Dilution Calculator

The Dilution Equation

The dilution equation C₁V₁ = C₂V₂ relates the concentration and volume of a solution before and after dilution:

• C₁ = initial (stock) concentration
• V₁ = initial volume (volume of stock to use)
• C₂ = final (desired) concentration
• V₂ = final (total) volume

This works because the amount of solute stays constant during dilution — you are only adding solvent.

Solving for Each Variable

• V₁ = (C₂ × V₂) / C₁ — how much stock solution to use
• C₂ = (C₁ × V₁) / V₂ — resulting concentration after dilution
• V₂ = (C₁ × V₁) / C₂ — total volume needed
• C₁ = (C₂ × V₂) / V₁ — required stock concentration

Example

Problem: Prepare 500 mL of 0.5 M NaCl from a 5 M stock solution.

Solution: V₁ = (C₂ × V₂) / C₁ = (0.5 × 500) / 5 = 50 mL

Take 50 mL of the 5 M stock and add 450 mL of solvent to reach 500 mL total volume.

Serial Dilutions

A serial dilution is a series of stepwise dilutions where each step uses the previous dilution as its stock. They are used to create a wide range of concentrations from a single stock, commonly in:

• Antibody titrations and ELISA assays
• Microbiology (CFU counting)
• Drug dose-response curves
• Standard curve preparation

For a dilution factor DF over n steps, the concentration at step n is:

C_n = C₁ × (1/DF)ⁿ

Important Notes

• C₁ must always be greater than C₂ (you cannot concentrate by diluting)
• V₂ must always be greater than V₁ (final volume includes the stock)
• Concentration units must be consistent on both sides of the equation
• Volume of solvent to add = V₂ − V₁

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