Dilution Calculator (C1V1 = C2V2)

The Dilution Equation: C1V1 = C2V2

The dilution equation C1V1 = C2V2 is used to determine how to dilute a concentrated stock solution to a desired final concentration and volume.

C1 is the initial concentration, V1 is the volume of stock solution to use, C2 is the final desired concentration, and V2 is the final total volume. Solve for any one unknown given the other three.

To make the dilution: pipette V1 of stock solution into a vessel, then add solvent (V2 − V1) to reach the final volume V2.

Dilution formula: C₁V₁ = C₂V₂. The moles of solute are conserved when you add more solvent. To prepare 250 mL of 0.05 M HCl from a 1.0 M stock: V₁ = C₂V₂/C₁ = (0.05 × 250) / 1.0 = 12.5 mL of stock solution. Measure 12.5 mL of stock into a 250 mL volumetric flask and fill to the mark with distilled water.

Serial dilution: when very low concentrations are needed, multiple dilution steps are more accurate than one large dilution. A 10⁻⁶ M concentration from a 1 M stock requires a 10⁶-fold dilution. Instead: three sequential 1:100 dilutions each multiplying by 10⁻² gives 10⁻⁶ — far more precise than trying to measure 0.001 mL into 1000 mL.

Dilution factor = final volume / initial volume = V₂/V₁. A 1:10 dilution (1 part stock + 9 parts diluent = 10 parts total) has a dilution factor of 10 and reduces concentration to 1/10. A 1:100 dilution reduces to 1/100. In biology, dilution factor is often expressed as the reciprocal: a 1:100 dilution gives a 100-fold dilution.

Mixing two solutions at different concentrations (not adding pure solvent): C_final = (C₁V₁ + C₂V₂) / (V₁ + V₂). This generalizes C₁V₁ = C₂V₂ and applies when mixing two non-zero concentration solutions.

See also: Molarity Calculator · pH Calculator