Dilution Calculator — C1V1 = C2V2 Formula
Solve the dilution equation C₁V₁ = C₂V₂. Enter any three of the four values (initial/final concentration and volume) to instantly calculate the missing value with step-by-step solution.
Enter any three values — leave the unknown field blank.
Initial (Stock) Solution
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Final (Diluted) Solution
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Result
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Dilution Factor
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Solvent to Add
Step-by-Step Solution
How to Use the Dilution Formula
The formula C₁V₁ = C₂V₂ is derived from conservation of moles of solute:
- Find V₁: V₁ = C₂ × V₂ / C₁ (how much stock solution to use)
- Find C₂: C₂ = C₁ × V₁ / V₂ (resulting concentration after dilution)
- Find V₂: V₂ = C₁ × V₁ / C₂ (final volume after adding solvent)
- Find C₁: C₁ = C₂ × V₂ / V₁ (original stock concentration)
Frequently Asked Questions
What is the dilution equation C1V1 = C2V2?
The dilution equation states that the number of moles of solute is conserved during dilution. C₁V₁ = C₂V₂ where C₁ is initial concentration, V₁ is initial volume, C₂ is final concentration, and V₂ is final volume. Enter any three values to find the fourth.
How do I dilute a stock solution?
To dilute a stock solution: (1) identify your starting concentration C₁ and desired final concentration C₂ and volume V₂; (2) calculate V₁ = C₂V₂/C₁ — this is how much stock solution to take; (3) add solvent (usually water) to reach the final volume V₂.
What is dilution factor?
Dilution factor (DF) = V₂/V₁ = C₁/C₂. It tells you how many times the solution was diluted. A dilution factor of 10 means the final solution is 10 times less concentrated than the original.
Can I use mL or L in the formula?
Yes, as long as V₁ and V₂ are in the same units. If both are in mL, C₁V₁ = C₂V₂ still holds. Just be consistent — do not mix L and mL. This calculator lets you choose units independently for each volume.
What is a serial dilution?
A serial dilution is a sequence of dilutions, each by the same factor. For example, a 1:10 serial dilution in 4 steps goes from 1 M to 0.1 M to 0.01 M to 0.001 M to 0.0001 M. Each step multiplies the concentration by the dilution factor (0.1 in this case).