SolveKit

Dilution Calculator (C1V1 = C2V2)

Tell it what you have and what you need; it returns the volume of stock to pipette and how much solvent to add.

By Dr. Priya Nair, science writer and former university physics lecturer · Updated

Dilution Calculator

Enter any 3 known values — the others are solved as you type. Change units at any time.

Fill in the values you know.

How to use this calculator

The usual question is "how much stock do I pipette?" — enter the stock concentration, the target concentration and the final volume. The calculator also returns the volume of solvent to add. You can run it in other directions too: from a known aliquot and final volume it gives the final concentration, and from a stock volume and the solvent you added it reconstructs the concentration you ended up with.

Concentration units can differ between the two fields (for example stock in M and target in mM); they are converted automatically. Volumes accept µL, mL and L as well as US units for non-lab use.

The formula

C₁ × V₁ = C₂ × V₂
V_solvent = V₂ − V₁
C₁
stock concentration
V₁
stock volume
C₂
final concentration
V₂
final volume
V_solvent
solvent to add

Dilution changes volume but not the amount of solute. The moles taken from the stock, C₁V₁, end up in the final solution, C₂V₂. The same equation works for any concentration unit — molarity, mg/mL, percent — as long as both sides use the same one.

Worked example

You need 100 mL of 0.5 M NaCl and have a 2 M stock solution.

  1. V₁ = C₂V₂ / C₁ = 0.5 × 100 / 2 = 25 mL of stock.
  2. Solvent = V₂ − V₁ = 100 − 25 = 75 mL.

Measure 25 mL of the 2 M stock and bring it to 100 mL total with about 75 mL of water.

Assumptions and limits

  • Volumes are additive. For water-based solutions this is close enough; mixing ethanol and water, for instance, produces slight volume contraction, so bring to the final volume in a volumetric flask instead of adding a calculated solvent volume.
  • The target concentration is lower than the stock — you cannot dilute upward.

Frequently asked questions

Should I add stock to water or water to stock?

For acids, always add acid to water. In general, add the stock to part of the solvent, mix, then make up to the final volume.

How do I make a 1:10 dilution?

Take one part stock and add nine parts solvent, so V₁ = V₂/10. For 10 mL final volume, that is 1 mL stock plus 9 mL solvent.

Does C1V1 = C2V2 work for percent solutions?

Yes. Any concentration unit that is "amount per volume" works, provided C₁ and C₂ use the same unit.

Sources

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