Dilution Calculator (C₁V₁ = C₂V₂)
Find the final volume or amount of solvent to add when diluting a stock solution using the dilution equation C₁V₁ = C₂V₂.
How to use this dilution calculator
- Enter the concentration of your stock solution.
- Enter how much stock you'll take (V₁).
- Enter the target concentration.
- Transfer V₁ mL of stock into a flask and add the calculated solvent volume to the V₂ mark.
Formula
C₁V₁ = C₂V₂ → V₂ = C₁V₁ ÷ C₂. Solvent to add = V₂ − V₁. Dilution factor = C₁ ÷ C₂.
About the Dilution Calculator
The dilution equation is used thousands of times daily in labs worldwide. To make 100 mL of 0.1 M HCl from 12 M stock: V₁ = (0.1 × 100) / 12 = 0.83 mL of concentrated acid — top up to 100 mL with water.
Always add acid to water, never water to acid — the dilution reaction is exothermic, and a large water volume dissipates heat safely.
Frequently asked questions
+What does C₁V₁ = C₂V₂ mean?
Moles of solute before dilution = moles after. You're just adding solvent — the amount of dissolved substance stays the same.
+What is a dilution factor?
The ratio C₁/C₂ (or V₂/V₁). A 1:10 dilution (10×) means the final concentration is 1/10 of the stock.
+What are serial dilutions?
A series of equal dilutions: each step multiplies the previous. Two 1:10 dilutions give 1:100 overall. Use this calculator for each step.