Calculator
Use C₁V₁ = C₂V₂. Keep both concentration values in the same unit and both volume values in the same unit.
Formula and assumptions
C₁V₁ = C₂V₂
For a simple dilution, the amount of solute is unchanged while solvent is added. Concentration and volume units must each be consistent across both sides of the equation.
Assumption: Solute amount is unchanged during a simple dilution.
Variables and units
Worked example
To prepare 400 mL at 0.50 from a 2.00 stock, V₁ = (0.50 × 400) / 2.00 = 100 mL.
Single and serial dilutions
To make 100 mL of 0.1 M solution from a 1 M stock, V₁ = 0.1 × 100 / 1 = 10 mL. Measure 10 mL of stock and add solvent up to 100 mL total, which means about 90 mL of solvent, not 100 mL.
| Step | Transfer | Dilution factor | Concentration from 1 M |
|---|---|---|---|
| 1 | 1 mL into 9 mL | 1 : 10 | 0.1 M |
| 2 | 1 mL into 9 mL | 1 : 100 | 0.01 M |
| 3 | 1 mL into 9 mL | 1 : 1,000 | 0.001 M |
| 4 | 1 mL into 9 mL | 1 : 10,000 | 0.0001 M |
Serial dilutions keep each pipetting volume practical when the overall factor is large; the total factor is the product of the individual steps.
Important limits
Concentration units and volume units must be internally consistent; reactions and non-ideal mixing are not modeled.
Reference and related tools
OpenStax: Molarity and dilution. Return to Chemistry Calculators for the other tools in this group.