Dilution calculator (C1V1 = C2V2)

The dilution formula is C1V1 = C2V2, so the volume of stock needed is the final concentration times the final volume, divided by the stock concentration. The formula returns the volume of stock, not the volume of diluent: to get the diluent, subtract that answer from the final volume.

When to use the dilution calculator

Use for any dilution where the drug quantity stays the same and only the volume changes. Both concentrations must be expressed in the same unit before the equation means anything.

The dilution formula

C1 × V1 = C2 × V2, so V1 = (C2 × V2) ÷ C1. V1 is the volume of stock solution required; the diluent added is V2 − V1.

Worked example

You need 100 mL of a 5% solution from a 50% stock. V1 = (5 × 100) ÷ 50 = 10 mL of stock, made up to 100 mL with 90 mL of diluent.

The mistake that costs marks

The equation returns the volume of stock, not the volume of diluent, and answering with the diluent volume is the commonest mistake on this format. The second trap is mixing units, such as a percentage against mg/mL, which invalidates the calculation entirely.

Study aid, not a clinical tool

This calculator exists so you can learn the method and check your working for an examination. It is not medical advice and not clinical decision support, and it must not be used to make a decision about a real patient. Verify any result against your local formulary, the product literature and a qualified pharmacist. Our medical disclaimer sets out the full position.

Calculators you will usually need alongside this

Most questions that reach for one of these reach for another a step later, so these are the three that most often pair with it.

• Alligation calculator — Alligation
• Ratio strength and percentage converter — Ratio strength
• IV drip rate calculator — IV drip rate

Keep going

Calculations are only half of what examinations test. The other half is knowing why a drug does what it does, which is what decides whether a number you calculated is even the right number to be calculating. Start with Best pharmacy calculators. The drug class pages cover the mechanism behind the number, or browse the rest of the free calculators and try the practice questions.