Dilution calculator
The C₁V₁ = C₂V₂ rule solved for either volume.
Fill in the fields and the result will appear here automatically.
Finds the final or stock-solution volume for dilution using C₁V₁ = C₂V₂. Concentrations must express amount or mass per solution volume, such as mol/L or g/L. Mass percentages cannot be used in this volume equation without density information. The separate solvent line estimates the difference of volumes.
How it works
Formula and logic
The dissolved amount is conserved: C₁V₁ = C₂V₂. Final volume is C₁V₁/C₂ and stock volume is C₂V₂/C₁. Volume fields use mL; both concentrations must use the same quantity definition and units. Subtracting volumes assumes additivity.
Example
Make 50 mL of a 2 mol/L solution up to a final volume of 200 mL to obtain 0.5 mol/L. The 150 mL difference estimates solvent addition; make up to the final volume rather than assume all mixing volumes add exactly.
Fields and units
- What to find — list option
- Initial concentration — in matching concentration-per-volume units
- Initial volume, mL — mL
- Final concentration — in matching concentration-per-volume units
- Final volume, mL — mL
How to use
- — Choose the final or stock volume.
- — Enter both concentrations using the same units per solution volume.
- — Enter the known volume in mL and read the result.
Method and limitations
- Calculation method
- Formula and logic
- Limitation
- The model conserves solute for concentration per volume. Solvent addition is approximate; mass fractions and nonadditive volumes need a different model.
FAQ
Which concentrations work in C₁V₁ = C₂V₂?
Amount or mass per volume, such as mol/L or g/L. Explicit mass/volume percentage in g per 100 mL is also proportional to mass concentration. Mass percentage has a different denominator: without solution masses or an appropriate density it cannot replace concentration per volume.
Can dilution increase the concentration?
No. This model adds solvent and requires the final concentration not to exceed the initial one. Concentration by evaporation is a different operation.
Is final volume the amount of solvent to add?
No. It includes the stock solution. V₂−V₁ estimates the solvent addition when volumes are additive; making up to the calculated final volume is more precise.
Does this work for every percentage mixture?
No. Identify what the percentage means. Mass and amount fractions are not concentrations per volume. Volume percentages require a consistent definition and volume assumptions; mixing contraction or expansion is not modelled here.