Solution Dilution Calculator
Solve the dilution equation C1V1 = C2V2 for any unknown.
Enter the other three values. Keep all concentrations in the same unit and all volumes in the same unit.
M
mL
M
mL
Result
Calculation Steps
The Dilution Equation (C₁V₁ = C₂V₂)
When you dilute a solution by adding more solvent, the amount of solute stays the same — only its concentration changes. This conservation of solute is captured by the dilution equation:
C₁ × V₁ = C₂ × V₂
- • C₁ = Initial (stock) concentration
- • V₁ = Initial (stock) volume taken
- • C₂ = Final (diluted) concentration
- • V₂ = Final (total) volume
Rearranged to solve for any single unknown:
- C₁ = (C₂ × V₂) / V₁
- V₁ = (C₂ × V₂) / C₁
- C₂ = (C₁ × V₁) / V₂
- V₂ = (C₁ × V₁) / C₂
How to Dilute a Stock Solution
- Identify your stock concentration (C₁), the target concentration (C₂), and the final volume you need (V₂).
- Calculate the volume of stock required: V₁ = (C₂ × V₂) / C₁.
- Measure V₁ of the stock solution into a clean container or volumetric flask.
- Add solvent (the amount to add = V₂ − V₁) until the total reaches the final volume V₂.
- Mix thoroughly so the solute is evenly distributed.
Example: To make 100 mL of 0.5 M solution from a 2 M stock, take V₁ = (0.5 × 100) / 2 = 25 mL of stock and add 75 mL of solvent to reach 100 mL total.
A Note on Units
The dilution equation works with any consistent units, because the units cancel on both sides. The two rules to follow are:
- • Use the same concentration unit for C₁ and C₂ (e.g. both in M, mM, or %).
- • Use the same volume unit for V₁ and V₂ (e.g. both in mL or both in L).
- • The solved quantity is reported in the matching unit (M for concentrations, mL for volumes in this calculator).