Dilution Calculator
Work out how much stock solution to dilute to make a given volume at a lower concentration — C₁V₁ = C₂V₂ — with the diluent volume and dilution factor.
How much stock to measure out, and how much water to add.
How the dilution calculator works
Diluting does not change the amount of solute, only the volume it sits in, so C₁V₁ = C₂V₂. Rearranged, the stock volume needed is V₁ = C₂V₂ ÷ C₁; add diluent to reach V₂. Any concentration unit works as long as both are the same — molar, percent, mg/mL.
For a very large dilution factor (over about 100) do it in two or more steps to keep the volumes measurable.
Formula: V₁ = C₂ × V₂ ÷ C₁
Worked examples
| Inputs | Stock volume to use (V₁) | Note |
|---|---|---|
| 1 M stock → 100 mL of 0.1 M | 10 mL | 10 mL of stock + 90 mL diluent |
| 10% stock → 250 mL of 2% | 50 mL | 50 mL stock |
| 5 mg/mL → 20 mL of 0.25 mg/mL | 1 mL | a 20× dilution |
FAQFrequently asked questions
Does the unit matter?
Not as long as C₁ and C₂ use the same one, and V₁ comes out in whatever unit V₂ is in.
What is a dilution factor?
C₁ ÷ C₂ (or V₂ ÷ V₁): a 1:10 dilution has a factor of 10. Serial dilutions multiply: three 1:10 steps give 1:1000.
Why not just add water to the stock?
You can, but the volumes would be stock plus diluent rather than a final volume — the calculator gives the diluent volume to add so the total is exactly V₂.
Is this the same as the C1V1 = C2V2 formula in pharmacology?
Yes — it is the same conservation of amount, used for drug dilutions, buffers and reagents alike.
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
- Royal Society of Chemistry — the UK chemistry professional body
Last checked: September 2026. Atomic masses are the IUPAC conventional values; constants are CODATA 2018; equations are the standard textbook forms.