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Dilution Calculator (C1V1 = C2V2)

Work out how much stock solution and water to mix for the strength you need, or the strength and volume you end up with, using C1V1 = C2V2.

Rules last checked 10 November 2026Every step shown

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Any unit (%, mol/L, mg/mL), as long as both strengths use the same one.

Stock to use

10 mL

Water or solvent to add
90 mL
Dilution
1 in 10 (10×)

Take 10 mL of the stock and add 90 mL of water or solvent to make 100 mL at a strength of 1, a 1 in 10 dilution.

How it's worked out

  1. The ruleC1 × V1 = C2 × V2the amount of substance stays the same
  2. Stock volume1 × 100 ÷ 1010 mL
  3. Solvent to add100 − 1090 mL
  • Make the solution up to the final volume rather than adding the exact solvent figure when accuracy matters: some liquids shrink a little when mixed.
  • When diluting a strong acid, add the acid to the water, never the water to the acid.

How it is worked out

To find the stock volume, the calculator multiplies the strength you want by the final volume and divides by the stock strength: V1 = C2 × V2 ÷ C1. The water to add is the final volume minus the stock volume.

Mixing it in practice

For lab work, measure the stock into a volumetric flask and fill to the mark, rather than adding a measured amount of water: some liquids take up slightly less space once mixed. With strong acids, always add the acid to the water.

Questions people ask

How do I make 100 mL of a 1% solution from a 10% stock?

Take 10 mL of the 10% stock and add 90 mL of water, for 100 mL in all. That's a 1 in 10 dilution.

What does C1V1 = C2V2 mean?

The amount of the dissolved substance doesn't change when you add water. Strength times volume before (C1 × V1) equals strength times volume after (C2 × V2), so you can solve for any one of the four.

Does it matter which unit I use for strength?

No, as long as both strengths use the same one: percent, mol/L, mg/mL or anything else. The volumes must share a unit too.

What is a 1 in 10 dilution?

One part of stock in ten parts of finished solution, so one part stock to nine parts water. It makes the solution a tenth as strong.

Formula and rules last checked 10 November 2026Written and tested by the CalculatorDex teamReport a problem