The dilution equation is C₁V₁ = C₂V₂: the amount of solute stays the same when you add solvent. To make 100 mL of a 1 M solution from a 10 M stock, take V₁ = (1 × 100) ÷ 10 = 10 mL of stock and add 90 mL of solvent, a 10-fold dilution.
How does the C1V1 = C2V2 formula work?
When you dilute a solution by adding solvent, the amount of dissolved substance (moles or mass) does not change, only the volume does. Amount = concentration × volume, so before dilution it is C₁ × V₁ and after dilution it is C₂ × V₂. Setting them equal gives the dilution equation. You can solve it for any one of the four unknowns as long as the other three are known, and concentration and volume can be in any units provided the two sides match.
Worked examples
| Task | Calculation | Result |
|---|---|---|
| Make 500 mL of 0.2 M from 2 M stock | V₁ = 0.2 × 500 ÷ 2 | 50 mL stock + 450 mL solvent |
| Dilute 25 mL of 12% solution to 3% | V₂ = 12 × 25 ÷ 3 | 100 mL final, add 75 mL |
| Final concentration: 5 mL of 4 M in 20 mL | C₂ = 4 × 5 ÷ 20 | 1 M |
Dilution factor and ratios
The dilution factor is C₁ ÷ C₂ (or V₂ ÷ V₁). A 10-fold dilution means 1 part stock to 9 parts solvent, written as 1:9, and the tool displays both forms. Don’t mix them up: “1:10 dilution” in some labs means 1 part stock plus 9 parts solvent (total 10), in others 1 part to 10 parts solvent (total 11). Always state which you mean in a protocol.
Practical tips
- Add stock to the solvent, and for acids always add acid to water, never the other way round.
- Use volumetric flasks for accuracy. Volumes of mixed liquids are not always exactly additive, especially for ethanol and water.
- For very large dilution factors, do a serial dilution in steps (for example 1:10 three times for 1:1000) because it is more accurate than pipetting a tiny volume.
- Cleaning and disinfecting products often give dilution as a percentage or a ratio. Convert to C₁V₁ = C₂V₂ for any container size.
The formula assumes no reaction between solute and solvent and no loss of solute. For percent calculations in other contexts, use the percentage calculator, or for general averages the average calculator.
How to use this calculator
- Choose which of the four variables you want to solve for.
- Enter the other three values (the unknown field is ignored).
- Use the same units for both concentrations and both volumes.
- Read the answer, the dilution factor and the amount of solvent to add.
Key figures at a glance
| Equation | C₁V₁ = C₂V₂ |
|---|---|
| Dilution factor | C₁ ÷ C₂ = V₂ ÷ V₁ |
| Solvent to add | V₂ − V₁ |
| Units | Must match on both sides |
Frequently asked questions
Use C₁V₁ = C₂V₂ and solve for the unknown. For V₁, V₁ = C₂V₂ ÷ C₁.
Usually 1 part stock plus 9 parts solvent (10 total), though some use 1 part plus 10 parts. State which.
Yes, as long as both concentrations are in the same unit.
Not always. Some mixtures, like ethanol and water, shrink slightly. For precise work, fill to the mark in a volumetric flask.
Dilute stepwise, for instance 1:10 several times, each time using the previous dilution as the stock.