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C₁V₁ = C₂V₂

Dilution calculator

C₁V₁ = C₂V₂ solved for the one value you leave empty, with the volume of stock to measure out and the solvent to add.

Initial solution (leave one field empty)

Short answer: dilute 25 mL of 2 M to 100 mL and the concentration becomes0.5 M. You add 75 mL of solvent, but the final volume is 100 mL — the two numbers differ and confusing them is the standard mistake.

Why the equation holds

Adding solvent changes the volume, not the number of moles. Since moles are concentration times volume, that product is fixed, and every dilution question is that one conservation statement with a different unknown.

Worked example

A bench needs 250 mL of 0.1 M HCl from a 1 M stock: V₁ = 0.1 × 250 ÷ 1 = 25 mL, made up to 250 mL with water. Half a litre of bench reagent from 25 mL of stock is the whole economy of a lab session explained by one equation.

Dilution questions

What does the equation say?

C₁V₁ = C₂V₂: the amount of solute does not change when you dilute, so the concentration times the volume is the same before and after. Leave exactly one of the four values empty and it is solved for.

Is the volume added the same as the final volume?

No, and this is where errors come from. Making 25 mL up to 100 mL adds 75 mL of solvent, but the final volume is 100 mL. The page reports both so "make up to the mark" and "add this much water" cannot be confused.

Do the units have to match?

The two volumes must use the same unit and the two concentrations must use the same unit; that is all. Any pair works — mL and mL, mol/L and mol/L — and the answer comes back in whatever unit you entered.

Does dilution change pH?

It moves it towards neutral: diluting a strong acid tenfold raises the pH by about 1 until the water’s own dissociation takes over near pH 7. The dilution equation gives the concentration, and the pH calculator turns that into a pH and says where the approximation stops holding.

Related tools

Molarity calculatorConcentration from moles and volume.Molar mass calculatorThe mass to weigh out.Mole calculatorMoles, mass and particles.