What molar mass is and why every calculation needs it
Molar mass is the mass of one mole of a substance, expressed in grams per mole. One mole is exactly 6.02214076 × 10²³ entities — the Avogadro constant fixed by the 2019 revision of the SI. So the molar mass of water, 18.015 g/mol, says that 18.015 grams of water contains 6.02214076 × 10²³ water molecules.
You need it because a balance measures mass and chemistry happens in whole-number ratios of particles. A balanced equation tells you that two molecules of hydrogen react with one of oxygen; it says nothing about grams. Molar mass is the only conversion factor that connects the two, and it appears in essentially every quantitative problem you will meet: mole–mass conversions, solution preparation, yield prediction and titration arithmetic.
Three names describe nearly the same number and are worth keeping straight. Relative molecular mass (Mᵣ) is a dimensionless ratio against one twelfth of a carbon-12 atom. Molecular weight is the older term for the same quantity. Formula weight is what you say for an ionic solid such as sodium chloride, which has no discrete molecule — you are weighing a formula unit, not a molecule. All three come out to the same digits; only molar mass carries the unit g/mol.
The formula, and why atomic weights are not whole numbers
The rule is a plain sum: multiply the count of each element in the formula by that element's standard atomic weight, then add. For H₂SO₄ that is 2 hydrogens, 1 sulfur and 4 oxygens.
The atomic weights themselves are not integers because almost every element on Earth is a mixture of isotopes. Chlorine is roughly three parts chlorine-35 to one part chlorine-37, so its standard atomic weight is 35.45 — an abundance-weighted average, not the mass of any single atom. This is why a mass spectrometer of a chlorinated compound shows two peaks two mass units apart while the balance sees only the average.
IUPAC publishes these values and revises them. Some elements have such variable terrestrial isotopic composition that IUPAC now quotes an interval rather than a single number: hydrogen is [1.00784, 1.00811] and sulfur is [32.059, 32.076]. This calculator uses the abridged standard atomic weights, the conventional single values IUPAC publishes for exactly this purpose. That is why you may see 98.07 here where an older textbook prints 98.08 for sulfuric acid — a difference of one part in ten thousand, far below the precision of any ordinary analytical balance.
Reading a formula correctly is half the job. A subscript multiplies only the symbol immediately before it. A bracket subscript multiplies everything inside the bracket. A dot introduces a separate unit whose leading number multiplies that whole unit, so CuSO₄·5H₂O means one copper sulfate plus five entire waters — ten hydrogens and five extra oxygens, not five hydrogens.
Worked example: copper(II) sulfate pentahydrate
Blue vitriol, CuSO₄·5H₂O, is the classic hydrate because the anhydrous salt is white and the pentahydrate is deep blue. Work it out term by term.
- Copper. One atom × 63.546 = 63.546 g/mol.
- Sulfur. One atom × 32.06 = 32.06 g/mol.
- Oxygen in the sulfate. Four atoms × 15.999 = 63.996 g/mol.
- Water of crystallisation. One water is 2 × 1.008 + 15.999 = 18.015 g/mol. Five of them: 5 × 18.015 = 90.075 g/mol.
- Add. 63.546 + 32.06 + 63.996 + 90.075 = 249.677 g/mol.
Now use it. To make 250 mL of 0.100 mol/L copper sulfate you need 0.100 × 0.250 = 0.0250 mol, so weigh 0.0250 × 249.677 = 6.242 g of the pentahydrate. Weigh 0.0250 × 159.602 = 3.990 g if you have the anhydrous salt instead. Using the wrong one over-delivers copper by 56%, which is the single most common preparation error in a teaching lab.
Note where the mass sits: the five waters carry 90.075 of the 249.677 g/mol, or 36.1% of the mass. Heat the crystals to constant mass and that is exactly the fraction you drive off, which is how a gravimetric water-of-hydration experiment is graded.
How to read the result
Check the magnitude first. A small inorganic salt lands between 40 and 300 g/mol; a common organic solvent between 30 and 200; a drug molecule typically 150–600; a protein runs to tens of thousands and is quoted in daltons rather than derived from a formula. If your answer is an order of magnitude away from the family you expect, you have mis-typed a subscript.
Then check the element shares in the table. For an organic compound you can compare the calculated carbon and hydrogen percentages with a CHN elemental analysis report; agreement within 0.4 percentage points is the usual publication criterion for a new compound. For a fertiliser you can read the nitrogen share directly — the percent composition calculator does that job specifically.
Finally, decide how many figures you need. Four significant figures on molar mass is enough for anything you weigh on a four-place analytical balance, because your mass uncertainty of ±0.0001 g on a 1 g sample is one part in ten thousand. Carrying more digits is harmless; rounding the atomic weight of chlorine to 35.5 before multiplying by six, on the other hand, has already cost you 0.3 g/mol.
Molar masses of common laboratory compounds
| Compound | Formula | Molar mass (g/mol) |
|---|---|---|
| Water | H₂O | 18.015 |
| Hydrogen chloride | HCl | 36.458 |
| Sodium hydroxide | NaOH | 39.997 |
| Carbon dioxide | CO₂ | 44.009 |
| Ethanol | C₂H₆O | 46.069 |
| Potassium hydroxide | KOH | 56.105 |
| Sodium chloride | NaCl | 58.440 |
| Calcium hydroxide | Ca(OH)₂ | 74.092 |
| Sodium hydrogen carbonate | NaHCO₃ | 84.006 |
| Sulfuric acid | H₂SO₄ | 98.072 |
| Calcium carbonate | CaCO₃ | 100.086 |
| Ammonium sulfate | (NH₄)₂SO₄ | 132.134 |
| Potassium permanganate | KMnO₄ | 158.032 |
| Iron(III) oxide | Fe₂O₃ | 159.687 |
| Calcium nitrate | Ca(NO₃)₂ | 164.086 |
| Silver nitrate | AgNO₃ | 169.874 |
| Glucose | C₆H₁₂O₆ | 180.156 |
| Copper(II) sulfate pentahydrate | CuSO₄·5H₂O | 249.677 |
Values here are the sums this calculator produces. A textbook using unabridged atomic weights may differ in the third decimal.
Mistakes that change the answer
- Dropping the hydrate. Ordering copper sulfate and weighing out the anhydrous molar mass for the pentahydrate in the bottle is the classic error. Always read the label, not the name.
- Getting capitalisation wrong.
COis carbon monoxide at 28.010 g/mol;Cois cobalt at 58.933. The calculator flags a symbol it cannot find, but it cannot flag a valid symbol you did not mean. - Applying a bracket subscript to only one atom. Ca(NO₃)₂ contains two nitrogens and six oxygens. Reading it as one nitrogen loses 14.007 g/mol.
- Rounding atomic weights before multiplying. Round at the end, never at each term.
- Confusing molar mass with equivalent mass. Sulfuric acid is 98.072 g/mol but 49.036 g per mole of protons. Normality problems need the second number.
- Using average molar mass where the monoisotopic mass is required. High-resolution mass spectrometry reports the exact mass of the most abundant isotopologue, which for glucose is 180.0634, not the average 180.156.
Where molar mass sits among related quantities
Molar mass is the input to almost everything else on this site's chemistry pages. Divide a mass by it to get moles, then apply a coefficient ratio with the stoichiometry calculator, or find which reactant runs out first with the limiting reagent calculator. Go the other way — from an experimentally determined percent composition back to a formula — with the empirical formula calculator.
Two related masses are worth naming because they are not interchangeable. The monoisotopic mass sums the masses of the most abundant isotope of each element and is what a high-resolution mass spectrometer measures; it is always a little lower than the average molar mass for organic molecules. The equivalent mass divides molar mass by the number of reacting units — protons for an acid, electrons for a redox agent — and survives in normality calculations and in water treatment practice.
For polymers there is no single molar mass at all, only a distribution, reported as a number-average Mₙ and a weight-average M𝓌 whose ratio is the dispersity. A formula-based calculator cannot give you those; you need gel permeation chromatography.
One historical note that still shapes the numbers: until 2019 the mole was defined as the number of atoms in 12 grams of carbon-12, which made molar mass in g/mol exactly equal to relative molecular mass by definition. The redefinition fixed the Avogadro constant instead, so the equality is now experimental rather than definitional — but it holds to about one part in a billion, which is why nothing in practical chemistry changed.
Key terms
- Mole
- The SI unit of amount of substance, containing exactly 6.02214076 × 10²³ elementary entities.
- Standard atomic weight
- The abundance-weighted average relative atomic mass of an element as found in normal terrestrial materials, published by the IUPAC Commission on Isotopic Abundances and Atomic Weights.
- Formula unit
- The smallest whole-number ratio of ions in an ionic compound. NaCl has no molecules; its formula unit is one Na⁺ with one Cl⁻.
- Water of crystallisation
- Water molecules held in a fixed stoichiometric ratio within a crystal lattice, written after a dot and counted fully in the molar mass.