Dilution Calculator
C₁V₁ = C₂V₂, solved for whichever value you leave blank.
Fill in three boxes and leave the one you want blank. Concentrations only have to match each other — molar, percent, mg/mL or ppm all work, because the units cancel across the equation.
V₁ — volume of stock to take
25 mL
- Dilution factor
- 4×
- Solvent to add
- 75 mL
Working
- V₁ = C₂V₂ ÷ C₁ = (0.5 × 0.100000) ÷ 2 = 0.0250000 L
Why the equation works
Diluting adds solvent and nothing else. The number of moles of solute in the flask is the same before and after, and since concentration times volume gives moles, that product is what stays constant. Everything else follows.
Making up the solution
Measure the calculated stock volume, put it in the flask, then make up to the final volume with solvent. Do not add the calculated volume of solvent to the stock — the two are only the same thing for dilute aqueous solutions, and for concentrated ones the volumes do not simply add.
Related: molar mass calculator, chemical equation balancer, periodic table.
What a dilution ratio means — and why 1:10 is ambiguous
A ratio says how much stock goes into how much finished solution, but it has two accepted readings and they differ by about 10%. In a laboratory, 1:10 almost always means one part stock made up to ten parts total — one part stock, nine parts diluent, a dilution factor of 10. In cleaning products, horticulture and cooking it usually means one part stock plus ten parts water — eleven parts in total, a factor of 11.
Neither is wrong, and no amount of arithmetic settles it: it depends on the convention of the field you are working in. The ratio tab above therefore gives both answers side by side rather than picking one for you. If a protocol matters, check which convention it was written in before you trust either number.
Serial dilution
A serial dilution repeats the same fold-dilution, each tube drawn from the one before. The essential point is that the factors multiply: three tenfold steps give a thousandfold dilution, not thirtyfold. That is what makes serial dilution the practical way to reach very low concentrations — a millionfold dilution takes six tenfold steps and a few millilitres, where doing it in one step would need an impractically large flask or an unmeasurably small transfer.
For a tenfold series, transfer one tenth of the tube volume and make up with nine tenths diluent. Mix each tube thoroughly before drawing from it — an unmixed transfer is the usual reason a standard curve comes out non-linear at the dilute end, and the error compounds down the series.
Diluting spirits to a target ABV
Proofing a spirit is the same equation with ABV as the concentration: multiply the starting strength by the volume you have, divide by the strength you want, and the answer is the volume you will finish with. The water to add is the difference.
One caveat that proofing calculators usually leave out: ethanol and water contract when mixed. At spirit strengths the measured final volume comes out roughly 2–3% below the sum of the parts. The amount of alcohol is unchanged, so the true strength lands slightly above target. Distillers correct by measuring with a hydrometer rather than by arithmetic, and if the strength has to be exact, so should you.
How it works
Diluting adds solvent and nothing else, so the amount of solute in the flask is the same before and after. Concentration times volume gives that amount, which is why the product C×V is what stays constant — every dilution question is a rearrangement of that one fact.
Dilution equation
C₁V₁ = C₂V₂ V₁ = C₂V₂ ÷ C₁ C₂ = C₁V₁ ÷ V₂ V₂ = C₁V₁ ÷ C₂ dilution factor = C₁ ÷ C₂ = V₂ ÷ V₁
- C₁
- concentration of the stock solution
- V₁
- volume of stock you take
- C₂
- concentration you want
- V₂
- final volume after adding solvent
Making 100 mL of 0.5 M from a 2 M stock
- C₁ = 2 M
- C₂ = 0.5 M
- V₂ = 100 mL
- V₁ = C₂V₂ ÷ C₁
- V₁ = (0.5 × 100) ÷ 2 = 25 mL
- Solvent to add = 100 − 25 = 75 mL
Take 25 mL of stock and make up to 100 mL — a fourfold, or 1:4, dilution.
Good to know
- The units of C₁ and C₂ only have to match each other. Molar, percent, mg/mL and ppm all work, because the units cancel across the equation.
- Add the stock to the flask and make up TO the final volume. Adding the calculated volume of solvent to the stock is a different thing, and for concentrated solutions the two are not the same — volumes do not simply add.
- A ratio like 1:10 is ambiguous. In a lab it usually means one part made up to ten parts total (factor 10); in cleaning and horticulture it usually means one part plus ten parts (factor 11). The ratio tab shows both.
- Serial dilution factors multiply. Three tenfold steps give a thousandfold dilution, not thirtyfold.
Related Calculators
Frequently Asked Questions
What is the dilution equation?
C₁V₁ = C₂V₂. The amount of solute does not change when you add solvent, so concentration times volume before equals concentration times volume after.
Do the concentration units matter?
Only that both are the same. Molar, percent, mg/mL or ppm all work, because the units cancel across the equation. The volumes must also match each other, which this calculator handles by converting both to litres.
How much solvent do I add?
The difference between the final and starting volumes, not the final volume itself. To make 100 mL from 25 mL of stock you add 75 mL — and you add it to the stock, rather than measuring 100 mL of solvent and adding the stock to that, which would overshoot.
What is a dilution factor?
The ratio of starting to final concentration. Diluting 2 M down to 0.5 M is a fourfold, or 1:4, dilution. Serial dilutions multiply: three successive tenfold steps give a thousandfold dilution overall.
Why does my calculated stock volume exceed the final volume?
Because the concentration you asked for is higher than the stock you have, so no amount of dilution will reach it. That is a concentration step, not a dilution, and it needs evaporation or a stronger stock.