Dilution Calculator

Solve C1V1 = C2V2 for stock concentration, stock volume, final concentration, or final volume.

At a glance

Computes
C1V1 = C2V2 for any unknown, plus dilution factors and 1:N ratios both ways.
You supply
Three of the four terms, or a ratio, with a shared unit per pair.
Use when
You are diluting a stock solution and one of the four terms is unknown.
Assumes
Volumes are additive and the solute amount is conserved through the dilution.
Mode
Solve for

Result

Enter your values

C1V1 = C2V2 mode infers the one missing value; factor mode returns the dilution factor.

Calculation summary
ItemValue
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C1 * V1 = C2 * V2 ; DF = V_final / V_initial = C_initial / C_final How?

How this is calculated

Dilution keeps the amount of solute constant while solvent is added. C1V1 = C2V2 mode converts concentrations and volumes to canonical units, solves the one missing value algebraically, then converts the displayed answer back to the selected unit.

A dilution factor is how many times more concentrated the stock is than the final solution: DF = V_final / V_initial = C_initial / C_final. The v/v percent is 100 / DF, the fraction of the final volume that is stock. Factor mode reads a factor from two volumes, two concentrations, a 1:N ratio, or a known factor, and can derive the final concentration or the diluent to add.

Formula: C1 * V1 = C2 * V2 ; DF = V_final / V_initial = C_initial / C_final

Alcohol and ABV dilution

Alcohol by volume is a percent concentration, so the ideal arithmetic follows C1V1 = C2V2. Select percent by volume and enter strengths directly. Taking 750 mL of a 40.0 percent spirit to 20.0 percent gives a final volume of 1,500 mL, so the arithmetic diluent is 750 mL and the dilution factor is 2.

To make 500 mL of 70.0 percent ethanol from 95.0 percent stock, the stock volume is 368.421 mL and the arithmetic diluent is 131.579 mL. The calculation is unit-independent as long as both concentrations use the same percent basis.

Why measured strength can finish slightly high

Ethanol and water contract on mixing, so their measured volumes are not perfectly additive. The calculator gives the ideal arithmetic target. Work requiring proof to a tenth of a percent should blend by mass or use an official alcoholometric gauging table. This limit is stated beside the result because silently treating volume as additive would overstate accuracy.

Dilution ratio and dilution factor

A 1:N ratio has two established readings. One part in N total gives a factor of N. One part stock to N parts diluent gives N + 1 total parts. The factor mode reports both readings so a written 1:10 instruction cannot silently become either 10 percent or 9.09 percent.

Sources

  1. OpenStax Chemistry 2e, Molarity. OpenStax. Retrieved .
  2. IUPAC Gold Book, amount concentration. IUPAC. Retrieved .

Method last reviewed