Molar mass calculator

How to calculate molar mass

Multiply each element's atom count by its standard atomic weight and add the products; the sum, in grams per mole, is the molar mass. Water, H2O, is 2 × 1.008 + 15.999 = 18.015 g/mol, and glucose, C6H12O6, is 180.156 g/mol. The atomic weights are the IUPAC 2021 abridged values.

Molar mass worked by hand

Glucose, C6H12O6, step by step:

1. Count the atoms: 6 C, 12 H and 6 O.
2. Multiply each count by its atomic weight: 6 × 12.011 = 72.066, 12 × 1.0080 = 12.096 and 6 × 15.999 = 95.994.
3. Add the products: 72.066 + 12.096 + 95.994 = 180.156 g/mol.

A symbol with no number after it counts once. The same method gives these totals:

Hydrogen gas is H2, at 2.016 g/mol, while a single hydrogen atom, H, is 1.008 g/mol. Oxygen gas, O2, is likewise 31.998 g/mol, twice the 15.999 of one oxygen atom.

Mass percent composition

Each element's share is its contribution divided by the molar mass, times 100. In water, hydrogen supplies 2.016 ÷ 18.015 = 11.19% of the mass and oxygen the other 88.81%.

Percentages rounded separately need not total exactly 100: glucose's 40.00% C, 6.71% H and 53.28% O add up to 99.99%.

Brackets and hydrates

A number after a bracket multiplies everything inside it. Ca3(PO4)2 holds 3 Ca, 2 × 1 = 2 P and 2 × 4 = 8 O, for 310.174 g/mol. Brackets can nest: K4[Fe(CN)6] holds 4 K, 1 Fe, 6 C and 6 N, for 368.345 g/mol.

A hydrate dot adds whole water molecules. CuSO4·5H2O is CuSO4 (159.602 g/mol) plus 5 × 18.015, for 249.677 g/mol. Using the anhydrous value for the hydrate overstates the moles in a weighed sample by 56%.

Atomic number and atomic weight of common elements

The atomic number Z is the number of protons, a whole number that identifies the element: chlorine has 17 protons and iron 26.

The standard atomic weight is the average mass of the element's atoms as found in nature, relative to one twelfth of a carbon-12 atom. It is rarely a whole number; chlorine's 35.45 reflects its mix of chlorine-35 and chlorine-37 atoms.

These are the 2021 abridged values of the IUPAC Commission on Isotopic Abundances and Atomic Weights (CIAAW table). Lithium, chlorine and a few others carry fewer digits because their isotope mix varies between natural sources.

Elements with no standard atomic weight, such as technetium, take the mass number of a long-lived isotope instead, written in brackets as [97].

Mass of one molecule

One molecule's average mass in daltons is the same number as the molar mass: a water molecule averages 18.015 Da. In grams, divide by the Avogadro constant: 18.015 ÷ (6.02214076 × 10²³) = 2.991 × 10⁻²³ g.

Ionic solids such as NaCl contain no separate molecules, so their 58.440 g/mol describes one formula unit. OpenStax explains formula mass and the mole in more detail.

Common mistakes

• Wrong capitalization. Co is cobalt (58.933 g/mol); CO is carbon monoxide (28.010 g/mol). Every symbol starts with a capital letter, so h2o is not a formula.
• Atom instead of molecule. "Molar mass of oxygen" usually means the gas, O2 at 31.998 g/mol, not the atom at 15.999.
• Hydrate or anhydrous. Use the form on the bottle's label: CuSO4·5H2O is 249.677 g/mol and CuSO4 is 159.602.
• Whole-number atomic weights. Using 12, 1 and 16 gives glucose 180 instead of 180.156, 0.09% low; close enough for an estimate, not for analytical work.

Inputs worth checking

• Counts are plain digits after the symbol, as in H2O.
• Groups can use ( ), [ ] or { } and can nest.
• Hydrates can be written with ·, . or *, as in CuSO4.5H2O. A leading number works only after the dot, so 2H2O is rejected.
• Leave out charges and isotope labels: sulfate is SO4, at 96.056 g/mol.

Related calculators

Turn a weighed mass into moles with the grams-to-moles calculator, or a solution's mass and volume into molarity with the molarity calculator.