Dilution Calculator
Solve C₁V₁ = C₂V₂ for any of the four variables.
Keep concentration and volume units consistent on both sides.
Dilution keeps the moles of solute constant, so C₁V₁ = C₂V₂. To make 250 mL of 0.10 M solution from 1.0 M stock, solve for V₁: (0.10 × 250) ÷ 1.0 = 25 mL of stock, then add solvent up to 250 mL total.
The dilution equation
Diluting a solution adds solvent without changing the amount of solute. The moles of solute before and after must be equal, and since moles = concentration × volume, the product of concentration and volume stays constant. Knowing any three of the four values fixes the fourth.
C is concentration, V is volume; subscript 1 = before, 2 = after
Worked example
How much 1.0 M stock do you need to make 250 mL of 0.10 M solution? Solve C₁V₁ = C₂V₂ for V₁.
- 1 Rearrange for the unknown. V₁ = C₂V₂ ÷ C₁ — divide both sides by the stock concentration C₁.
- 2 Substitute the values. V₁ = (0.10 M × 250 mL) ÷ 1.0 M = 25 ÷ 1.0.
- 3 Compute and interpret. V₁ = 25 mL of stock. Measure 25 mL, then add solvent up to 250 mL total.
Common dilution factors
Dilution factor = V₂ ÷ V₁ = C₁ ÷ C₂; the concentration drops by the same factor.
| Dilution | Factor | Example (from 1.0 M) |
|---|---|---|
| 1 in 2 | 2× | → 0.50 M |
| 1 in 5 | 5× | → 0.20 M |
| 1 in 10 | 10× | → 0.10 M |
| 1 in 100 | 100× | → 0.010 M |
| 1 in 1000 | 1000× | → 0.0010 M |
When it applies and where it slips
Units must be consistent. The equation is unit-agnostic, but the two concentrations must share a unit and the two volumes must share a unit. Mixing mL with L on opposite sides is the most common error.
Add solvent to reach the final volume. V₁ is how much stock to take, not how much solvent to add. The solvent you add is V₂ − V₁ (here 250 − 25 = 225 mL).
Assumes ideal mixing. Volumes are treated as additive and temperature constant. For most aqueous dilutions this holds; concentrated solutions and large temperature swings can introduce small volume changes.