The dilution formula
This formula states that the amount of solute is the same before and after you add solvent:
C1 × V1 = C2 × V2
- C1 – concentration of the starting (stock) solution
- V1 – volume of the starting solution used
- C2 – concentration after dilution
- V2 – final volume after dilution (stock plus solvent)
Concentration multiplied by volume gives the amount of solute, whether that is moles (molarity × liters) or grams (g/L × liters). Adding solvent increases the volume and lowers the concentration, but the product stays constant. When the concentrations are molarities the dilution equation is often written M1V1 = M2V2; see the M1V1 = M2V2 calculator for molarity-only problems. The formula is covered in every general chemistry text, for example OpenStax Chemistry 2e, section 3.3.
How to calculate concentration after dilution
Rearrange the equation for C2:
C2 = C1 × V1 ÷ V2
Example 1. 100. mL of 2.0 M HCl is diluted to 500. mL. C2 = 2.0 M × 100 mL ÷ 500 mL = 0.40 M. This example comes from the LibreTexts chapter on solution dilution and is the default problem in the calculator above.
Example 2. 0.2 L of a 50 g/L sucrose solution is brought to 2 L. C2 = 50 g/L × 0.2 L ÷ 2 L = 5 g/L (Rice University, Making Dilutions).
Example 3. 250 mL of a 65% solution is mixed with 700 mL of water, for 950 mL in total. C2 = 65% × 250 ÷ 950 ≈ 17%. Notice that V2 is the total, 950 mL, not the 700 mL of water.
Rearranging C1V1 = C2V2 for other unknowns
| You know | You want | Formula |
|---|---|---|
| C2, V2, C1 | Volume of stock | V1 = C2 × V2 ÷ C1 |
| C1, V1, C2 | Final volume | V2 = C1 × V1 ÷ C2 |
| C2, V2, V1 | Stock concentration | C1 = C2 × V2 ÷ V1 |
| C1, V1, V2 | Final concentration | C2 = C1 × V1 ÷ V2 |
Switch the “Solve for” button in the calculator to try each version. When you change the unknown, the value that was calculated is copied into its field, so you can check the reverse calculation immediately.
Units in C1V1 = C2V2
The formula only works if C1 and C2 are in the same unit and V1 and V2 are in the same unit. Converting 0.5 M to 500 mM, or 25 mL to 0.025 L, before multiplying is where most errors happen. The main dilution calculator lets you pick a unit on each line and does those conversions for you, including molar to mass units when you supply the molecular weight.
When C1V1 = C2V2 does not apply
C1V1 = C2V2 assumes that only solvent is added. It does not describe mixing two solutions that both contain the solute at different concentrations, and it does not apply when the solute reacts. For repeated dilutions, apply the formula once per step or use the serial dilution calculator, which multiplies the step factors for you.