How it works
Diluting a stock solution doesn't change the total amount of solute — only the volume it's spread through. That means concentration times volume stays constant before and after, which is the whole calculation.
C₁V₁ = C₂V₂
stock volume (V₁) = C₂V₂ ÷ C₁ — how much stock to measure out
diluent to add = V₂ − V₁ — topped up with solvent to reach the desired volume
Worked example
Diluting a 10 M stock down to 500 mL of a 1 M solution.
- Multiply desired concentration by desired volume: 1 × 500 = 500.
- Divide by stock concentration: 500 ÷ 10 = 50.
Measure out 50 mL of stock, then add 450 mL of diluent to reach 500 mL total.
Common questions
Do the units of concentration matter?
Not as long as C₁ and C₂ use the same unit — molar, mg/mL, percent, whatever your protocol calls for. The unit cancels out of the equation, so mixing units is the one thing that will give you a wrong answer.
Why is the desired concentration always lower?
Dilution only ever spreads the same amount of solute through more volume, so it can only lower concentration, never raise it. If C₂ isn't lower than C₁, there's no valid dilution — you'd need a more concentrated stock instead.
What if my volumes are in litres, not millilitres?
Enter whichever volume unit you like — the calculator labels it mL, but the arithmetic is identical for any consistent unit as long as V₁ and V₂ match.