Dilution calculator (C₁V₁ = C₂V₂)

The formula

$$C_1 V_1 = C_2 V_2$$

$C_1$ and $V_1$ are the concentration and volume of the stock you pipette; $C_2$ and $V_2$ are the concentration and total volume of the diluted solution.

Where it comes from

Dilution adds solvent, never solute. So the amount of solute you transfer from the stock is exactly the amount that ends up in the final solution:

$$n_{\text{stock}} = n_{\text{final}}$$

From the definition of concentration, $n = C \cdot V$. Substituting on both sides:

$$C_1 V_1 = C_2 V_2$$

Any one value follows by dividing through. For the stock volume you need:

$$V_1 = \frac{C_2 V_2}{C_1}$$

Worked example

To make 100 mL of 50 mM from a 1 M stock:

$$V_1 = \frac{0.050\ \text{M} \times 100\ \text{mL}}{1\ \text{M}} = 5\ \text{mL}$$

Add 5 mL of stock to 95 mL of solvent.

Watch out for

• $V_2$ is the total volume, not the volume of solvent you add. Solvent added is $V_2 - V_1$.
• The concentration units on each side must match, which the calculator handles for you.

Last checked November 11, 2026