C1V1 = C2V2 Explained: How to Do Dilutions Correctly

When you dilute a solution, the amount of solute stays the same; only the volume of solvent increases. That gives the dilution equation C1V1 = C2V2. Skip the maths with our dilution calculator.

What each letter means

• C1 – concentration of the stock
• V1 – volume of stock to use
• C2 – concentration you want
• V2 – final total volume

Example 1: Lab solution

Make 250 mL of 0.1 M solution from 2 M stock: V1 = 0.1 × 250 ÷ 2 = 12.5 mL stock, topped up to 250 mL.

Example 2: Cleaning concentrate

A 20% concentrate should be used at 2%. For a 1 L spray bottle: V1 = 2 × 1,000 ÷ 20 = 100 mL concentrate + 900 mL water.

Ratio notation

“1:10” usually means 1 part stock in 10 parts total (1 + 9 water) in science, but some product labels mean 1 part to 10 parts water. Check which your instructions use.

Serial dilutions

Repeated 1:10 dilutions multiply: three 1:10 steps give a 1:1,000 dilution. This is common in microbiology for counting bacteria.

Safety tip

When diluting acids, always add acid to water, never water to acid.