Solution Dilution Calculator
Enter any three of C₁, V₁, C₂, and V₂ — the calculator solves the fourth using C₁V₁ = C₂V₂.
Worked examples
Diluting a 10% stock to a 2% working solution
A lab needs 500 mL of a 2% working solution but only stocks 10% concentrate on the shelf.
- C₁
- 10 %
- C₂
- 2 %
- V₂
- 500 mL
Use 100 mL of stock, add 400 mL water
Diluting a 5 M stock to 0.5 M for an experiment
A researcher needs 250 mL of a 0.5 M working solution from a 5 M concentrated stock.
- C₁
- 5 M
- C₂
- 0.5 M
- V₂
- 250 mL
Use 25 mL of stock, add 225 mL water
How the formula works
Adding solvent to a solution doesn't change how much solute is dissolved in it — it only spreads that same amount of solute through a larger volume, which lowers the concentration. The amount of solute is concentration times volume, so that quantity — C₁V₁ before dilution, C₂V₂ after — must stay the same on both sides. Setting them equal gives the formula below; rearrange it for whichever of the four values you're solving for, and the difference V₂ − V₁ tells you how much solvent to add.
Frequently asked questions
What does C₁V₁ = C₂V₂ actually mean?
It's a statement of mass balance: the amount of solute in solution doesn't change when you add solvent — only its concentration and the volume it's spread through change, and they change in inverse proportion. C₁V₁ (stock concentration × stock volume) is the amount of solute before dilution; C₂V₂ (final concentration × final volume) is that same amount after. Since nothing was added or removed, the two products must be equal, which lets you solve for whichever of the four values you don't already know.
Why do C₁ and C₂ have to use the same concentration unit?
Percent, molarity, and mg/mL aren't interchangeable without extra information — converting between them needs a molar mass (for percent ↔ molarity) or a solution density (for percent ↔ mg/mL), neither of which this calculator collects. So the tool keeps C₁ and C₂ locked to one shared unit at a time: change either dropdown and both update together. If your stock and target are specified in different unit families, convert one of them to match the other first.
Is the amount of water I add the same as the final volume V₂?
No — this is the most common mistake. You don't add V₂ of water; you add the difference between the final and stock volumes (V₂ − V₁), because the stock solution you're diluting already accounts for part of that final volume. The calculator shows this as "Add solvent" in the results so you don't have to subtract it yourself.
My calculated stock volume is tiny (a few microliters) — is that a problem?
Very small volumes are hard to pipette accurately, and a small absolute error becomes a large relative error at that scale. Two common fixes: prepare a larger total batch so every volume scales up proportionally, or make an intermediate dilution first and dilute that instead of pulling straight from the concentrated stock — which is exactly what a serial dilution does.
Can I use this for percent, molar, or fold (X) concentrations?
Yes. The math only depends on concentration and volume being paired consistently, not on which unit family you pick — % w/v stock diluted to a lower %, molar stock diluted to a working molarity, or a 10X buffer diluted down to 1X all use the identical C₁V₁ = C₂V₂ relationship.
How do I avoid wasting concentrated stock solution?
Calculate the exact volume you need here rather than rounding up generously — add only a small margin (5–10%) to cover pipetting dead volume, not double. It also helps to keep your main stock in smaller aliquots instead of one large bottle, so repeated opening, temperature swings, or contamination only affect a portion of your supply rather than the whole batch.