Dilution calculator: C₁V₁ = C₂V₂
Work out how to dilute a stock solution: the volume of stock to use, the final volume, or the concentration before or after diluting, using C₁V₁ = C₂V₂.
C₁V₁ = C₂V₂
C₁ and V₁ are the concentration and volume of the stock solution, C₂ and V₂ those of the diluted solution. Use the same volume unit on both sides.
How to use the calculator
Choose the value you need under Solve for and enter the other three. The two concentrations only need the same unit (mol/L, % or mg/mL all work), and so do the two volumes.
To prepare a dilution, solve for V₁: it tells you how much stock to measure out before adding water up to the final volume V₂.
Worked example
You have 2.0 mol/L hydrochloric acid and need 200 mL at 0.50 mol/L. V₁ = C₂V₂ ÷ C₁ = 0.50 × 200 ÷ 2.0 = 50 mL. Measure 50 mL of the stock and add water to make 200 mL in total, which means adding 150 mL of water.
Why it works
Diluting adds solvent but never removes solute, so the amount of solute stays the same. Amount is concentration times volume, so C₁ × V₁ before equals C₂ × V₂ after.
For acids, always add the acid to the water, not water to the acid: mixing releases heat, and adding water to concentrated acid can make it spatter.
FAQ
What does C₁V₁ = C₂V₂ mean?
It says the amount of solute before diluting (concentration C₁ times volume V₁) equals the amount after (C₂ times V₂), because adding water does not change how much solute there is.
Do I need to convert units?
Only so that they match: both concentrations in the same unit and both volumes in the same unit. The answer comes out in that same unit.
How much water do I add?
Subtract the stock volume from the final volume: V₂ − V₁. In the example, 200 mL − 50 mL = 150 mL of water.