Molar Mass Calculator

What molar mass is and where the numbers come from

Molar mass is the mass of one mole of a substance, quoted in grams per mole. Add the standard atomic weights of every atom in the formula and the total is the molar mass, which is why 18.015 g of water holds 6.02214076 x 10²³ molecules and 58.44 g of sodium chloride holds one mole of formula units.

The weights come from the CIAAW abridged standard atomic weights, in the 2024 revision used here. The commission quotes five significant figures for most elements plus a stated uncertainty, so hydrogen is 1.0080 +/- 0.0002 and carbon is 12.011 +/- 0.002. Those uncertainties are not decoration: they decide how many decimals belong in your answer.

Fourteen elements have a standard atomic weight that is written as an interval rather than a single number, because the isotopic mix shifts with where the sample came from. Hydrogen runs from 1.00784 to 1.00811, carbon from 12.0096 to 12.0116, chlorine from 35.446 to 35.457. For everyday work the commission also publishes a conventional single value for each of them (hydrogen 1.008, carbon 12.011, chlorine 35.45), and the abridged table rounds those to the same figures. A formula built from these elements gives a mass that is right for normal material, with the interval folded into the uncertainty column.

The mole itself is not an approximation. Since the 2019 revision of the SI, one mole is exactly 6.02214076 x 10²³ entities, and the BIPM SI brochure gives the full definition. The bridge from atomic weight to grams per mole is therefore accurate to better than one part in a billion, and the atomic-weight uncertainty is always the larger error. The NIST atomic weights table publishes the same values with the isotopic compositions behind them if you want to see how each number was built.

How to read a chemical formula

A formula is a list of element symbols with counts attached. H2O means two hydrogen atoms and one oxygen atom. CH3COOH means two carbons, four hydrogens and two oxygens, which is why acetic acid is also written C2H4O2.

Brackets multiply everything inside them. Ca(OH)2 is one calcium, two oxygens and two hydrogens, 74.092 g/mol. K4[Fe(CN)6] is four potassium, one iron, six carbon and six nitrogen, 368.345 g/mol. Square brackets and round brackets behave the same way, and the calculator nests them to any depth.

Hydrates use a dot. CuSO4.5H2O is one copper sulfate unit plus five water molecules, so the counts are Cu 1, S 1, O 9 and H 10, and the molar mass is 249.677 g/mol. The dot separates two independent parts; it does not multiply the left side by the right side. Type the dot as a middle dot, an asterisk or a period and the calculator treats it the same.

Case matters, because the second letter of a symbol is always lowercase. Co is cobalt at 58.933 and CO is carbon monoxide at 28.010. Type the capitals the way a textbook prints them.

A charge is not part of the mass. SO4^2- and NH4+ keep their atoms and drop the charge sign. An electron weighs about 1/1836 of a proton, so leaving it out changes the sixth decimal place, far below the atomic-weight uncertainty.

Every element from hydrogen to uranium that has a recommended standard atomic weight is in the calculator, 84 symbols in all. Technetium and promethium are missing because no natural sample defines a standard atomic weight for them.

Worked example: glucose from the formula up

Take glucose, C6H12O6. Six carbons at 12.011 give 72.066. Twelve hydrogens at 1.0080 give 12.096. Six oxygens at 15.999 give 95.994. Add the three parts and 72.066 + 12.096 + 95.994 = 180.156 g/mol.

The uncertainty follows the counts. Carbon contributes 6 x 0.002, which is 0.012; hydrogen contributes 12 x 0.0002, which is 0.0024; oxygen contributes 6 x 0.001, which is 0.006. Combine those three in quadrature and the total uncertainty is 0.0136 g/mol. Write the answer as 180.156 +/- 0.014, or as 180.16 g/mol in a lab report. Dropping to 180.2 throws away a digit the atomic weights support.

The same recipe covers any formula. Sodium chloride is 22.990 + 35.45 = 58.440 g/mol. Calcium carbonate is 40.078 + 12.011 + 3 x 15.999 = 100.086 g/mol. Caffeine, C8H10N4O2, is 8 x 12.011 + 10 x 1.0080 + 4 x 14.007 + 2 x 15.999 = 194.194 g/mol, and the arithmetic is the whole method.

Two sugars with the same atoms per molecule is a reminder that molar mass and formula size are different things: glucose and caffeine both have 24 atoms, and caffeine is 14 g heavier per mole.

From grams to moles, and back again

Once the molar mass is known, the conversion is one division. Moles equal grams divided by grams per mole, so 5.844 g of sodium chloride is 5.844 / 58.440 = 0.1000 mol. Going the other way, 2.5 mol of glucose weighs 2.5 x 180.156 = 450.39 g.

Small samples are easier in millimoles, and the arithmetic is friendly: one millimole weighs the molar mass in milligrams. Glucose is 180.156 mg per mmol, so 0.500 g of it is 0.500 / 180.156 = 0.002776 mol, which is 2.775 mmol. A balance that reads to 0.001 g is quoting four significant figures, and millimoles keep the numbers short.

Counting particles is the same move with one more factor. One mole holds 6.02214076 x 10²³ formula units, so 0.1000 mol of sodium chloride is 6.022 x 10²² formula units and twice that many ions, 1.204 x 10²³, because each unit splits into one sodium and one chloride.

Three conversions cover most bench work: grams to moles, moles back to grams, and moles to particles. The fourth, moles per liter, needs a volume and belongs to the molarity calculator, not here.

Percent composition by mass

Percent composition answers a different question from molar mass: not how heavy one mole is, but where that weight sits. Divide the mass of one element in the formula by the molar mass and multiply by 100. For water the two hydrogens weigh 2.016 g and the oxygen 15.999 g, so hydrogen is 2.016 / 18.015 x 100 = 11.19 percent and oxygen is 88.81 percent.

The result is a mass fraction, not a count fraction. Hydrogen is two of the three atoms in water and only 11.19 percent of the weight, because an oxygen atom is roughly sixteen times heavier than a hydrogen atom.

Rounded percentages can add to 99.99 or 100.01 on a page, which is a printing artifact and not an error in the formula. The unrounded fractions always sum to exactly one.

Molar mass is not molarity, and a formula unit is not a molecule

Three quantities get mixed up because they all involve moles. Molar mass is grams per mole of substance, a property of the formula alone. Molarity is moles per liter of solution, and it changes when you add water or warm the beaker. Molality is moles per kilogram of solvent, and it does not. A compound has one molar mass and any number of molarities.

The worked difference: sodium chloride is 58.440 g/mol no matter what you do to it. Dissolve 58.44 g in water and top the flask to one liter and you have a 1.000 M solution, which is a different statement with a different unit. Add another liter of water and the molarity halves to 0.500 M while the molar mass is unchanged. The molality calculator covers the per-kilogram version and the freezing point shift that follows from it.

The second mix-up is between formula units and molecules. A mole of sodium chloride holds a mole of sodium ions and a mole of chloride ions and no NaCl molecules at all, because the solid is a lattice. The 58.440 figure is a formula mass. The same is true of calcium carbonate and of every ionic solid. Molecular substances such as water, glucose and caffeine do have molecules, and there the number is a molecular mass.

Molecular weight and molar mass are used as synonyms in most labs, and the difference is only in the unit: molecular weight is a dimensionless ratio, molar mass carries grams per mole. For any calculation on this page the two numbers are identical.

Where molar mass calculations go wrong

The first trap is the hydrate. Copper sulfate is sold as the blue pentahydrate, 249.677 g/mol, while the white anhydrous salt is 159.602 g/mol. Weigh 10.0 g of the blue crystals, divide by the anhydrous figure and you get 0.0627 mol instead of the true 0.0401 mol, an overstatement of 56 percent. Read the label, then use the formula that matches the bottle.

The second trap is rounding in the middle. Adding 6 x 12.01 instead of 6 x 12.011 moves glucose from 180.156 to 180.150, which looks harmless until the number is multiplied by an assay factor. Keep four significant figures through the steps and round once at the end.

The third is the interval element in a large molecule. Insulin is C257H383N65O77S6 and its molar mass is 5807.629 g/mol with an uncertainty of 0.54, most of it from 257 carbon atoms at 0.002 each. That is fine for a molecular weight determination and useless for distinguishing two insulins that differ by one methyl group, which is a 14 g/mol gap and still 26 times the uncertainty. Mass spectrometry resolves that by measuring isotopes, not average weights.

The fourth is treating a mixture as a compound. Air, seawater and gasoline have an average molar mass that depends on composition, and quoting a single value without the mix is meaningless. The fifth is the unit: 0.5 g is not 0.5 mg, and a molar mass entered in kg/mol is 1000 times too large. Check the units on the label before blaming the arithmetic.