Dilution Calculator (C₁V₁ = C₂V₂)

How much stock solution to take to reach a target concentration and volume.

Result

Stock volume to take (V₁)

100.00

Solvent to add

400.00

How it works

V₁ = C₂ × V₂ ÷ C₁

Diluting a solution adds solvent without adding solute: the amount of dissolved substance stays put while the volume grows, so the concentration falls. That conservation is the whole content of C₁V₁ = C₂V₂. Rearranged, V₁ = C₂ × V₂ ÷ C₁ tells you how much concentrated stock to take. To make 500 mL at 0.1 M from a 2 M stock: V₁ = 0.1 × 500 ÷ 2 = 25 mL of stock, topped up to 500 mL with solvent — so 475 mL of solvent added. Two practical rules. The units only need to be consistent, not identical: both concentrations in the same unit, both volumes in the same unit. And "top up to the final volume" is not the same as "add the difference" — for accurate work, place the stock in a volumetric flask and fill to the mark, since mixing can change the total volume slightly.

Advertisement

Frequently asked questions

How much solvent do I add?

The final volume minus the stock volume taken — shown as the second result.

Do the units have to match?

Concentrations must share a unit, and so must the volumes; the result is in the volume unit you used.

Can I dilute in several steps?

Yes, and for large factors you should. A 1:10,000 dilution is far more accurate as four successive 1:10 steps than as one huge step, because pipetting a tiny volume once carries a much larger relative error.

Advertisement

Related calculators