Molar Mass Calculator

What a molar mass actually is

Weigh out 6.02214076 × 10²³ formula units of a substance and record what the balance says in grams: that figure, per mole, is its molar mass. Its usefulness comes from a coincidence of definition rather than anything deep: because the mole was set up so that a mole of carbon-12 weighs almost exactly 12 g, the molar mass of any substance in g/mol is numerically the same as the mass of one of its formula units in unified atomic mass units. That is why the periodic table can be read directly as a table of molar masses.

Calculating one is arithmetic. Read the formula, count how many atoms of each element it contains, multiply each count by that element's standard atomic weight, and add. The only place it goes wrong is the counting, which is why the worked example above sets the atom count beside each element's weight instead of going straight to a total. A miscount is invisible in a total and obvious in a column.

Reading a formula correctly

Chemical notation has a small set of rules for what a number in a formula refers to. These are the ones that are easy to get wrong by hand.

• A subscript counts only the symbol it is attached to. H₂SO₄ contains two hydrogens; the sulfur and the oxygen are untouched by that 2.
• A subscript after a bracket multiplies everything inside it. Ca(OH)₂ is one calcium, two oxygen and two hydrogen, not one of each with two hydroxides mentioned.
• Brackets nest. K₄[Fe(CN)₆] contains six carbon and six nitrogen, because the 6 inside multiplies the CN group and the outer bracket then multiplies nothing further.
• A dot introduces water of crystallisation, and the number in front of it counts whole water molecules. CuSO₄·5H₂O is copper sulfate plus five waters, so its oxygen count is nine, not four.

Two-letter symbols are the classic trap. CO is carbon monoxide; Co is cobalt. NO is nitrogen monoxide; No is nobelium. Case is not decoration in a chemical formula, and a calculator that silently guesses which one you meant is worse than one that asks.

Charges are usually written with a caret — SO4^2- — or in brackets, PO4(3-). Written bare, as in Fe3+, a numeric charge is genuinely ambiguous, because NH4+ has exactly the same shape and its 4 is an atom count rather than a charge. The habit worth acquiring is to mark the magnitude explicitly, so that a digit sitting between a symbol and a sign can only be read one way. Nothing about that is a quirk of any particular tool; it is a defect in the notation that predates all of them.

Why the answer may differ from your textbook's

Molar masses drift slightly between references, and the reason is not sloppiness.

For fourteen of the elements there is no single standard atomic weight to look up. Isotopic composition varies measurably with the origin of the sample, so IUPAC publishes an interval in place of a number: hydrogen sits somewhere in [1.00784, 1.00811], sulfur in [32.059, 32.076]. Alongside the intervals, IUPAC issues a single conventional atomic weight per element for use wherever a range cannot be. Those are the weights behind the figures on this page. Older textbooks predate the intervals and quote whatever single value was current when they were printed.

The practical effect is small but real. Sulfuric acid comes out at 98.072 g/mol from the current conventional weights and is quoted as 98.08 in a great many older sources. Neither is wrong; they are answers to slightly different questions.

Knowing which elements those fourteen are is what tells you how many of your figures are load bearing. Hydrogen, carbon, nitrogen, oxygen, sulfur and chlorine are all on the list, so almost every formula in an introductory course contains at least one of them, and sulfuric acid happens to contain nothing else. Work the sum from the ends of the intervals instead of the conventional values and H₂SO₄ lands anywhere between 98.071 and 98.091 g/mol — the sulfur alone accounts for 0.017 of that, because sulfur from a sulfide ore and sulfur from a sulfate deposit are not quite the same substance. Three figures are defensible anywhere; the fourth depends on where the sample was dug up; a fifth is decoration. A formula whose elements are all off the list, KMnO₄ among them, carries no such caveat and is good to the last digit its weights are published to.

Elements with no stable isotope have a related problem in a sharper form. Technetium has no standard atomic weight at all, only the mass of its longest-lived isotope, and a molar mass containing technetium inherits that caveat wholesale.

Getting the arithmetic right by hand

The worked example above is laid out the way the calculation should be laid out on paper, because the most common failure in a hand calculation is not the multiplication — it is a running total quietly attributed to the wrong symbol.

Work element by element, write the count and the atomic weight side by side, multiply, and only then add the column. Round at the end and not before. Trimming every subtotal to two decimals on the way down and adding those trimmed figures shifts the answer by a few hundredths — precisely the margin that makes a correct method look like a wrong one.

If a percent composition is what you are after, the same breakdown gives it directly — each element's contribution divided by the total. That calculation has its own page, with the empirical-formula step attached to it.

Molar mass, molecular mass and formula mass

Three terms get used almost interchangeably and are not quite the same thing, which matters when a question is worded precisely.

Molecular mass is the mass of one molecule, in unified atomic mass units. It only applies to substances that genuinely exist as molecules — water, carbon dioxide, glucose.

Formula mass is the same arithmetic applied to an ionic compound, which has no molecules at all. What the formula NaCl records is a one-to-one ratio of ions held in a lattice, and its formula mass is the mass of one unit of that ratio.

Molar mass is either of those scaled up to a mole and expressed in g/mol. It is the one you almost always want, because it is the number that converts between a mass you can weigh and an amount you can use in a reaction.

Numerically all three are the same. Using the right word is about describing the substance correctly, not about getting a different answer.

What to do with it next

A molar mass on its own is rarely the endpoint. It is the bridge between the balance in front of you and the equation on the page:

• Grams to moles: divide the mass by the molar mass.
• Moles to particles: multiply by Avogadro's number.
• Moles to moles across a reaction: use the coefficients of the balanced equation.
• Moles back to grams: multiply by the molar mass of whatever you have ended up with.

Every stoichiometry problem is some path through those four steps, and a wrong molar mass at the start propagates through all of them without ever looking wrong.