Common Registration Assessment, Part 1
Dilution calculations with C1V1 = C2V2
Three original dilution questions, each worked two ways so the answer can be checked.
Published 4 October 2026. Independent revision material, not GPhC questions, not for patient care.
A dilution changes the volume but not the amount of drug. That one idea is behind C1 × V1 = C2 × V2 and it lets you check the answer by common sense: more volume, lower concentration.
The question may ask for the stock volume, the final concentration or the diluent to add. Decide which before you start.
The method
- Identify the concentration and volume you know on each side.
- Substitute into C1 × V1 = C2 × V2.
- Solve for the missing term.
- Check: a larger final volume must mean a lower concentration.
- If asked for diluent, subtract stock volume from final volume.
Three practice questions
Work each one on paper first, then open the answer. All drugs and patients are fictional.
Question 1
20 mL of a 5% solution is diluted to 100 mL with water. What is the new percentage strength?
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Answer: 1%
Working: 5 × 20 = C2 × 100, so C2 = 100 ÷ 100 = 1%.
Question 2
You need 500 mL of a 0.1% solution from a 10% stock. What volume of stock do you use?
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Answer: 5 mL
Working: 10 × V1 = 0.1 × 500, so V1 = 50 ÷ 10 = 5 mL of stock, made up to 500 mL.
Question 3
2 mL of a 40 mg/mL solution is added to 38 mL of water. What is the final concentration?
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Answer: 2 mg/mL
Working: Final volume = 2 + 38 = 40 mL. Amount = 40 × 2 = 80 mg. 80 ÷ 40 = 2 mg/mL, a 20-fold dilution.
Wording is a common source of error
The Pharmaceutical Journal's dilution article says failing to understand dilution terminology is a frequent source of error, and gives the example that an instruction to dilute 10 mL to 100 mL gives a final volume of 100 mL. It also suggests drawing beakers with volumes and concentrations, and that is a good way to check any multi-step dilution before you calculate.
Where marks are lost
- Adding the diluent volume instead of the final volume to the stock volume.
- Mixing units across the two sides of the equation.
- Giving the stock volume when the question asks for the diluent.
Frequently asked questions
Is the volume I add the same as the final volume?
No. The final volume is stock plus diluent. For 5 mL made up to 50 mL, you add 45 mL.
Can I use the formula with percentages?
Yes, as long as both concentrations use the same unit.
Sources
- The Pharmaceutical Journal, medication maths: dilutions (20 March 2025)
- GPhC, Common Registration Assessment specification and permitted items for 2026
The questions above are original and use fictional drugs. PreRegExamPrep is not affiliated with or endorsed by the General Pharmaceutical Council.
Practise until the method is automatic
Try 15 free questions with worked answers. No sign-up required.
More calculation topics
- Dose by weight calculations for the GPhC assessment
- Volume to give: liquid medicine calculations
- Percentage strength calculations: w/v, w/w and ratios
- Infusion rate calculations in mL per hour
- Drip rate calculations: drops per minute
- Body surface area calculations
- Creatinine clearance (Cockcroft-Gault) calculations
- Moles and millimoles calculations
- Displacement volume calculations for reconstitution
See also the formula sheet, the eight sample questions and the approved calculator page.