Do the units need to match?

The two concentrations must share one unit and the two volumes must share another, but the concentration and volume units can differ from each other. As long as C1 and C2 use the same unit and V1 and V2 use the same unit, the equation holds.

How much solvent do I actually add?

The calculator gives the stock volume V1 and the final volume V2. The solvent to add is the difference, V2 − V1 — for example, adding 400 mL of water to 100 mL of stock to reach 500 mL.

Why can’t the denominator be zero?

Solving for a variable requires dividing by one of the knowns. If that divisor — such as C1 when solving for V1 — is zero, the division is undefined and the calculator cannot return a value.

Does C1V1 = C2V2 work for any kind of solution?

It applies to any dilution where the amount of solute is conserved and only solvent is added. It does not account for chemical reactions, volume changes on mixing, or saturation limits.

Dilution Calculator

C1 (mol/L)

V1 (mL)

C2 (mol/L)

V2 — Solved Value25.0000

The dilution calculator solves the classic C1V1 = C2V2 relationship that governs how concentration and volume trade off when you dilute a stock solution. Tell it which of the four quantities is unknown and supply the other three, and it rearranges the equation to find the missing value. It is a staple of lab work for preparing working solutions from concentrated stock.

Formula

C1 · V1 = C2 · V2

C1: Concentration of the stock (starting) solution
V1: Volume of stock solution needed
C2: Concentration of the final (diluted) solution
V2: Total volume of the final solution

How it works

Choose which variable to solve for: the stock concentration C1, the stock volume V1, the final concentration C2, or the final volume V2.
Enter the three known values. The calculator rearranges C1V1 = C2V2 to isolate your unknown — for example V1 = C2·V2 ÷ C1.
It returns the solved quantity in the same units you used, since the equation is unit-consistent as long as concentrations match and volumes match.

Worked example

You need 500 mL of a 2 M solution from a 10 M stock. How much stock is required?

Solve for V1: V1 = (C2 × V2) ÷ C1.
Substitute: V1 = (2 × 500) ÷ 10 = 1000 ÷ 10.
Compute: V1 = 100 mL of stock.

Take 100 mL of the 10 M stock and dilute to a final volume of 500 mL.

Frequently asked questions

Do the units need to match?: The two concentrations must share one unit and the two volumes must share another, but the concentration and volume units can differ from each other. As long as C1 and C2 use the same unit and V1 and V2 use the same unit, the equation holds.
How much solvent do I actually add?: The calculator gives the stock volume V1 and the final volume V2. The solvent to add is the difference, V2 − V1 — for example, adding 400 mL of water to 100 mL of stock to reach 500 mL.
Why can’t the denominator be zero?: Solving for a variable requires dividing by one of the knowns. If that divisor — such as C1 when solving for V1 — is zero, the division is undefined and the calculator cannot return a value.
Does C1V1 = C2V2 work for any kind of solution?: It applies to any dilution where the amount of solute is conserved and only solvent is added. It does not account for chemical reactions, volume changes on mixing, or saturation limits.

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