To calculate molar mass, multiply the atomic weight of each element by the number of atoms of that element in the formula, then add everything up. For water, H₂O, that is 2 × 1.008 (hydrogen) + 1 × 15.999 (oxygen) = 18.015 g/mol. One mole of water, about 6.022 × 10²³ molecules, therefore has a mass of 18.015 grams.
Molar mass is the bridge between the mass you can weigh on a balance and the number of particles that take part in a reaction. Almost every quantitative chemistry calculation passes through it.
The formula
Here n is the number of atoms of each element and A is that element’s standard atomic weight, in grams per mole.
Steps
- Write the formula and list each element.
- Count the atoms of each element, applying any subscripts outside parentheses and any hydrate coefficients.
- Look up each atomic weight.
- Multiply and add.
- Report in g/mol, usually to two or three decimal places.
Atomic weights you will use most
These are the IUPAC conventional values used in most textbooks and labs.
| Element | Symbol | Atomic weight (g/mol) |
|---|---|---|
| Hydrogen | H | 1.008 |
| Carbon | C | 12.011 |
| Nitrogen | N | 14.007 |
| Oxygen | O | 15.999 |
| Sodium | Na | 22.990 |
| Magnesium | Mg | 24.305 |
| Aluminum | Al | 26.982 |
| Phosphorus | P | 30.974 |
| Sulfur | S | 32.06 |
| Chlorine | Cl | 35.45 |
| Potassium | K | 39.098 |
| Calcium | Ca | 40.078 |
| Iron | Fe | 55.845 |
| Copper | Cu | 63.546 |
The International Union of Pure and Applied Chemistry (IUPAC) reviews these values regularly. For some elements, including hydrogen, carbon and oxygen, it now publishes an interval reflecting natural variation in isotopes, along with a single conventional value for everyday calculations.
Worked examples
Carbon dioxide, CO₂
C: 1 × 12.011 = 12.011
O: 2 × 15.999 = 31.998
M = 44.009 g/mol
Glucose, C₆H₁₂O₆
| Element | Atoms | Atomic weight | Subtotal |
|---|---|---|---|
| C | 6 | 12.011 | 72.066 |
| H | 12 | 1.008 | 12.096 |
| O | 6 | 15.999 | 95.994 |
| Total | 180.156 g/mol |
Parentheses: calcium hydroxide, Ca(OH)₂
The subscript 2 applies to both O and H inside the parentheses.
Ca: 1 × 40.078 = 40.078
O: 2 × 15.999 = 31.998
H: 2 × 1.008 = 2.016
M = 74.092 g/mol
Nested groups: aluminum sulfate, Al₂(SO₄)₃
Three sulfate groups give 3 sulfur and 12 oxygen atoms.
Al: 2 × 26.982 = 53.964
S: 3 × 32.06 = 96.18
O: 12 × 15.999 = 191.988
M = 342.132 g/mol
Hydrates: copper(II) sulfate pentahydrate, CuSO₄·5H₂O
The “·5H₂O” means five water molecules are built into each formula unit of the crystal.
CuSO₄: 63.546 + 32.06 + 4 × 15.999 = 159.602
5H₂O: 5 × 18.015 = 90.075
M = 249.677 g/mol
About 36% of the hydrate’s mass is water. If you weigh out the blue crystals but calculate with the anhydrous molar mass, your solution will be about 36% weaker than intended. The molar mass calculator parses parentheses and hydrate dots automatically.
Common molar masses
| Compound | Formula | Molar mass (g/mol) |
|---|---|---|
| Water | H₂O | 18.015 |
| Ammonia | NH₃ | 17.031 |
| Carbon dioxide | CO₂ | 44.009 |
| Ethanol | C₂H₅OH | 46.069 |
| Sodium chloride | NaCl | 58.44 |
| Sulfuric acid | H₂SO₄ | 98.072 |
| Calcium carbonate | CaCO₃ | 100.086 |
| Iron(III) oxide | Fe₂O₃ | 159.687 |
| Glucose | C₆H₁₂O₆ | 180.156 |
Using molar mass: grams, moles and particles
Molar mass converts between mass and amount of substance. The Avogadro constant, fixed at exactly 6.02214076 × 10²³ per mole since the 2019 SI redefinition, converts moles to particles.
How many moles and molecules are in 25.0 g of CO₂?
n = 25.0 ÷ 44.009 = 0.568 mol
N = 0.568 × 6.022 × 10²³ ≈ 3.42 × 10²³ molecules
Going the other way, half a mole of glucose has a mass of 0.500 × 180.156 = 90.1 g. The grams to moles calculator handles both directions, and the same step is the first move in how to calculate molarity.
Percent composition
Each element’s share of the molar mass is its percent composition by mass:
For water: hydrogen is 2.016 ÷ 18.015 = 11.19% and oxygen is 15.999 ÷ 18.015 = 88.81%. For iron(III) oxide, iron is 111.69 ÷ 159.687 ≈ 69.94%, which tells a metallurgist the most iron an ore of pure Fe₂O₃ could yield. The percent composition calculator works for any formula, and the empirical formula calculator runs the process in reverse, from percentages back to a formula.
Why atomic weights have decimals
An element’s atomic weight is the average mass of its atoms as they occur in nature, weighted by how common each isotope is. Chlorine is about 75.76% chlorine-35 (34.969 u) and 24.24% chlorine-37 (36.966 u):
0.7576 × 34.969 + 0.2424 × 36.966 ≈ 35.45
That is why a periodic table lists 35.45 rather than 35 or 37. In a mass spectrometer, which sorts individual molecules by mass, you see separate peaks for each isotope instead of one peak at the average.
Finding molar mass by experiment
When the formula is unknown, molar mass can be measured. For a gas, the ideal gas law gives the moles from pressure, volume and temperature, and dividing the measured mass by the moles gives the molar mass:
1.00 g of an unknown gas fills 0.560 L at 273.15 K and 1.00 atm
n = PV ÷ RT = (1.00 × 0.560) ÷ (0.082057 × 273.15) ≈ 0.02498 mol
M = 1.00 ÷ 0.02498 ≈ 40.0 g/mol, which matches argon
The ideal gas law calculator solves for moles from any three gas properties.
Molar mass in reactions
Balanced equations are written in moles, so stoichiometry problems almost always follow the path grams → moles → mole ratio → moles → grams. Finding which reactant runs out first is a direct application; the limiting reactant calculator works through it.
Common mistakes
- Applying a subscript to only one atom in a parenthesized group.
- Forgetting water of hydration.
- Using mass numbers instead of atomic weights, such as 35 for chlorine instead of 35.45.
- Confusing diatomic elements. Oxygen gas is O₂, so its molar mass is 31.998 g/mol, not 15.999.
- Rounding too early. Keep three decimal places through the calculation and round the final answer; see significant figures rules.
Frequently asked questions
How do you calculate molar mass?
Multiply each element's atomic weight by the number of atoms of that element in the formula, then add the results. For water, H₂O: 2 × 1.008 + 1 × 15.999 = 18.015 g/mol.
What is the difference between molar mass and molecular weight?
Numerically they are the same. Molar mass has units of grams per mole (g/mol), while molecular weight (relative molecular mass) is a unitless ratio, and molecular mass is often given in daltons (Da). Water is 18.015 g/mol, 18.015 Da per molecule, or a relative molecular mass of 18.015.
How do parentheses affect molar mass?
A subscript after parentheses multiplies everything inside. In Ca(OH)₂ there is 1 calcium, 2 oxygen and 2 hydrogen atoms, so the molar mass is 40.078 + 2 × (15.999 + 1.008) = 74.092 g/mol.
How do you include water in a hydrate's molar mass?
Add the molar mass of the water molecules shown after the dot. CuSO₄·5H₂O is 159.602 + 5 × 18.015 = 249.677 g/mol. Leaving out the water is a common source of error when weighing out solutions.
Why aren't atomic weights whole numbers?
Most elements are mixtures of isotopes with different masses, and the atomic weight is their abundance-weighted average. Chlorine, for example, is roughly three-quarters chlorine-35 and one-quarter chlorine-37, giving an average of about 35.45.