Mix Two Solutions Calculator

Find the final concentration when you combine two known volumes containing the same solute. The calculation weights each concentration by its solution volume.

Mix two solutions

Combine known volumes of two solutions containing the same solute and calculate the final concentration.

Cf = (C₁V₁ + C₂V₂) / (V₁ + V₂)
Try an example

Concentration basis: Use molarity (M, mM, µM, nM, pM) or % v/v throughout a calculation. % v/v is the volume of a liquid component per 100 volume units of final solution; it is not % w/v or % w/w. These tools do not convert between concentration categories or percentage bases. Solute must be conserved. Calculated added volumes and mixture concentrations assume additive solution volumes; measure the final volume for precise preparation.

Concentration is weighted by volume

When two solutions contain the same solute, their solute amounts add. If their volumes also add and no solute is lost or reacts, the final concentration follows:

M₁V₁ + M₂V₂ = Mf(V₁ + V₂)

  • M₁ and M₂: concentrations of solutions 1 and 2, labeled C₁ and C₂ in the calculator.
  • V₁ and V₂: volumes of solutions 1 and 2.
  • Mf: final concentration of the mixed solution.
  • Vtotal: final volume, assumed to equal V₁ + V₂.

Divide the total solute amount by the total solution volume: Mf = (M₁V₁ + M₂V₂)/(V₁ + V₂). A simple arithmetic average works only when the two volumes are equal.

Practical mixing examples

Mix 250 µL of 100 mM solution with 750 µL of 20 mM solution of the same solute. The final concentration is (100 × 250 + 20 × 750)/(250 + 750) = 40 mM in 1,000 µL. It is closer to 20 mM because that solution contributes more volume.

For equal volumes, 1 mL of 1 M NaCl plus 1 mL of 3 M NaCl gives an estimated 2 mL at 2 M. Both volumes must be positive; either input concentration may be zero to represent a solute-free diluent.

Laboratory safety and non-additive volumes

Mixing can release heat and change volume. Ethanol and water, for example, can warm and contract on mixing, as demonstrated by Harvard’s ethanol–water experiment. Follow the chemicals’ safety instructions and the laboratory’s mixing procedure; allow the mixture to reach the measurement temperature before checking its volume.

This calculator always uses V₁ + V₂ as the final volume. If contraction or expansion is appreciable, the displayed concentration is an approximation. For molarity, use the conserved total moles divided by the measured final volume in liters for an accurate result. This tool does not model reactions, precipitation, evaporation, or heat release.

Keep the concentration basis consistent

For molarity, each M·V term represents moles when V is in liters. For % v/v, each concentration-times-volume term divided by 100 represents the equivalent volume of the same liquid component. The % v/v estimate still assumes additive solution volumes; do not combine % v/v with molarity, % w/v, or % w/w. No molecular-weight or density conversion is performed.