Solution Dilution Calculator
The dilution equation solved for whichever variable you need — stock volume, final volume, or either concentration.
C₁V₁ = C₂V₂ says the amount of solute does not change when you add solvent.
How the solution dilution calculator works
C₁V₁ = C₂V₂ says the amount of solute does not change when you add solvent. Rearranged, it gives whichever quantity is unknown.
The practical form is V₁ = C₂V₂ ÷ C₁: to make 500 mL of 0.1 M from a 2 M stock, take 25 mL of stock and make it up to 500 mL. Make *up to*, not add 475 mL — for concentrated solutions those differ.
Formula: C₁V₁ = C₂V₂
Worked examples
| Inputs | Result | Note |
|---|---|---|
| 500 mL of 0.1 M from 2 M | 25 | 25 mL of stock |
| What does 25 mL in 500 give? | 0.1 | 0.1 M |
| How far can 25 mL go? | 1,000 | 1,000 mL |
FAQFrequently asked questions
What is C₁V₁ = C₂V₂?
The statement that diluting does not change how much solute is present — only the volume it is spread through.
How do I make 500 mL of 0.1 M from 2 M stock?
Take 25 mL of stock and make up to 500 mL with solvent.
Should I add 475 mL or make up to 500?
Make up to 500. Volumes are not perfectly additive, and for concentrated solutions the difference is real.
Do the units matter?
Only that they match on each side. Molarity with millilitres works as long as both concentrations use the same unit.
Can I use this to concentrate a solution?
No — the equation only describes adding solvent. Concentrating means removing solvent, and the amount of solute stays fixed while the volume falls.
Where these figures come from
- IUPAC — Standard atomic weights (2021 conventional values) — the molar-mass table
- NIST — CODATA 2018 fundamental physical constants — Avogadro constant, gas constant, speed of light
- NIST Chemistry WebBook — thermochemical data
- CSIRO — Australia's national science agency
Last checked: September 2026. Atomic masses are the IUPAC conventional values; constants are CODATA 2018; equations are the standard textbook forms.