To calculate molar mass, write out the formula, count the atoms of each element, multiply each count by that element's standard atomic weight from the periodic table, and add the results. The total is the mass of one mole of the substance in grams per mole (g/mol). Water, for example, is 2(1.008) + 15.999 = 18.015 g/mol.
The adding is easy. Marks are lost in the counting: a subscript outside a bracket that only gets applied to one atom, or the five waters in a hydrate that get added once. This guide uses one counting method for brackets and hydrate dots alike, sorts out the three names for the same number (molar mass, Mr and molecular weight), and explains why the same hydrate comes out as 249.5 on one website and 249.68 on another.
The Molar Mass Formula
M = Σ (number of atoms of the element × its atomic weight), in g/mol. Then n = m / M turns a mass in grams into moles, and m = n × M turns moles back into grams.Why does a number read off the periodic table come out in grams per mole? The atomic mass unit and the mole are both defined from the same reference, so a molecule of water with a mass of about 18 u means a mole of water has a mass of about 18 g. OpenStax Chemistry 2e, section 3.1 uses exactly this water example. That shared reference is the whole trick: you never have to multiply by the Avogadro constant to get a molar mass.
This guide uses the abridged standard atomic weights published by IUPAC's Commission on Isotopic Abundances and Atomic Weights (CIAAW abridged table, based on the 2021 IUPAC technical report). Your textbook or exam data sheet may round them differently; the section on rounding below shows what that changes.
| Element | Atomic weight used here | Whole-number estimate |
|---|---|---|
| H | 1.008 | 1 |
| C | 12.011 | 12 |
| N | 14.007 | 14 |
| O | 15.999 | 16 |
| Na | 22.990 | 23 |
| Mg | 24.305 | 24 |
| Al | 26.982 | 27 |
| S | 32.06 | 32 |
| Cl | 35.45 | 35.5 |
| Cu | 63.546 | 64 |
How to Calculate Molar Mass, Step by Step
- Write the formula and expand it
Every subscript multiplies the atom (or bracket) directly in front of it. A subscript after a closing bracket multiplies everything inside. A number in front of a formula multiplies the whole formula.
- Make a count table
One row per element: element, number of atoms, atomic weight. Writing the count before you touch a calculator is what catches bracket mistakes.
- Multiply each row
Atoms × atomic weight gives that element's contribution in g/mol.
- Add the rows and attach the unit
The sum is the molar mass in g/mol. Keep the decimal places of the least precise atomic weight you used (the addition rule for significant figures).
- Estimate with whole numbers
Redo the sum with H = 1, C = 12, O = 16 and so on. Your answer should land within about one unit of the estimate for a small molecule.
Find the molar mass of H₂O.
Count: 2 H (the subscript 2 belongs to H) and 1 O (no subscript means 1).
Multiply: H: 2 × 1.008 = 2.016 g/mol and O: 1 × 15.999 = 15.999 g/mol.
Add: 2.016 + 15.999 = 18.015 g/mol. Estimate: 2(1) + 16 = 18. Close, so the count is right.
M(H₂O) = 18.015 g/molHow Brackets Change the Count
A bracket groups a polyatomic ion, and the subscript after the bracket says how many of those ions the formula holds. So every atom inside gets multiplied, not only the last one. Ammonium sulfate, a common fertiliser, has two brackets' worth of ammonium and one sulfate.
Find the molar mass of (NH₄)₂SO₄.
Expand the bracket: (NH₄)₂ is 2 N and 2 × 4 = 8 H. Then SO₄ adds 1 S and 4 O.
| Element | Atoms | Atoms × atomic weight (g/mol) |
|---|---|---|
| N | 2 | 2 × 14.007 = 28.014 |
| H | 8 | 8 × 1.008 = 8.064 |
| S | 1 | 1 × 32.06 = 32.06 |
| O | 4 | 4 × 15.999 = 63.996 |
Add: 28.014 + 8.064 + 32.06 + 63.996 = 132.134 g/mol. Sulfur's weight has only two decimal places, so round to two: 132.13 g/mol.
Estimate: 28 + 8 + 32 + 64 = 132.
M((NH₄)₂SO₄) = 132.13 g/molApplying the bracket's 2 to nitrogen and forgetting the hydrogens. Counting 4 H instead of 8 gives 28.014 + 4.032 + 32.06 + 63.996 = 128.10 g/mol, which is about 4 g/mol too low, exactly the four missing hydrogen atoms. The count table stops this, because you write "H: 8" before any multiplying happens.
How to Calculate the Molar Mass of a Hydrate
A hydrate is a crystal that holds a fixed number of water molecules per formula unit, called water of crystallisation. The raised dot in CuSO₄·5H₂O is not a multiplication sign. It means "plus": one CuSO₄ unit together with five whole water molecules. The coefficient 5 multiplies all of H₂O, both hydrogens and the oxygen.
Find the molar mass of CuSO₄·5H₂O, the blue crystals in most school labs.
Route 1, in two parts. Anhydrous part: 63.546 + 32.06 + 4(15.999) = 63.546 + 32.06 + 63.996 = 159.602 g/mol.
Water part: 5 × 18.015 = 90.075 g/mol. Total: 159.602 + 90.075 = 249.677 g/mol.
Route 2, one count table. Cu 1, S 1, O 4 + 5 = 9, H 5 × 2 = 10. So 63.546 + 32.06 + 9(15.999) + 10(1.008) = 63.546 + 32.06 + 143.991 + 10.08 = 249.677 g/mol. Both routes agree.
Round to two decimal places (sulfur again): 249.68 g/mol. Estimate: 64 + 32 + 64 + 90 = 250.
M(CuSO₄·5H₂O) = 249.68 g/molA useful by-product: water makes up 90.075 ÷ 249.677 × 100 = 36.08% of the crystal's mass. Heating the blue crystals drives that water off and leaves white anhydrous CuSO₄, which is the basis of the hydrate practice problem at the end (in a real lab, follow your course's own safety rules for heating).
Adding the water once. 159.602 + 18.015 = 177.617 g/mol is the molar mass of a monohydrate, not the pentahydrate. The opposite slip, reading the dot as "times" and multiplying 159.602 × 90.075, gives over 14,000 g/mol, which no estimate would accept.
Molar Mass vs Mr vs Molecular Weight
Three names describe the same digits, and different courses prefer different ones. The difference is only the unit.
| Name | Symbol | Unit | Water | Where you see it |
|---|---|---|---|---|
| Molar mass | M | g/mol (SI: kg/mol) | 18.015 g/mol | Every mole calculation, n = m / M |
| Relative formula (or molecular) mass | Mr | none | 18.015 | UK courses such as GCSE combined science |
| Molecular mass, molecular weight | none fixed | u (Da), often called amu | 18.015 u | The mass of one molecule |
Mr has no unit because it is a ratio: the mass of one molecule divided by the unified atomic mass unit, as the IUPAC Gold Book defines relative molecular mass. The units cancel. So on a GCSE paper write Mr = 18 with nothing after it, and in a mole calculation write M = 18 g/mol. Ionic compounds such as NaCl are not made of molecules, which is why the name relative formula mass fits them better.
The official SI unit of molar mass is kg/mol, so water is 0.018015 kg/mol. Chemistry almost always uses g/mol, but physics formulas such as the root-mean-square speed of a gas need the kg/mol value.
Why Atomic Weights Are Not Whole Numbers
Most elements are a mix of isotopes, and the atomic weight is the abundance-weighted average of their masses. Chlorine shows this clearly. The NIST isotopic composition data for chlorine gives chlorine-35 (mass 34.968853) at 75.76% and chlorine-37 (mass 36.965903) at 24.24%:
0.7576 × 34.968853 + 0.2424 × 36.965903 = 26.4924 + 8.9605 = 35.4529
That rounds to the 35.45 in the table, and it is why no chlorine atom actually has a mass of 35.45. For sulfur, chlorine, hydrogen, oxygen and several others, natural samples vary slightly in their isotope mix, so IUPAC now gives their standard atomic weight as a range and the CIAAW abridged table lists a single value for everyday calculations. That is the value you use.
Using Molar Mass to Convert Grams and Moles
Molar mass is rarely the final answer. It is the conversion factor between what a balance measures (grams) and what a balanced equation counts (moles). The grams cancel in n = m / M, leaving mol, which is the unit check.
A tablet contains 325 mg of aspirin, C₉H₈O₄. How many moles of aspirin is that?
Molar mass: 9(12.011) + 8(1.008) + 4(15.999) = 108.099 + 8.064 + 63.996 = 180.159 g/mol. Estimate: 108 + 8 + 64 = 180.
Convert the mass to grams first: 325 mg = 0.325 g.
n = 0.325 g ÷ 180.159 g/mol = 0.001804 mol. The grams cancel, leaving mol.
325 mg has 3 significant figures, so the answer gets 3: 1.80 × 10⁻³ mol (see scientific notation for the format).
n = 1.80 × 10⁻³ molA lab finds that 0.0500 mol of an unknown gas has a mass of 2.20 g. What is its molar mass, and could it be CO₂ or N₂O?
Rearrange n = m / M to M = m / n = 2.20 g ÷ 0.0500 mol = 44.0 g/mol. Grams divided by moles gives g/mol, the unit a molar mass should have.
Candidates: CO₂ = 12.011 + 2(15.999) = 44.009 g/mol and N₂O = 2(14.007) + 15.999 = 44.013 g/mol. Both round to 44.0 g/mol.
Propane, C₃H₈ = 3(12.011) + 8(1.008) = 44.097 g/mol, rounds to 44.1, only one unit in the last digit away, so a 3-significant-figure measurement can't safely rule it out either. You would need another test (does it burn? does it turn limewater cloudy?).
M = 44.0 g/mol; CO₂ and N₂O both fit, and C₃H₈ is not excludedExample 5 is worth remembering for multiple-choice questions: a molar mass narrows the options, but it is not a fingerprint. Once you can turn grams into moles, the next step is using the mole ratios from a balanced chemical equation, which is the core of stoichiometry.
How Many Decimal Places to Use
The same hydrate shows up online as 249.5, 249.7 and 249.68 g/mol. None of these is a calculation error. They come from different roundings of the atomic weights:
| Atomic weights used | Sum for CuSO₄·5H₂O | Result |
|---|---|---|
| Cu 63.5, S 32, O 16, H 1 (GCSE-style data sheet) | 63.5 + 32 + 9(16) + 10(1) | 249.5 |
| Cu 63.55, S 32.07, O 16.00, H 1.008 (4 significant figures) | 63.55 + 32.07 + 9(16.00) + 10(1.008) | 249.70 |
| CIAAW abridged values (this guide) | 63.546 + 32.06 + 9(15.999) + 10(1.008) | 249.68 |
The rule is simple: use the values your exam board or textbook prints, and say which ones you used. Then keep the decimal places of the least precise atomic weight, because molar mass is a sum. Atomic weights are usually far more precise than anything you weigh in the lab, so in a later step it's your measured mass that limits the significant figures, as in Example 4.
How to Check Your Answer
- Whole-number estimate. Redo the sum with rounded atomic weights. For a small compound the two should agree within about 1 g/mol; for a large hydrate, within 1 or 2.
- Unit check. A molar mass is in g/mol. If a conversion leaves you with g²/mol or mol/g, the fraction is upside down.
- Size check. The molar mass must be larger than any one element's share of it. CuSO₄·5H₂O can't be under 63.5 g/mol, and a pentahydrate must be at least
5 × 18 = 90g/mol heavier than its anhydrous salt. - Diatomic elements. "Oxygen gas" means
O₂, so its molar mass is2 × 15.999 = 31.998 g/mol, not 15.999. The same goes for H₂, N₂, Cl₂ and the other diatomics.
To check a full mole problem after working it yourself, you can photograph it with Solver AI on iPhone or iPad and compare its step-by-step solution with your count table. If the two disagree, the count table usually shows which atom went missing; the chemistry solver page lists the kinds of chemistry questions it handles.
Practice Problems
Use the atomic weights from the table at the top of this guide.
- Find the molar mass of carbon dioxide,
CO₂. - Find the molar mass of magnesium hydroxide,
Mg(OH)₂. - Find the molar mass of washing soda,
Na₂CO₃·10H₂O. - How many moles are in 50.0 g of aluminium sulfate,
Al₂(SO₄)₃? - A 2.50 g sample of hydrated copper(II) sulfate,
CuSO₄·xH₂O, is heated until all the water is gone. The anhydrous CuSO₄ left behind has a mass of 1.60 g. Find x.
1. 12.011 + 2(15.999) = 44.009 g/mol.
2. 24.305 + 2(15.999) + 2(1.008) = 58.319 g/mol.
3. 2(22.990) + 12.011 + 3(15.999) + 10(18.015) = 105.988 + 180.150 = 286.138 g/mol.
4. M = 2(26.982) + 3(32.06) + 12(15.999) = 53.964 + 96.18 + 191.988 = 342.13 g/mol, so n = 50.0 g ÷ 342.13 g/mol = 0.146 mol.
5. Water lost = 2.50 − 1.60 = 0.90 g. Moles of water = 0.90 g ÷ 18.015 g/mol = 0.04996 mol (about 0.050 mol; keep the extra digits for the ratio); moles of CuSO₄ = 1.60 g ÷ 159.60 g/mol = 0.01003 mol. Ratio 0.04996 ÷ 0.01003 = 4.98, which rounds to the whole number x = 5, the pentahydrate from Example 3.