Dilution Formula Calculator: C1V1 = C2V2 for Molarity

This calculator solves the dilution equation C1V1 = C2V2 for the volume of stock solution you need. Enter the stock concentration, the target concentration and the final volume you want; you get the volume of stock to measure, the volume of solvent to add and the dilution factor.

Formula

C₁ × V₁ = C₂ × V₂, so V₁ = C₂ × V₂ ÷ C₁.

• C₁: concentration of the stock solution
• V₁: volume of stock to take
• C₂, V₂: concentration and volume of the diluted solution
• Diluent volume ≈ V₂ − V₁; dilution factor = C₁ ÷ C₂
• Both concentrations must be in the same unit (M, mM or µM); V₁ comes out in the unit of V₂

Worked Example

You have a 2 M stock and need 250 mL of a 0.1 M solution.

1. V₁ = 0.1 × 250 ÷ 2 = 12.50 mL of stock
2. Diluent: 250 − 12.5 = 237.50 mL
3. Dilution factor: 2 ÷ 0.1 = 20.0
4. Check: 2 × 12.5 = 25 and 0.1 × 250 = 25, so C₁V₁ = C₂V₂.

Assumptions

• The amount of solute does not change on dilution; only solvent is added.
• Volumes are additive, which is close for dilute water solutions; for concentrated stocks, make up to the mark in a volumetric flask instead of adding the calculated diluent.
• The target concentration is below the stock. If it is above, no dilution can reach it and the calculator shows “Cannot compute”.

How to read the result

V₁ is what you pipette from the stock; then bring the solution to the final volume V₂. A dilution factor of 20 means one part stock in twenty parts total. For a dilution described by volumes, use the dilution factor calculator; for repeated steps, the serial dilution calculator.

Limits and common mistakes

• Mixing units: a stock in M and a target in mM gives an answer 1000 times off. Convert both to the same unit first.
• Adding V₂ of solvent to V₁ of stock gives too large a volume; the final total must be V₂.

Frequently Asked Questions

How much 2 M stock do I need for 250 mL of 0.1 M?

12.5 mL of stock, made up to 250 mL (237.5 mL of solvent if the volumes add).

What does C1V1 = C2V2 mean?

The moles of solute taken from the stock (C1 × V1) equal the moles in the diluted solution (C2 × V2).

Why does it say Cannot compute?

The target concentration is higher than the stock. Dilution can only lower a concentration.

Can I use mM or µM?

Yes, as long as C1 and C2 are in the same unit.

in c1 | Stock concentration (C1) | mol/L | 2 | 0
in c2 | Target concentration (C2) | mol/L | 0.1 | 0
in v2 | Final volume (V2) | mL | 250 | 0
out v1 | Volume of stock needed (V1) | mL | c2 * v2 / c1 | 2
out vd | Volume of diluent to add | mL | v2 - v1 | 2
out df | Dilution factor | - | c1 / c2 | 1