Dilution calculator (C1V1 = C2V2)
Find the final volume and how much water to add to dilute a solution to the target concentration.
Use the same concentration unit (mol/L, %) and volume unit (mL, L). C1V1 = C2V2.
How the calculation works
When you dilute a solution, you add solvent (usually water), but the amount of solute stays the same. Hence the dilution equation:
C1 · V1 = C2 · V2
Where C1/V1 are the initial concentration and volume, C2/V2 the final. Solving: V2 = (C1·V1) ÷ C2. Water to add is V2 − V1.
Step-by-step example
Dilute 100 mL of a 2 mol/L solution to 0.5 mol/L:
- V2 = (2 × 100) ÷ 0.5 = 400 mL
- Water to add: 300 mL
Examples
- 50 mL at 10% to 2%: V2 = 250 mL → add 200 mL of water.
- Diluting 5× means multiplying volume by 5 and concentration falls to 1/5.
Frequently asked questions
Does it work for any concentration?
Yes — molarity, %, ppm — as long as the unit is the same on both sides.
Add water to acid or acid to water?
Always add acid TO water (slowly), never the reverse — the reaction releases heat and can splash.
What is the dilution factor?
It is the ratio V2 ÷ V1 (or C1 ÷ C2). A 1:10 dilution means a factor of 10.
Why does C₁V₁ = C₂V₂ work?
Because the amount of solute does not change when diluting — only solvent is added. Concentration × volume is the amount of substance, equal on both sides.
Acid into water or water into acid?
Always acid into water, never the reverse. Dilution releases heat, and water poured onto concentrated acid can boil and splash.
What is serial dilution?
Repeating smaller dilutions in sequence to reach very low concentrations: five 1:10 steps give 1:100,000.
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See all →Updated on June 18, 2026 · by Rafael Rossi · Methodology & sources