Dilution Calculator
Solve C₁V₁ = C₂V₂ for one unknown or generate a serial-dilution table with concentration, per-step factor and cumulative factor.
Dilution formulas
For an ideal dilution in which the amount of solute transferred is conserved:
C₁V₁ = C₂V₂.
Therefore V₁ = C₂V₂ ÷ C₁, C₂ = C₁V₁ ÷ V₂, and the dilution factor is C₁ ÷ C₂ = V₂ ÷ V₁.
For a serial dilution with transfer volume t and diluent volume d: factor per step = (t + d) ÷ t, and concentration after step n is C₀ ÷ factorⁿ.
Scope and safety: concentrations must use the same basis before applying C₁V₁ = C₂V₂. The formula assumes solute conservation and ideal volume behavior. It does not account for reactions, density contraction, assay/purity corrections, activity, pH, temperature or instrument uncertainty. Follow the reagent SDS and laboratory procedure; never infer a safe mixing order from this calculator.
Six calculated examples
| Inputs | Calculated result |
|---|---|
| 10 M stock; 0.1 M target; 500 mL final | V₁ = 5 mL stock; 495 mL volume difference; factor 100 |
| 2 M stock; 25 mL stock; 100 mL final | C₂ = 0.5 M; factor 4; 75 mL volume difference |
| Unknown C₁; V₁ = 10 mL; C₂ = 0.2 M; V₂ = 100 mL | C₁ = 2 M; factor 10 |
| 5 M stock; V₁ = 4 mL; C₂ = 0.1 M | V₂ = 200 mL; 196 mL volume difference |
| 1 M start; transfer 1 mL + 9 mL diluent; 3 steps | 0.1 M, 0.01 M, 0.001 M; cumulative factor 1,000 |
| 1,000 µM start; transfer 200 µL + 800 µL diluent; 4 steps | 200, 40, 8 and 1.6 µM; cumulative factor 625 |
How to use the dilution calculator
- For one dilution, choose units and leave exactly one of C₁, V₁, C₂ or V₂ empty.
- Use the same concentration basis for C₁ and C₂. For example, do not mix molarity with mass percent.
- Use the same volume unit for V₁ and V₂. The solved result remains in that selected unit.
- For a serial dilution, enter the concentration before the first step, the aliquot transferred, fresh diluent per vessel and number of steps.
- Check that the planned transfer volume is practical for the available calibrated equipment and that the protocol specifies adequate mixing.
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