Dilution Calculator (C₁V₁ = C₂V₂)
Work out how much stock solution and solvent you need to make a diluted solution.
Step-by-step working
- C₁V₁ = C₂V₂ → V₁ = C₂V₂ / C₁ = 1 × 100 / 10 = 10
Mathematical Formula
Overview & Explanation
Dilution conserves the amount of solute, so concentration × volume stays constant.
How It Works
- Multiply target concentration by final volume.
- Divide by stock concentration.
- Top up with solvent to V₂.
Practical Applications
- Lab reagent preparation.
- Diluting cleaning concentrates.
Example 1: 10 M → 1 M, 100 mL
10 mL stock.
Inputs
Stock concentration C₁: 10 · Target concentration C₂: 1 · Final volume V₂: 100
Step 1
C₁V₁ = C₂V₂ → V₁ = C₂V₂ / C₁ = 1 × 100 / 10 = 10
Stock volume needed (V₁)
Result
Example 2: 70% → 30%, 500 mL
Alcohol dilution.
Inputs
Stock concentration C₁: 70 · Target concentration C₂: 30 · Final volume V₂: 500
Step 1
C₁V₁ = C₂V₂ → V₁ = C₂V₂ / C₁ = 30 × 500 / 70 = 214.2857
Stock volume needed (V₁)
Result
How it's calculated & sources
C₁V₁ = C₂V₂ ⇒ V₁ = C₂V₂ / C₁; solvent = V₂ − V₁.
Frequently Asked Questions
Can I use percentages?
Why can’t C₂ exceed C₁?
Do volumes add exactly?
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