Relative formula mass (Mr) and how to calculate it

Relative formula mass, written Mr, is the sum of the relative atomic masses of all the atoms in a formula. To calculate it, count how many atoms of each element the formula shows, multiply each count by that element's relative atomic mass (Ar) from the periodic table, and add the results. For water, H₂O, that is (2 × 1) + 16 = 18. Mr has no units.

What is relative formula mass?

Atoms are far too light to weigh in grams one at a time, so chemists compare them instead. Each element's relative atomic mass, Ar, says how heavy its atoms are on a scale where a carbon-12 atom is exactly 12. Relative formula mass does the same job for a whole compound: it tells you how heavy one formula unit is on that scale.

That makes it the bridge between the formula of a substance and a mass you can weigh. The Mr of a substance in grams is the mass of one mole of it, so 18 g of water is one mole of water.

Relative formula mass and relative molecular mass

You will see both names. Relative molecular mass is used for substances made of molecules, such as water or carbon dioxide. Relative formula mass works for everything, including ionic compounds such as sodium chloride, which do not form molecules. Both use the symbol Mr and are calculated in exactly the same way, so GCSE courses usually just say relative formula mass.

The relative formula mass equation

There is no single fixed formula to learn. The method is the equation:

In words: for each element, multiply the number of its atoms in the formula by its relative atomic mass, then add the totals together.

How to calculate relative formula mass

1. Write the formula and list each element in it.
2. Count the atoms of each element. A small number after a symbol counts that atom only. A number after a bracket multiplies everything inside the bracket.
3. Look up each Ar on the periodic table.
4. Multiply and add.

These relative atomic masses come from the periodic table insert AQA gives with GCSE Chemistry and Combined Science papers. It rounds every value to a whole number except copper and chlorine.

Relative formula mass examples

Example 1: carbon dioxide, CO₂

One carbon atom and two oxygen atoms.

Example 2: calcium carbonate, CaCO₃

One calcium, one carbon and three oxygen atoms.

Example 3: magnesium hydroxide, Mg(OH)₂

The subscript 2 sits outside the bracket, so it applies to the O and the H alike. Find the mass of one OH group first, 16 + 1 = 17, then double it.

Example 4: ammonium sulfate, (NH₄)₂SO₄

Two ammonium groups, each with one nitrogen and four hydrogens, then one sulfur and four oxygens.

Example 5: a hydrate, CuSO₄·5H₂O

The dot means the crystal also holds five water molecules, and they count towards the mass. Each water is 18.

Copper is one of the two elements whose Ar is not rounded on the GCSE table, so this Mr ends in .5.

Check any of these in the Molar Mass Calculator: type a formula and it shows the count and mass of each element.

Using relative formula mass

Working out Mr is rarely the end of a question. It is the first step in most calculations in quantitative chemistry.

Percentage by mass of an element

In calcium carbonate, oxygen contributes 3 × 16 = 48 out of an Mr of 100, so it is 48% oxygen by mass. In ammonium nitrate, NH₄NO₃, Mr = 80 and the two nitrogen atoms contribute 28, so it is 28 ÷ 80 × 100 = 35% nitrogen. That is why it is used as a fertiliser.

Moles and mass

At GCSE Higher and A-level, Mr links mass and amount in moles:

So 22 g of carbon dioxide is 22 ÷ 44 = 0.5 mol, and 25 g of calcium carbonate is 25 ÷ 100 = 0.25 mol. In grams per mole, Mr is called the molar mass.

Checking a balanced equation

In a balanced equation, the total Mr of the reactants equals the total Mr of the products, because mass is conserved. For CaCO₃ → CaO + CO₂, the left side is 100 and the right side is 56 + 44 = 100.

The relative atomic mass formula

The Ar values on the periodic table are averages. Most elements are a mixture of isotopes, atoms with the same number of protons but different numbers of neutrons, so their atoms do not all weigh the same. The relative atomic mass is the mean mass of the atoms, weighted by how common each isotope is:

For example, if neon is 91% neon-20 and 9% neon-22:

So neon's Ar is 20.2 to 1 decimal place. The answer is close to 20 because nearly all neon atoms are neon-20. A weighted average always lies between the lightest and heaviest isotope, and nearer the commoner one.

Working backwards to find an abundance

An element X has two isotopes, X-63 and X-65, and its Ar is 63.5. What percentage is X-63?

Let the percentage of X-63 be p, so X-65 is (100 − p).

So p = 75: the element is 75% X-63 and 25% X-65.

Now try one. Work out the relative atomic mass from the isotopes given, then press Mark to check your answer in the course.

Common mistakes

• Ignoring brackets. In Mg(OH)₂ the 2 multiplies both O and H. Doubling only the hydrogen gives 24 + 16 + 2 = 42, which is wrong; the right answer is 58.
• Using atomic number instead of relative atomic mass. On the periodic table, the larger number is the relative atomic mass. Oxygen is 16, not 8.
• Forgetting the water in a hydrate. CuSO₄·5H₂O includes five whole water molecules, adding 90.
• Using Cl = 35. Use 35.5 for chlorine and 63.5 for copper, as your exam's table shows. NaCl is 58.5.
• Adding units. Mr is a ratio, so it has no units. Molar mass, the same number in grams per mole, does.
• Taking a plain average of isotopes. The relative atomic mass is weighted by abundance, so multiply each mass by its percentage first.

Is relative formula mass on the GCSE syllabus?

Yes. In AQA's GCSE Chemistry and Combined Science specifications, calculating relative formula mass is in quantitative chemistry, which is on both Foundation and Higher papers. You do not need to memorise any Ar values: they are on the periodic table insert that comes with every paper. Moles, and using Mr to convert between mass and moles, are Higher tier only.

Practise in a short timed paper

Relative formula mass sits underneath most chemistry calculations, so it turns up across GCSE Chemistry papers. GCSE Chemistry Foundation and GCSE Chemistry Higher each give you a short timed paper every day, with 8 questions worth 25 to 35 marks. To build up from atoms and isotopes first, the Atomic Structure course covers relative atomic mass step by step.

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Chemistry · Atoms and the periodic tableWhat is relative atomic mass? Definition and calculationRelative atomic mass is the weighted average mass of an element's atoms compared with carbon-12. The definition and how to calculate it from isotopes.