How to Calculate Molar Mass: From Chemical Formula to g/mol and Mass Percent

If a lab instruction says "weigh out 0.5 mol of glucose", how many grams should you put on the balance? Atoms and molecules are far too small to count one by one, so chemists use a counting unit, the mole, and a conversion factor, the molar mass. This guide explains how to find molar mass from scratch and works through several real calculations.

The mole and the Avogadro constant

The mole (mol) is the SI base unit for amount of substance. Just as a dozen means 12 items, one mole means a fixed number of particles. That number is the Avogadro number:

1 mol = 6.02214076 × 10²³ particles

Since the revision of the SI in May 2019, this value is a defined constant rather than a measurement. The Avogadro constant N_A is exactly 6.02214076 × 10²³ mol⁻¹, with no uncertainty. Before 2019 the mole was defined as the number of atoms in 12 g of carbon-12; now it is defined by the count itself. For practical purposes the two definitions give almost identical results.

The number is enormous because atoms are so tiny. Just 18 g of water, a little more than a tablespoon, contains about 6 × 10²³ water molecules.

What molar mass means

Molar mass (M) is the mass of one mole of a substance, in grams per mole (g/mol). For an element, the molar mass has the same numerical value as the atomic weight on the periodic table. Atomic weight is a dimensionless relative value; molar mass is that value with g/mol attached.

• Carbon: atomic weight 12.011 → molar mass 12.011 g/mol
• Oxygen: atomic weight 15.999 → molar mass of oxygen atoms 15.999 g/mol

For a compound, add up the atomic weights of every atom in the formula. The calculations here use the CIAAW 2024 abridged standard atomic weights, the same values used on this site.

Some textbooks use rounded values such as H = 1, C = 12 and O = 16, which changes the answer slightly after the decimal point. Always check which values you are expected to use.

Step 1: count the atoms in the formula

Most mistakes in molar mass problems happen while counting atoms. Four rules cover almost everything.

1. A subscript applies only to the element immediately before it. H₂O has 2 H and 1 O.
2. A subscript after parentheses multiplies everything inside. Ca(OH)₂ has 1 Ca, 2 O and 2 H.
3. A coefficient after a raised dot (·) multiplies the whole unit that follows. In CuSO₄·5H₂O, the 5H₂O contributes 10 H and 5 O.
4. If an element appears in more than one place, add all occurrences. NH₄NO₃ has 2 N, 4 H and 3 O.

Step 2: add the masses element by element

Once you have the counts, multiply each atomic weight by its count and add the results. Start with the simplest cases.

Water (H₂O)

• H: 1.008 × 2 = 2.016
• O: 15.999 × 1 = 15.999
• Total: 18.015 g/mol

Carbon dioxide (CO₂)

• C: 12.011 × 1 = 12.011
• O: 15.999 × 2 = 31.998
• Total: 44.009 g/mol

Example 1: glucose (C₆H₁₂O₆)

The mass of 0.500 mol of glucose is 0.500 mol × 180.156 g/mol = 90.078 g, or about 90.1 g. That answers the opening question.

Example 2: parentheses, aluminium sulfate (Al₂(SO₄)₃)

The 3 outside the parentheses multiplies the whole sulfate group. That gives 1 × 3 = 3 S and 4 × 3 = 12 O.

• Al: 26.982 × 2 = 53.964
• S: 32.06 × 3 = 96.18
• O: 15.999 × 12 = 191.988
• Total: 342.132 g/mol

If you ignore the parentheses and count only 4 O, you get a completely different answer. When a formula has parentheses, it is safest to write out the full atom count first.

In the same way, calcium hydroxide, Ca(OH)₂, is 40.078 + (15.999 + 1.008) × 2 = 74.092 g/mol.

Example 3: a hydrate, copper(II) sulfate pentahydrate (CuSO₄·5H₂O)

The blue crystals of copper sulfate hold water molecules inside the crystal structure. This water of crystallization is written after the raised dot, and it must be included in the molar mass.

It is easiest to split the formula into two parts.

• CuSO₄: 63.546 + 32.06 + 15.999 × 4 = 159.602
• 5H₂O: 18.015 × 5 = 90.075
• Total: 249.677 g/mol

Counting atoms all at once gives the same result: 1 Cu, 1 S, 9 O (4 + 5) and 10 H, so 63.546 + 32.06 + 15.999 × 9 + 1.008 × 10 = 249.677 g/mol.

Heating the crystals drives off the water and leaves white anhydrous copper sulfate. The mass fraction of water in the crystal is 90.075 ÷ 249.677 × 100 ≈ 36.08%, so heating 10.0 g of crystals thoroughly should reduce the mass by about 3.6 g.

Mass percent

Mass percent is the share of a compound's mass contributed by one element.

Mass percent (%) = (atomic weight × number of atoms) ÷ molar mass of compound × 100

Example 4: nitrogen content of ammonium nitrate (NH₄NO₃)

• Molar mass: 14.007 × 2 + 1.008 × 4 + 15.999 × 3 = 80.043 g/mol
• Mass of nitrogen: 14.007 × 2 = 28.014
• Percent nitrogen: 28.014 ÷ 80.043 × 100 ≈ 35.00%

The nitrogen content printed on fertilizer bags comes from calculations like this. By the same method, carbon makes up 72.066 ÷ 180.156 × 100 ≈ 40.00% of glucose, and copper makes up 63.546 ÷ 249.677 × 100 ≈ 25.45% of copper sulfate pentahydrate.

The percentages of all elements in a compound should add up to 100%, which is a quick way to check your work.

Converting between mass, moles and particles

With the molar mass you can move freely among three quantities.

• Moles n = mass m ÷ molar mass M
• Mass m = moles n × molar mass M
• Number of particles N = moles n × 6.02214076 × 10²³

Example 5: molecules in 9.00 g of water

1. Moles: 9.00 g ÷ 18.015 g/mol ≈ 0.4996 mol
2. Molecules: 0.4996 × 6.02214076 × 10²³ ≈ 3.01 × 10²³

About two teaspoons of water, 9 g, contains roughly 3 × 10²³ molecules.

Example 6: mass of copper in 10.0 g of copper sulfate pentahydrate

1. Moles: 10.0 g ÷ 249.677 g/mol ≈ 0.04005 mol
2. Each formula unit contains one copper atom, so there are also 0.04005 mol of copper.
3. Mass of copper: 0.04005 × 63.546 ≈ 2.55 g

Multiplying 10.0 g by the copper mass percent found above (25.45%) gives the same answer.

Significant figures and common mistakes

• Significant figures: round the final answer to match the precision of the measured data (for example, 9.00 g has three significant figures). Keep extra digits during intermediate steps and round only once at the end.
• Diatomic molecules: oxygen gas is O₂, not O, so its molar mass is 31.998 g/mol. The same applies to H₂, N₂ and Cl₂.
• Missed parentheses or water of crystallization: counting only one H in Ca(OH)₂ or leaving out the water in a hydrate are very common slips.
• Bracketed atomic weights: for elements such as technetium [97], the bracketed value is the mass number of the most stable isotope, not a natural average. If you know which isotope your sample contains, use that isotope's mass.

Knowing how to do these calculations by hand means you can tell at a glance whether a calculator's answer makes sense. Look up the atomic weights on the periodic table and rework the examples above yourself.