C1V1 = C2V2 Dilution Calculator

Find the stock aliquot for a new solution, or solve for either concentration or the final volume. Enter three known values and choose the unknown.

Prepare from stock

Make a new working solution from a stock. Enter any three values and choose the unknown.

C₁ × V₁ = C₂ × V₂
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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.

How C₁V₁ = C₂V₂ works

Dilution lowers concentration by increasing solution volume while keeping the amount of solute unchanged. For molarity, the amount in moles is n = C × V when volume is in liters. Equating the amount in the stock aliquot with the amount in the final solution gives:

C₁V₁ = C₂V₂

  • C₁: stock concentration.
  • V₁: stock volume transferred into the new solution.
  • C₂: target concentration.
  • V₂: target total volume after dilution.

Rearrange to find the unknown: V₁ = C₂V₂/C₁, C₁ = C₂V₂/V₁, C₂ = C₁V₁/V₂, or V₂ = C₁V₁/C₂. Use compatible concentration units and volume units; the calculator normalizes them before solving.

Example: 100 mL of 1 M solution from 10 M stock

  1. Set C₁ = 10 M, C₂ = 1 M, and V₂ = 100 mL; choose V₁ as the unknown.
  2. Calculate V₁ = (1 M × 100 mL) / 10 M = 10 mL.
  3. Measure a 10 mL stock aliquot and prepare the solution with the appropriate diluent, following the chemical’s handling procedure.
  4. Bring the solution to a final volume of 100 mL and mix thoroughly. Do not add 100 mL of diluent to the stock.

The estimated diluent volume is 100 − 10 = 90 mL if volumes are additive. The solute balance itself uses the measured final volume and does not require volumes to be additive.

Using volume percentages

For % v/v, C × V / 100 represents the equivalent volume of the liquid component, not moles. Use the same component and % v/v basis on both sides. For example, preparing 250 mL of 0.2% v/v from 2% v/v stock requires 25 mL of stock brought to 250 mL. Do not substitute a mass percentage into this volume-based calculation.

This workflow assumes no reaction, evaporation, or other loss of solute and a diluent containing none of that solute. A target above the stock concentration cannot be achieved by dilution.