Solution Dilution Calculator (C₁V₁ = C₂V₂)
Volume of stock solution needed to make a given volume at a lower concentration.
Results
Stock solution to take
62.500
mL
Solvent to add
437.500
mL
Dilution factor
8.0000
Percentage
12.5000
%
What this tool does
Diluting does not change how much solute you have, only how much liquid it is spread through — which is the whole of C₁V₁ = C₂V₂. The units cancel, so millilitres and litres both work as long as both volumes use the same one, and the same goes for the two concentrations.
Formula
C₁V₁ = C₂V₂
Variables
| Symbol | Meaning | Unit |
|---|---|---|
c1 | Stock concentration | mol/L |
c2 | Final concentration | mol/L |
v2 | Final volume | mL |
V1 | Stock solution to take | mL |
VS | Solvent to add | mL |
DF | Dilution factor | — |
PC | Percentage | % |
Worked example
- Stock concentration2 mol/L
- Final concentration0.25 mol/L
- Final volume500 mL
- Stock solution to take62.500 mL
- Solvent to add437.500 mL
- Dilution factor8.0000
- Percentage12.5000 %
Limitations
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
Frequently asked questions
Do I add the solvent volume, or make up to the final volume?
Make up to the final volume. Mixing liquids does not always give the sum of their volumes, so the solvent figure here is a guide to how much you will roughly need, not a quantity to measure out. Put the stock in the flask first, then add solvent until the meniscus reaches the mark.