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Dilution Calculator

M₁V₁ = M₂V₂: solve any one dilution value from the other three.

By CalcHub Editorial · Last reviewed

Quick answer

  • Formula: M₁ × V₁ = M₂ × V₂
  • Worked example — Stock molarity (M₁): 2.00000 mol/L (full example below).

Dilution Calculator

Leave at 0 if this is the value you are solving for — it is ignored.
Leave at 0 if this is the value you are solving for — it is ignored.
Leave at 0 if this is the value you are solving for — it is ignored.
Leave at 0 if this is the value you are solving for — it is ignored.
Worked example result
Stock molarity (M₁)2.00000 mol/L
Stock volume (V₁)0.50000 L
Final molarity (M₂)0.50000 mol/L
Final volume (V₂)2.00000 L

Diluting 0.5 L of a 2 M stock down to 0.5 M gives a final volume of 2 L — add about 1.5 L of solvent.

Diagram: how the Dilution Calculator works — you enter Solve for, Stock molarity (M₁), Stock volume (V₁), Final molarity (M₂), Final volume (V₂); it applies the formula M₁ × V₁ = M₂ × V₂; and the worked example gives Stock molarity (M₁): 2.00000 mol/L.
How the Dilution Calculator works — the inputs, the formula, and a worked example (Stock molarity (M₁): 2.00000 mol/L).

Diluting a solution adds solvent without changing the amount of solute, so the products of concentration and volume before and after are equal: M₁V₁ = M₂V₂.

Choose the value you want to find and enter the other three — leave the value you are solving for at 0, it is ignored. Use consistent volume units (both litres or both millilitres) and the result comes out in the same unit.

The formula

M₁ × V₁ = M₂ × V₂

Worked example

Diluting 0.5 L of a 2 M stock down to 0.5 M gives a final volume of 2 L — add about 1.5 L of solvent.

Worked example for the Dilution Calculator: with Solve for Final volume (V₂), Stock molarity (M₁) 2, Stock volume (V₁) 0.5, the result is Stock molarity (M₁): 2.00000 mol/L; Stock volume (V₁): 0.50000 L.
The worked example, with the example values entered and the results they give.

The example is pre-loaded in the result panel — press Calculate with your own numbers to replace it.

Frequently asked questions

Why is it M₁V₁ = M₂V₂?

M × V is the number of moles. Dilution adds no solute and removes none, so the moles before (M₁V₁) must equal the moles after (M₂V₂).

Can I mix litres and millilitres?

Only if both volumes use the same unit. The equation is unit-consistent as long as V₁ and V₂ match — the answer then comes out in that same unit.

Category: Science calculators

Sources & methodology

This calculator applies the formula shown on this page exactly as written, using the standard definitions for its inputs. Results are computed from the values you enter — no data is stored — and are rounded only for display.

Content last reviewed by CalcHub Editorial.

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