Solution Dilution Calculator

Solve for

Stock concentration C1

Stock volume V1

Target concentration C2

Target volume V2

Result

The unknown100
Solvent to add140
Dilution factor2.4
C196
V1100
C240
V2240

The amount of solute does not change

Solves C1V1 = C2V2 for any of the four values and shows how much solvent to add.

All dilution rests on one idea: adding solvent does not change how much solute is present, only the volume it occupies. Hence C1V1 = C2V2 — concentration times volume stays the same.

The formula works in any concentration unit — percent, moles per litre, milligrams per millilitre — as long as both sides match. The same goes for volume: just do not mix litres with millilitres.

What this calculator shows

Any of the four values from the other three
The volume of solvent to add
The dilution factor

What to keep in mind

The formula treats volumes as additive. For ethanol and water that is false — those need a mass-based calculation.
Solvent goes into the concentrate rather than the other way round, and with acids that rule is absolute.

FAQs

What does C1V1 = C2V2 mean?

The amount of solute before dilution equals the amount after. Concentration falls by exactly the factor the volume rises by.

What units should I use?

Any, as long as they match on both sides: percent with percent, moles per litre with moles per litre.

How much water do I add?

The difference between the final and starting volumes. Taking 100 ml of concentrate to 240 ml means adding 140 ml.

Why does the formula fail for alcohol?

Because ethanol and water volumes do not add: the mixture takes up less room than its parts. That calculation runs on mass.

Worked example

Diluting to forty percent

Input: C1 = 96%, C2 = 40%, V2 = 240 ml

Output: V1 = 100 ml, add 140 ml of solvent

Note: A dilution factor of 2.4. For ethanol this arithmetic is wrong: the mixture contracts and slightly more water is needed — there is a separate calculator for that.

Useful links

All tools in Math & Statistics

Solution Dilution Calculator

Result

Related tools

Molar Mass Calculator

pH Calculator

Alcohol Dilution Calculator

Useful links