Molar mass calculator

What a molar mass is

A mole is a counted quantity, not a weight: the SI fixes it at exactly 6.022 140 76 × 10²³ elementary entities, which is the Avogadro number. The molar mass of a substance is what one mole of it weighs, in grams per mole, and working it out is addition: take each element's standard atomic weight, multiply by how many of that atom the formula holds, and add the results. The calculator above shows those steps as a table rather than only the answer, because the table is the method.

That addition works in grams per mole because of a constant that is almost exactly one. The molar mass constant converts an atom's relative mass into grams per mole, and CODATA's 2022 value for it is 1.000 000 001 05(31) × 10⁻³ kg/mol — one gram per mole to within about three parts in ten billion. So a standard atomic weight, which is a ratio and carries no unit of its own, doubles as a molar mass in grams per mole, and the two ways this site writes the same figure are both right: an element page gives lead's standard atomic weight as 207.2 daltons, the mass of one average atom, while this page gives 239.2 grams per mole for lead dioxide, the mass of a mole of formula units.

Why the answer has a bracket after it

A standard atomic weight is not a constant of nature. CIAAW publishes these values for what it calls normal materials, and names three reasons they carry an uncertainty: isotopic abundances that genuinely vary from sample to sample, the limits of measuring those abundances, and the limits of measuring the isotope masses themselves. Lead's weight is printed 207.2(11), the bracketed digits being the uncertainty in the last decimal place shown.

Lead is the clearest case on this site, which is why the worked example uses it. It falls in the first of those three groups, and CIAAW's full table gives its weight as an interval rather than a single figure, from 206.14 to 207.94 daltons — a spread of roughly one part in two hundred, where many elements are settled to one part in a hundred thousand. Lead's own page explains where that spread comes from. The effect is visible in the table above: lead's uncertainty contributes more than five hundred times what both oxygen atoms contribute, so it alone decides how precisely the molar mass of lead dioxide can be quoted.

The calculator adds the uncertainties straight rather than in quadrature. CIAAW states that its uncertainties are set so that the weight of a normal material should fall inside the quoted range, which makes each one a bound rather than the scatter of a single measurement, and adding bounds keeps the total a bound. The sum is then rounded to two significant figures, the ordinary convention for a combined uncertainty.

The elements with no standard atomic weight

Thirty-four of the 118 elements have no standard atomic weight at all — technetium, promethium, everything from polonium to actinium, and everything from neptunium onwards. CIAAW's table leaves them blank, so a formula containing one of them has no molar mass in the sense this page means. The calculator says so rather than substituting the mass of a single long-lived isotope, which would be a different quantity wearing the same name. The breakdown table still fills in for the other elements, and the element's own page explains what it prints instead.

Uranium, thorium and protactinium are not in that group: all three have standard atomic weights, so formulas containing them work normally.

What this calculator does not do

It reads neutral formulas with counts and brackets, and nothing else. A charge is refused rather than ignored: a charged species has gained or lost electrons, so it is not the neutral formula that a standard atomic weight describes, and dropping the charge silently would suggest it makes no difference. Hydrate dots are refused too. Capitals are never corrected without saying so, because CO is carbon monoxide while Co is cobalt: the calculator points out the rule rather than guessing which you meant.