Molar mass is a sum, and the best way to learn a sum is to watch it done several times on compounds you actually meet. This guide works six of them — water, table salt, glucose, caffeine, aspirin and sulfuric acid — with every atomic weight, every multiplication and every addition shown, so that any single line can be checked by hand. It then turns those masses into the two conversions every laboratory task needs, grams to moles and moles to grams, and closes with the two refinements that change the answer: hydrates, where the water counts, and ionic compounds, where the same sum goes by the name formula mass. Every number uses the standard atomic weights the calculator uses: hydrogen 1.008, carbon 12.011, nitrogen 14.007, oxygen 15.999, sodium 22.990, sulfur 32.06, chlorine 35.45.

The one method, stated once

For any formula, the molar mass is the sum of each element’s contribution, and each contribution is the number of atoms of that element in the formula times that element’s standard atomic weight. Water, H2O, has two hydrogens and one oxygen, so its molar mass is 2 × 1.008 + 1 × 15.999 = 2.016 + 15.999 = 18.015 g/mol. That is the entire method. Everything in this guide is that sentence applied to longer formulas, and the only skills that matter are reading subscripts correctly — including the unwritten 1, as in the O of H2O — and adding carefully. Brackets multiply everything inside them, and a dot in a hydrate formula adds a whole water unit, both covered in the final section.

Two reading rules prevent most errors. First, a subscript belongs to the element directly before it, and a bracket’s subscript belongs to the whole bracket: in Ca(OH)2 the 2 doubles both the oxygen and the hydrogen, giving Ca1O2H2, not Ca1O1H2. Second, capitalisation is part of the symbol: Co is cobalt and CO is carbon monoxide, and a formula typed with the wrong case names a different substance or no substance at all. The calculator enforces the same rule, which is why its first FAQ is about capitalisation. With those two rules, every example below can be reproduced by hand in under a minute.

Water and table salt: the two simplest sums

Water, H2O, is the reference example: 2 × 1.008 = 2.016 for hydrogen and 1 × 15.999 = 15.999 for oxygen, totalling 18.015 g/mol. Its percent composition follows by division: hydrogen is 2.016 ÷ 18.015 = 11.2% and oxygen is 15.999 ÷ 18.015 = 88.8%, which is a useful self-check — if a candidate molar mass for water does not give roughly 11% hydrogen, the arithmetic has gone wrong. Table salt, NaCl, is simpler still: sodium 1 × 22.990 = 22.990 and chlorine 1 × 35.45 = 35.45, totalling 58.440 g/mol. Salt is also the example that introduces the second name for the same sum: because NaCl is an ionic compound that exists as a lattice rather than as discrete molecules, chemists call 58.440 g/mol its formula mass rather than its molecular weight. The number is computed identically; only the name changes, and the calculator returns it by the same addition either way.

Table 1 — The two simplest sums, with percent composition as a check.

Glucose: the six-carbon sum, checked by percentages

Glucose, C6H12O6, is the first sum where keeping the columns tidy matters. Carbon contributes 6 × 12.011 = 72.066, hydrogen contributes 12 × 1.008 = 12.096, and oxygen contributes 6 × 15.999 = 95.994. Adding them gives 72.066 + 12.096 + 95.994 = 180.156 g/mol. The percent composition is the backward check that ties this guide to its companion on empirical formulas: carbon is 72.066 ÷ 180.156 = 40.0%, hydrogen is 12.096 ÷ 180.156 = 6.7%, and oxygen is 95.994 ÷ 180.156 = 53.3% — exactly the analysis from which the empirical formula CH2O is derived, and the reason the multiplier from empirical to molecular formula is 180.156 ÷ 30.026 = 6. A molar mass that does not reproduce its own percent composition has an addition error, and this check finds it in seconds.

Glucose is also the compound where the difference between average and monoisotopic mass first becomes visible, though it does not change the answer here. The value 180.156 g/mol is the average molar mass, built from standard atomic weights that average over natural isotopes. The monoisotopic mass, built from the lightest isotope of each element, is a different and smaller number used in mass spectrometry. For weighing, dissolving and converting grams to moles, the average mass is the correct one, and it is the one the calculator returns. The distinction is stated here so that a monoisotopic value found elsewhere is recognised as a different quantity, not a correction to this one.

Caffeine: four elements, one careful addition

Caffeine, C8H10N4O2, is the longest sum in this guide and the best test of the method. Carbon contributes 8 × 12.011 = 96.088, hydrogen contributes 10 × 1.008 = 10.080, nitrogen contributes 4 × 14.007 = 56.028, and oxygen contributes 2 × 15.999 = 31.998. Adding in stages keeps the addition honest: 96.088 + 10.080 = 106.168, plus 56.028 = 162.196, plus 31.998 = 194.194 g/mol. The staged addition is not pedantry; with four elements, a single dropped digit is the most likely error, and staging localises it to one step. Caffeine’s percent composition — carbon 49.5%, hydrogen 5.2%, nitrogen 28.9%, oxygen 16.5% — sums to 100.1% only because each figure is rounded to one decimal place, which is a rounding artefact, not an error: the unrounded figures sum to exactly 100%.

Caffeine also shows why the calculator’s element-by-element breakdown is more useful than a bare total. A total of 194.194 g/mol cannot be checked by inspection, but a breakdown can: nitrogen’s 56.028 is more than a quarter of the total, which is plausible for a four-nitrogen compound, while a breakdown showing nitrogen at, say, 14.007 would immediately reveal that the subscript 4 had been read as 1. When a formula is typed into the calculator, read the breakdown before trusting the total, especially for formulas with subscripts above 4, where a misread subscript changes the total by tens of grams per mole.

Aspirin: nearly the same mass as glucose, a different compound

Aspirin, C9H8O4, is included for one reason: its molar mass is 180.159 g/mol, within 0.003 g/mol of glucose’s 180.156 g/mol, and the two compounds have nothing else in common. The addition is carbon 9 × 12.011 = 108.099, hydrogen 8 × 1.008 = 8.064, oxygen 4 × 15.999 = 63.996, totalling 108.099 + 8.064 + 63.996 = 180.159 g/mol. Its percent composition — carbon 60.0%, hydrogen 4.5%, oxygen 35.5% — is entirely different from glucose’s, which is how the two are told apart by analysis even though a balance alone could barely distinguish them. The lesson generalises: molar mass is a property of a formula, not an identity card for a substance, and two different formulas can share a mass to within weighing error.

The near-coincidence also explains a practical laboratory caution. Weighing out 180 grams of an unknown and calling it one mole is only valid if the formula is known; weighing out 180.159 grams of aspirin is one mole of aspirin, and weighing out 180.156 grams of glucose is one mole of glucose, but the two piles are not interchangeable in any reaction, because the reactions count molecules, not grams. Molar mass converts between the countable and the weighable for a known substance; it does not identify an unknown one. Identification needs the formula first, from analysis or labelling, and then the mass follows.

Sulfuric acid and calcium carbonate

Sulfuric acid, H2SO4, is the compound the calculator’s own guide uses as its default conversion example, so it is worth having by hand: hydrogen 2 × 1.008 = 2.016, sulfur 1 × 32.06 = 32.06, oxygen 4 × 15.999 = 63.996, totalling 2.016 + 32.06 + 63.996 = 98.072 g/mol. That makes 98.072 grams exactly one mole, and 2 moles exactly 196.144 grams — the pair of numbers the hub’s moles section uses, and a good pair to memorise, since sulfuric acid is the most common concentrated laboratory acid. Calcium carbonate, CaCO3, exercises the bracket-free multi-element sum with a metal: calcium 1 × 40.078 = 40.078, carbon 1 × 12.011 = 12.011, oxygen 3 × 15.999 = 47.997, totalling 40.078 + 12.011 + 47.997 = 100.086 g/mol. A useful consequence is that 100 grams of calcium carbonate is 0.9991 moles — just short of one mole, a figure the hub’s conversion table uses and a reminder that round masses rarely give round mole counts.

Table 2 — All six worked masses in one place.

Turning the masses into grams and moles

With the masses in hand, the two conversions are single divisions and multiplications. Moles from grams: divide the mass by the molar mass. So 36.030 grams of water is 36.030 ÷ 18.015 = 2.000 moles, and 10 grams of table salt is 10 ÷ 58.440 = 0.1711 moles. Grams from moles: multiply the moles by the molar mass. So 0.5 moles of glucose weighs 0.5 × 180.156 = 90.078 grams, and 0.25 moles of glucose weighs 0.25 × 180.156 = 45.039 grams. The calculator’s Advanced options panel performs both directions from the formula above, reading the molar mass from the calculator itself, so changing the formula changes the conversion without retyping — but the arithmetic is exactly the arithmetic shown here, and any panel result that disagrees with a hand calculation has a mistyped formula behind it, not a different method.

The unit check is the fastest error-catcher in both directions: grams divided by grams per mole leaves moles, and moles times grams per mole leaves grams. If a calculation produces grams where moles were expected, a division has been done upside down. A second check is magnitude: one mole of any of these compounds weighs between 18 and 195 grams, so a result claiming thousands of moles from a benchtop mass, or a fraction of a gram for a mole of caffeine, has a decimal error. Keep both checks — units and magnitude — and the conversions stop being a source of lost marks.

Hydrates and ionic compounds: the two refinements

A hydrate formula carries its water as a dot unit, and the dot water counts in full. Copper(II) sulfate pentahydrate, CuSO4·5H2O, is anhydrous CuSO4 at 63.546 + 32.06 + 63.996 = 159.602 g/mol plus five waters at 5 × 18.015 = 90.075 g/mol, totalling 249.677 g/mol. Weighing the pentahydrate with the anhydrous mass understates the weighed moles by more than a third — the water is 36.1% of the total — and every solution made from that weighing inherits the error. The calculator handles dot formulas, and the hub’s hydrates section works the same example at length; the point here is only that the dot is not decoration and the multiplier after it multiplies the whole water unit, not just the hydrogen.

Ionic compounds carry the second refinement, and it is only a name. Sodium chloride’s 58.440 g/mol is a formula mass because the compound forms a lattice, not molecules; calcium carbonate’s 100.086 g/mol is likewise a formula mass in strict usage. The calculator and this guide use molar mass for both, because the arithmetic and the conversions are identical and because most users meet the term molar mass first. Nothing in the method changes: count the atoms in the formula unit, multiply by atomic weights, add. Whether the result is called molecular weight, molar mass or formula mass, it is the same sum, and the same sum is what the calculator returns.

Frequently asked questions

How do you calculate molar mass from a formula?

Multiply the number of atoms of each element in the formula by that element’s standard atomic weight, then add the contributions together. For water, H2O, that is 2 times 1.008 for hydrogen plus 15.999 for oxygen, giving 18.015 grams per mole. Brackets multiply everything inside them, and a dot in a hydrate adds a whole water unit.

What is the molar mass of water and of glucose?

Water, H2O, is 18.015 grams per mole: 2 times 1.008 plus 15.999. Glucose, C6H12O6, is 180.156 grams per mole: 6 times 12.011 plus 12 times 1.008 plus 6 times 15.999. Both use standard atomic weights, the same weights the calculator uses, so typing either formula into the calculator returns the same total with the same breakdown.

Is molar mass the same as molecular weight?

For molecular substances, yes: molecular weight and molar mass name the same number, in grams per mole. For ionic compounds such as table salt, the strict name is formula mass, because the compound forms a lattice rather than discrete molecules, but the number is computed by the same addition. This guide uses molar mass throughout for both cases.

What is gram formula mass?

Gram formula mass is the mass in grams of one mole of formula units of an ionic compound — the same sum as molar mass, under the name used when the substance has no molecules. Table salt’s gram formula mass is 58.440 grams: 22.990 for sodium plus 35.45 for chlorine. It converts grams to moles for ionic compounds exactly as molar mass does for molecular ones.

How do you convert grams to moles with these numbers?

Divide the mass in grams by the molar mass in grams per mole. For example, 36.030 grams of water is 36.030 divided by 18.015, which is 2.000 moles, and 10 grams of table salt is 10 divided by 58.440, which is 0.1711 moles. To go the other way, multiply: 0.5 moles of glucose weighs 0.5 times 180.156, which is 90.078 grams.

Does the calculator use average or monoisotopic masses?

Average masses, built from standard atomic weights that average over natural isotopes. That is the correct mass for weighing, dissolving and converting grams to moles. Monoisotopic masses, built from the lightest isotope of each element, are a different quantity used in mass spectrometry, and they are not what the calculator returns or what this guide’s examples use.