How to use this calculator
- Select the unknown concentration or volume.
- Enter the other three values and select the units.
- Calculate the stock aliquot and diluent volume.
Formula and variables
C₁V₁ = C₂V₂
| Symbol | Meaning | Unit |
|---|---|---|
| C₁ | stock concentration | concentration |
| V₁ | stock aliquot volume | volume |
| C₂ | final concentration | concentration |
| V₂ | final solution volume | volume |
Worked example
To prepare 1.0 L of 0.10 M solution from a 1.0 M stock, V1 = (0.10 × 1.0) / 1.0 = 0.10 L. Add 0.90 L diluent to reach final volume.
Interpretation
A physical dilution has final concentration no greater than stock concentration and final volume no smaller than the stock aliquot.
Common mistakes
- Do not enter more than one unknown.
- Use concentration units from the same dimension.
- Do not target a concentration above the stock.
Frequently asked questions
What does C1V1 = C2V2 assume?
It assumes that dilution conserves the amount of solute.
How much diluent should I add?
Add diluent until the solution reaches the final volume. The planning value is V2 minus V1.
Can a dilution make a more concentrated solution?
No. The final concentration cannot exceed the stock concentration in a dilution workflow.
Can I use scientific notation?
Yes. Enter values such as 6.022e23 or 1.0e-6 in a numeric field.
How should I round the result?
Keep extra digits during the calculation. Round the final result to the precision required by your data.