Solution math
Dilution calculator
The standard dilution relationship, C₁V₁ = C₂V₂. Fill in any three of stock concentration, stock volume, final concentration, and final volume — the fourth is solved. Units are yours to keep consistent; the math is unit-agnostic.
What this calculator does
Diluting means making a strong solution weaker by adding more liquid. The amount of dissolved substance stays the same, so concentration × volume is equal before and after — written C₁V₁ = C₂V₂. Give any three of the four values and the tool finds the fourth. Keep your units consistent (the math doesn't care which you use, as long as both concentrations match and both volumes match).
How to use it
- Stock concentration (C₁)How strong your starting solution is.
- Stock volume (V₁)How much of the starting solution you use. Leave this blank to find out how much stock to take.
- Final concentration (C₂)The weaker strength you want to end up with.
- Final volume (V₂)The total amount you want at the end.
Reading your results
- SolvedThe one value you left blank, calculated from the other three.
- Add diluentHow much solvent to add to the stock to reach the final volume (final volume minus stock volume).
A worked example
You have a 10 mg/mL stock and want 5 mL at 2 mg/mL:
V₁ = (2 × 5) ÷ 10 = 1 mL of stock
add 5 − 1 = 4 mL of diluent
Common questions
What's the difference between stock and final?
"Stock" is your concentrated starting solution; "final" is the diluted solution you want to end up with.
What units should I use?
Any — the formula is unit-agnostic. Just keep both concentrations in the same unit, and both volumes in the same unit.
Can I use it to make a solution stronger?
No. Adding liquid only dilutes. If the final concentration you enter is higher than the stock, the tool flags it.
The math, for the curious
C₁ × V₁ = C₂ × V₂ — dissolved amount is conserved, so concentration times volume is constant. "Add diluent" is V₂ − V₁.