Dilution Calculator (C₁V₁ = C₂V₂)
Preparing a calibration standard or diluting a sample? Enter your stock strength and the target concentration and volume — the calculator tells you exactly how much stock to pipette and how much diluent to add.
Dilution Volumes
| Item | Value |
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How the calculation works
Formulas
V₁ = (C₂ × V₂) / C₁
Diluent volume = V₂ − V₁
Dilution factor = C₁ / C₂
Add the stock volume (V₁) to a volumetric flask, then bring to the final volume V₂ with diluent.
V₁ = (C₂ × V₂) / C₁
Diluent volume = V₂ − V₁
Dilution factor = C₁ / C₂
Add the stock volume (V₁) to a volumetric flask, then bring to the final volume V₂ with diluent.
Notes & limitations
The mass-balance behind C₁V₁ = C₂V₂ is conservation of solute mass: the amount of solute taken from the stock (C₁ × V₁) equals the amount in the final solution (C₂ × V₂). This is standard analytical chemistry (see any quantitative analysis text, e.g. Harris, Quantitative Chemical Analysis).
- This only works for a true dilution: the target concentration must be lower than the stock. To concentrate a solution you need evaporation or another method.
- Both concentrations must be in the same unit (the unit cancels, so any consistent unit works).
- Volumes are assumed additive; for concentrated acids or organics, verify final volume and mix with cooling as your SOP requires.
- Use calibrated pipettes and volumetric flasks for standards — a graduated cylinder is not accurate enough for calibration work.
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