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Process Design

Dilution Calculator

This calculator solves the dilution equation C₁V₁ = C₂V₂ for any one of the four concentrations and volumes when the other three are known, and reports the volume of solvent to add.

The dilution equation C₁V₁ = C₂V₂ relates starting and final concentrations and volumes for a simple dilution. This calculator solves for any one of the four variables when the other three are provided. It also calculates the volume of solvent to add when applicable.

TypeInteractive engineering calculator

Calculator

any consistent basis

same basis as C₁

Result
V₂4 L
Added solvent3 L

Formulas

Dilution equation
C₁ × V₁ = C₂ × V₂
Solve for C₁
C₁ = C₂ × V₂ / V₁
Solve for V₂
V₂ = C₁ × V₁ / C₂
Added solvent
V_added = V₂ − V₁

Diagram

Dilution: C₁V₁ = C₂V₂C₁V₁Before+ solventC₂V₂AfterC₁ × V₁ = C₂ × V₂

Worked example

You have 1 L of solution at concentration 100. You want to dilute to concentration 25. What final volume is needed, and how much solvent do you add?

  1. 01C₁ = 100, V₁ = 1 L, C₂ = 25
  2. 02V₂ = C₁ × V₁ / C₂ = 100 × 1 / 25
  3. 03V₂ = 4 L
  4. 04Added solvent = V₂ − V₁ = 4 − 1 = 3 L
Result

The final volume is 4 L. You need to add 3 L of solvent.

FAQ

Does this calculator handle pH dilution?
No. pH dilution involves logarithmic acid–base equilibrium and is not a simple C₁V₁ = C₂V₂ relationship. This calculator is for simple concentration dilution only.
Does this model chemical reactions during dilution?
No. This assumes no reaction occurs. If dilution triggers precipitation, heat release, or other reactions, additional modelling is required.
What concentration units should I use?
Any consistent basis — g/L, mg/L, %, ppm, etc. The calculator uses C₁V₁ = C₂V₂ with the assumption that both concentrations are on the same basis. No unit conversion is applied to concentrations.
Does this assume additive volumes?
Yes. For most aqueous dilutions this is a reasonable approximation. For systems with significant volume-of-mixing effects (e.g., concentrated ethanol–water), this assumption introduces error.

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