronger one, and you take a smaller volume of it.
- Forgetting that a ratio such as 1 in 10,000 is a very weak solution. 0.01% is a sensible answer, 10% is not.
See also the pharmacy calculations guide and the guide to doses by weight and body surface area.
Sources
- 0.9% Sodium Chloride Intravenous Infusion Solution, Summary of Product Characteristics (emc). https://www.medicines.org.uk/emc/product/13131/smpc. Accessed 22 October 2026.
- Adrenaline 1 mg/10 ml (1:10,000) solution for injection in pre-filled syringe, Summary of Product Characteristics (emc). https://www.medicines.org.uk/emc/product/2024/smpc. Accessed 22 October 2026.
Not affiliated with the General Pharmaceutical Council. Revision only, not clinical or legal advice. Worked examples use invented numbers and products. Every source above was read on 22 October 2026; check anything that matters against a current source. See our terms of use and privacy notice.