Dilution Calculator (C₁V₁ = C₂V₂)
Calculate stock solution dilutions using C₁V₁ = C₂V₂. Enter any three of initial concentration C₁, initial volume V₁, final concentration C₂, final volume V₂ to find the fourth. Includes solvent volume to add.
How to use this tool
- Enter initial concentration c₁, initial volume v₁, final concentration c₂ and final volume v₂ in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your final concentration c₂ and the full breakdown beneath it.
The dilution law C₁V₁ = C₂V₂ states that the amount of solute is conserved when you dilute a solution. C is concentration (mol/L) and V is volume (L). Enter three known values to find the fourth.
Formula
C1V1 = C2V2
Solve for any unknown:
C2 = C1V1 ÷ V2 | V2 = C1V1 ÷ C2 | C1 = C2V2 ÷ V1 | V1 = C2V2 ÷ C1
Solvent to add = V2 − V1
How it works
This tool applies the conservation of moles during dilution: the number of moles of solute in the stock solution (C1V1) equals the number of moles in the diluted solution (C2V2). Enter any three of the four variables (set the unknown to zero) and the calculator solves algebraically for the fourth.
Concentrations are in mol/L (molarity) and volumes in litres. It also reports how much solvent to add (V2 − V1). The formula assumes ideal solution behaviour — density changes on mixing and activity coefficients are not accounted for.
Worked example
Worked example — find final volume
- Stock solution: C1 = 1.0 mol/L, V1 = 0.1 L; desired concentration C2 = 0.1 mol/L; V2 unknown.
- Apply C1V1 = C2V2: V2 = (1.0 × 0.1) ÷ 0.1 = 1.0 L.
- Solvent to add = V2 − V1 = 1.0 − 0.1 = 0.9 L.
Final volume V2 = 1.0 L; add 0.9 L of solvent to the 0.1 L of stock solution.
Key terms
- Molarity (M)
- Concentration expressed as moles of solute per litre of solution (mol/L).
- Dilution
- The process of reducing solution concentration by adding more solvent, keeping the total moles of solute constant.
- Stock solution
- A concentrated solution prepared in advance and diluted to make working solutions of lower concentration.
- Moles of solute
- The quantity of chemical substance (n = C × V) that is conserved during dilution — the basis of the C1V1 = C2V2 relationship.
- Serial dilution
- A stepwise dilution process where each step uses the previous step's diluted solution as the new stock, used to achieve very low concentrations.
Frequently asked questions
- What does 'solvent to add' mean?
- It is V₂ − V₁: the volume of pure solvent (usually water) you need to add to the stock to reach the target volume and concentration.
- Can C₁V₁ = C₂V₂ be used for concentrating a solution?
- Yes — if you evaporate solvent (V₂ < V₁), C₂ > C₁. The solvent to add will be negative, indicating solvent removed.