Dilution of Solution Calculator
Use this dilution of solution calculator to solve the dilution equation C₁V₁ = C₂V₂. Enter any three of the four values — stock concentration, stock volume, final concentration and final volume — and leave the one you want blank to solve it, plus the solvent to add.
Fill in any three values — the fourth is solved automatically. (3 more to go.)
How to calculate the dilution of a solution
Diluting a solution lowers its concentration by adding more solvent while the amount of solute stays the same. Because the moles of solute are conserved, concentration times volume is constant:
C₁ and V₁ describe the concentrated stock; C₂ and V₂ describe the diluted solution. Rearranging solves for whichever value you leave blank — the calculator above does it as you type, and the solvent to add is simply V₂ − V₁.
Worked example
You have a 10 M stock and need 50 mL of a 2 M solution. Set C₁ = 10, C₂ = 2, V₂ = 50 and leave V₁ blank: V₁ = (2 × 50) ÷ 10 = 10 mL of stock, topped up with 40 mL of solvent to reach 50 mL.
Common lab solution dilutions
A few named recipes come up constantly on the bench — the stock and working strengths are already standard:
| Solution | Stock | Working strength |
|---|---|---|
| PBS buffer | 10× stock | 1× working |
| Bleach disinfectant | Concentrated (~8.25%) | 1:10 (~0.5–0.8%) diluted |
| Tris buffer | 1 M stock | 10 mM working |
| SDS (sodium dodecyl sulfate) | 20% stock | 0.1–1% working |
| NaCl (saline) | 5 M stock | 150 mM (physiological) |
Related tools
This is the same maths as the home dilution calculator. To find only the concentration after mixing, use the final concentration calculator; to work from a ratio instead, try the dilution ratio calculator.
Frequently asked questions
›What is the dilution equation?
The dilution of a solution follows C₁V₁ = C₂V₂, where C₁ and V₁ are the concentration and volume of the concentrated stock, and C₂ and V₂ are the concentration and volume after dilution. Because the amount of solute is unchanged, the product of concentration and volume stays constant, so you can solve for any one value from the other three.
›How do I calculate the volume needed to dilute a solution?
Leave the stock volume (V₁) blank and enter C₁, C₂ and V₂. The calculator returns V₁ = (C₂ × V₂) ÷ C₁, and the solvent to add is V₂ − V₁. For example, to make 50 mL of 2 M from a 10 M stock, V₁ = (2 × 50) ÷ 10 = 10 mL of stock plus 40 mL of solvent.
›Do the concentration and volume units have to match?
C₁ and C₂ must share one concentration unit, and V₁ and V₂ must share one volume unit. The equation is a ratio, so any consistent pair of units gives a correct answer. Use the unit selectors to keep each pair aligned.
›Is this dilution of solution calculator free?
Yes. It runs entirely in your browser, needs no sign-up, and never sends your numbers to a server.
›What if I already know a named recipe, like making 1× PBS from 10× stock?
Those are just C₁V₁ = C₂V₂ with the stock and working strengths already known — see the common lab dilutions table below for the numbers to plug in directly.
Related calculators
Solve C₁V₁ = C₂V₂ for any unknown — stock concentration, volume, or final concentration.
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Dilute a stock solution to a target concentration with full unit switching.
Convert mg/mL to molarity (and back) using molecular weight — both directions.