Molecular Weight Calculator

Molar mass = Σ (atoms of an element × the atomic weight of that element) · for a hydrate, add the coefficient times 18.015

M

Molar mass of the compound, in grams per mole — the number this page reports

atoms

How many atoms of that element the formula contains: the subscript after its symbol, or the multiplier after a bracket, or both multiplied together

atomic weight

The atomic weight of the element, in grams per mole — a property of the element, taken from the reference table below

Σ

Summed over every element in the formula, including the ones written inside brackets

·

The dot in a hydrated formula such as CuSO4·5H2O. The number after it counts the whole water group, so five waters mean ten hydrogen atoms and five oxygen atoms

Use it when you have a formula and need its molar mass — to weigh out a mole of something, to convert grams to moles, or to check a number printed on a reagent bottle. It is also the page to check when a formula has brackets or water of crystallisation, because those are the two places a hand calculation goes wrong: in Ca(OH)2 the subscript outside the bracket multiplies both atoms inside it, and in CuSO4·5H2O the five multiplies two hydrogen and one oxygen per water.

1. The molar mass of water, down to the mass of each element

   1. Read the formula as two hydrogens and one oxygen: H2O
   2. Hydrogen: 2 × 1.008 = 2.016 grams per mole
   3. Oxygen: 1 × 15.999 = 15.999 grams per mole
   4. Add them: 2.016 + 15.999 = 18.015 grams per mole
   5. The atom count is 2 + 1 = 3 atoms per molecule

   The same sum splits the mass by element: oxygen is 15.999 ÷ 18.015 = 88.81% of the mass and hydrogen the other 11.19%. That ratio is what makes water's molar mass worth knowing — a gram of water is not a gram of hydrogen.

2. A hydrated salt, where the dot does the work

   1. Split the formula at the dot: CuSO4 on the left, 5H2O on the right
   2. Left side: 63.546 (Cu) + 32.06 (S) + 4 × 15.999 (O) = 159.602 grams per mole
   3. Right side: 5 × 18.015 = 90.075 grams per mole — five whole water molecules
   4. Add the two: 159.602 + 90.075 = 249.677 grams per mole
   5. Count the atoms: 1 + 1 + 4 = 6 on the left, and 5 × 3 = 15 on the right, so 21 in total

   The five waters are 90.075 ÷ 249.677 = 36.08% of the mass of the blue crystals. That is why the anhydrous and hydrated forms of the same salt are not interchangeable by weight, and why a bottle that has sat open gives a low reading.

The atomic weights behind this page are the CIAAW abridged values for the elements' natural terrestrial abundance, quoted to four or five significant figures. They are standard atomic weights, not exact masses, so the third decimal place of a molar mass is already beyond what the source supports: water is 18.015 here, and a more precise figure would be 18.0153, with the last digit still moving depending on the sample. For weighing out a reagent this is far more precision than you need; for a mass spectrometer it is not enough, and you should use the exact isotopic masses instead. Thirty-four elements have no standard atomic weight at all — technetium, promethium, polonium, astatine, radon, francium, radium, actinium and everything from neptunium upward — because they have no stable isotopes for a natural abundance to be measured from. Formulas containing them are rejected rather than answered with the mass of a particular isotope, since that number would look entirely normal while resting on an assumption the page never stated. Isotopes are not understood either: D2O is not a formula this page accepts, and neither is an ion such as Na+, a structural formula with hyphens such as CH3-CH2-OH, or a state symbol. Finally, molar mass is a property of the formula alone — this page says nothing about how a substance behaves, whether it dissolves, or whether the compound exists at all.

What is the difference between molecular weight and molar mass?

Numerically they are the same number, which is why this calculator reports a single figure. Molecular weight is the mass of one molecule relative to one twelfth of a carbon-12 atom, so it is a pure ratio with no unit; molar mass is the mass of one mole of the substance, so it carries the unit grams per mole. Both come out at 18.015 for water. The distinction matters in writing rather than in arithmetic, and the symbol differs too: M for molar mass, and the dimensionless relative molecular mass for the other.

How do I calculate the molar mass of a compound by hand?

Multiply each element's atomic weight by the number of atoms of that element in the formula, then add the results. For glucose, C6H12O6, that is 6 × 12.011 = 72.066 for carbon, 12 × 1.008 = 12.096 for hydrogen and 6 × 15.999 = 95.994 for oxygen, giving 180.156 grams per mole. The two places a hand calculation goes wrong are brackets and the dot: the subscript after a bracket multiplies every element inside it, and the number after the dot in a hydrate multiplies a whole water molecule.

Why can't I get a figure for PuO2 or Tc2O7?

Because those elements have no standard atomic weight. Technetium, promethium, polonium, astatine, radon, francium, radium, actinium and every element from neptunium upward are radioactive with no stable isotopes, so there is no natural abundance to average over and the CIAAW table prints a dash in place of a value. Filling in the mass of one isotope would produce a number that looks perfectly ordinary — plutonium-244 gives 276.998 for PuO2 — while silently assuming you meant that isotope and not another, which differ by around 2%.

How many decimal places should I keep?

Three is what textbooks print and what this page shows, and it is more than the underlying data justifies. Standard atomic weights are quoted to four or five significant figures, so the last digit of a molar mass is already uncertain; water is 18.015 by these figures and 18.0153 by more precise ones. For weighing a reagent on a balance that reads to a milligram, 0.01 g/mol is ample: the error from the atomic weights is smaller than the error from the balance.

Does the formula parser understand brackets and water of crystallisation?

Yes to both, and they nest. Round brackets, square brackets and the dot are all understood, and a coefficient in front of the whole formula multiplies through everything after it: 2Fe4[Fe(CN)6]3 expands to 7 iron, 18 carbon and 18 nitrogen atoms once the inner 6 is multiplied by the outer 3 and then by the 2. Spaces are ignored in most positions — around the dot, between elements, at either end — but there is one place they are not: a digit may not follow a space. That is because the failure it would hide is invisible. Copy the dot of a hydrated salt badly and CuSO4·5H2O arrives as CuSO4 5H2O, which is a perfectly legal formula reading forty-six oxygens and two hydrogens, 833.576 grams per mole instead of 249.677, with nothing on the page to suggest anything went wrong. So the field refuses that shape instead of guessing, and the fix is to put the dot back. Leading zeros such as H02O are read as H2O.

• Standard Atomic Weights — abridged to four significant figures — Commission on Isotopic Abundances and Atomic Weights (CIAAW), IUPAC
• SI Units — Amount of Substance: the mole — National Institute of Standards and Technology (NIST)