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Dilution Calculator (C1V1 = C2V2)

Find how much stock and how much diluent to combine for a target concentration and volume, or solve C₁V₁ = C₂V₂ for any one of its four terms.

Formula

C1V1=C2V2C_1 V_1 = C_2 V_2
V1=C2V2C1V_1 = \dfrac{C_2 V_2}{C_1}
Vdiluent=V2−V1V_{\text{diluent}} = V_2 - V_1
C1C_1
concentration of the stock
V1V_1
volume of stock to take
C2C_2
concentration after dilution
V2V_2
final volume after dilution

How it works

Diluting a solution does not change the amount of solute in it, only the volume it is spread through. The amount taken from the stock (C₁ × V₁) therefore equals the amount in the diluted solution (C₂ × V₂).

The two concentrations can be in any unit (M, mg/mL, %, ×) as long as both use the same one. The ratio C₁ / C₂ is the dilution factor.

Worked example

Make 50 mL of 1× buffer from a 10× stock.

  1. V₁ = C₂ × V₂ / C₁ = 1 × 50 mL / 10 = 5 mL.
  2. Diluent = 50 mL − 5 mL = 45 mL.

Combine 5 mL of 10× stock with 45 mL of water. The dilution factor is 10.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • Both concentrations are expressed in the same unit.
  • Volumes are additive, which holds for dilute aqueous solutions but not for mixtures such as ethanol and water.

Common mistakes

  • Reading a 1:10 dilution as 1 part stock plus 10 parts diluent. By convention 1:10 means 1 part in a total of 10.
  • Mixing units, for example a stock in mg/mL and a target in µg/mL, without converting first.
  • Adding V₂ of diluent to V₁ of stock instead of making the mixture up to V₂.

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