Mole Fraction Calculator (amount-of-substance fraction)

Background.

Weigh 46.069 g of ethanol into 100 g of water and, by mass, nearly a third of the mixture is ethanol: 31.54%. Count molecules instead and fewer than one in six is ethanol, a mole fraction of 0.1527. The gap comes from the molecules themselves. An ethanol molecule is about 2.56 times as heavy as a water molecule, so a given number of them accounts for far more of the weight.

The mole fraction is the counting version of composition: the amount of one component in moles divided by the total amount of everything in the mixture. Physical chemistry reaches for it whenever a property depends on how many particles are present rather than on what they weigh. Raoult's law gives a component's vapour pressure above an ideal solution as its mole fraction times the vapour pressure of the pure liquid. Dalton's law gives a gas's partial pressure as its mole fraction times the total pressure. Freezing-point depression, boiling-point elevation and osmotic pressure all depend on the number of solute particles.

You can start from whatever you have measured: two amounts in moles, two masses with their molar masses, a molality, or a mole fraction you want to express as a mass percent. Every route ends at the same set of results, the mole fractions of both components plus the mole percent and mass percent of component 1, with the amounts used shown alongside. The calculator works on two-component mixtures; component 1 is usually the solute, but the arithmetic treats the two alike.

The ratio itself is exact for any mixture, ideal or not. Where approximations come in is in the laws that use it, which assume ideal behaviour or dilute solutions.

What is mole fraction calculator?

Mole fraction, written x for liquids and solids and often y for gas mixtures, is x_B = n_B ⁄ Σn: the amount of substance B divided by the total amount of all components. It is a pure number between 0 and 1, and the fractions of all the components add to exactly 1. No volume enters it, so a mole fraction stays the same when a mixture is heated, cooled or compressed, which is not true of molarity. The IUPAC Green Book accepts three names, mole fraction, amount-of-substance fraction and amount fraction. NIST Special Publication 811 prefers amount-of-substance fraction, arguing that a quantity's name should not contain a unit, in the same way that mass fraction is not called kilogram fraction.

How to use this calculator.

1. 01Choose the mode that matches what you know: two amounts in moles, two masses, a molality, or a known mole fraction to convert into mass percent.
2. 02Enter both molar masses whatever the mode, since the mass percent needs them even when the mole fraction does not. Work them out from the exact formula, water of crystallisation included. The defaults are ethanol, 46.069 g/mol, and water, 18.015 g/mol.
3. 03In the masses mode, enter grams of each component; each mass is turned into moles before any ratio is taken.
4. 04In the molality mode, enter moles of component 1 per kilogram of component 2. The calculation works on exactly 1 kg of solvent, which for water is 55.51 mol.
5. 05To convert a mole percent, divide it by 100 first, so 15.3% goes in as 0.153.

The formula.

For two components, x₁ = n₁ ⁄ (n₁ + n₂) and x₂ = n₂ ⁄ (n₁ + n₂), so x₁ + x₂ = 1. The modes differ only in how n₁ and n₂ are found. From masses, each amount is nᵢ = mᵢ ⁄ Mᵢ. From a molality b, take exactly 1 kg of solvent: by definition it holds b moles of solute, and 1000 g of a solvent with molar mass M₂ is 1000 ⁄ M₂ moles, so x₁ = b ⁄ (b + 1000 ⁄ M₂). To turn a mole fraction into a mass percent, take 1 mol of mixture. It contains x₁ mol of component 1 weighing x₁M₁ grams and x₂ mol of component 2 weighing x₂M₂ grams, so mass percent = 100 × x₁M₁ ⁄ (x₁M₁ + x₂M₂).

That last expression shows when the two percentages part company. If component 1 has the larger molar mass, its mass percent is above its mole percent; if it is the lighter one, below; the two agree only when M₁ = M₂. Mole fractions outside 0 to 1, negative amounts or masses, molar masses of zero or less, and a mixture containing no substance at all have no meaning and are rejected. The endpoints are valid: x = 1 is a pure substance and x = 0 a component that is absent.

A worked example.

Frequently asked questions.

References& sources.

1. [1]IUPAC, 'Quantities, Units and Symbols in Physical Chemistry' (the Green Book), 3rd edition, 2nd printing 2012 (ISBN 978-0-85404-433-7), section 2.10, composition-of-mixtures table: 'mole fraction, amount-of-substance fraction, amount fraction', symbols x and y, definition x_B = n_B/Σᵢnᵢ, SI unit 1, with note 10 giving the x-for-condensed-phases and y-for-gases convention. Free full-text searchable PDF; retrieved 2026-07-29.
2. [2]NIST Special Publication 811, 2008 edition, section 8.6.2 'Mole fraction of B; amount-of-substance fraction of B' — quantity symbol x_B (also y_B), SI unit one (1), 'ratio of the amount of substance of B to the amount of substance of the mixture: x_B = n_B/n', with note 1 recording NIST's preference for the name 'amount-of-substance fraction'. Consulted as an authority independent of IUPAC; it agrees on every element of the definition. Retrieved 2026-07-29.
3. [3]NIST Special Publication 811, 2008 edition, section 7.10.2 '%, percentage by, fraction', worked example: 'x_B = 0.0025 = 0.25 %', together with the instruction to avoid '% (mol/mol)' and 'percentage by amount of substance', and the permitted ratio form x_B = 185 mmol/mol. Used as this page's independent numeric cross-check of the mole-percent output. Retrieved 2026-07-29.
4. [4]IUPAC Commission on Isotopic Abundances and Atomic Weights (CIAAW), Standard Atomic Weights 2021, abridged values — used to build the default molar masses on this page: carbon 12.011, hydrogen 1.008, oxygen 15.999, giving M(C2H6O) = 46.069 g/mol and M(H2O) = 18.015 g/mol. Retrieved 2026-07-29.