Dilution Calculator (C1V1 = C2V2)
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/5/2026
The volume of stock solution to draw for a dilution is calculated with V1 = (C2 × V2) ÷ C1. To dilute a 1 mol/L solution down to 0.1 mol/L while preparing 500 mL, you need to draw 50 mL of stock solution and top up with 450 mL of solvent.
Explanation
Diluting a solution means adding solvent to a more concentrated stock solution to get a less concentrated one, without changing the amount of dissolved substance. This principle is captured by the conservation law C1 × V1 = C2 × V2, where C1 and V1 are the concentration and volume of stock solution drawn, and C2 and V2 are the target final concentration and volume. This calculator solves this equation to find V1 (the volume of stock solution to draw), then works out the volume of solvent to add (V2 − V1) to reach the final volume. Both concentrations must be expressed in the same unit for the result to be correct — this calculator assumes that's the case. To calculate a molar concentration directly from an amount of substance and a volume, see our molar concentration calculator.
Example: diluting 1 mol/L down to 0.1 mol/L, final volume 500 mL
Inputs
Stock concentration: 1 mol/L. Final concentration: 0.1 mol/L. Final volume: 500 mL.
Calculation
V1 = (C2 × V2) ÷ C1 = (0.1 × 500) ÷ 1 = 50 mL. Volume of solvent to add = 500 − 50 = 450 mL.
Result
Draw 50 mL of stock solution and top up with 450 mL of solvent to get 500 mL at 0.1 mol/L.
Frequently asked questions
Why doesn't the amount of substance change during a dilution?
Because diluting means adding only solvent (often water), without adding or removing any solute. The amount of dissolved substance therefore stays the same before and after (n1 = n2), which, replacing n with C × V, directly gives the law C1V1 = C2V2 used by this calculator.
In what order should the liquids be poured in practice?
For safety, in chemistry you generally pour the concentrated product into the solvent (water, for example), not the other way around, particularly for concentrated acids whose dilution can be exothermic. This calculator only gives the volumes to use, not the handling protocol — follow the safety guidelines specific to the product you're using.
What happens if I enter a final concentration higher than the initial one?
The calculation would give a stock-solution volume larger than the target final volume, and therefore a negative solvent volume — a result with no physical meaning. A dilution can only lower concentration, never raise it: to concentrate a solution, you need to evaporate solvent or add solute, two operations this calculator doesn't cover.