Relative formula mass: how to calculate Mr
Relative formula mass, written Mr, is the sum of the relative atomic masses of all the atoms in a chemical formula. Count each atom, multiply by its relative atomic mass and add the results. Mr has no unit because it is a comparison, not a mass measured in grams.
Try a round of Relative Formula Mass to practise finding the total yourself.
How to calculate relative formula mass
A relative atomic mass, written Ar, compares the average mass of an atom of an element with one twelfth of the mass of a carbon-12 atom. Mr adds the Ar values for every atom shown in a formula.
- Read the formula and count the atoms of each element. A small number after a symbol applies to that element. No number means one atom.
- If a group is in brackets, multiply every atom inside by the small number after the closing bracket.
- Find each Ar on the periodic table. Multiply it by the number of atoms of that element.
- Add the totals. Write the Mr without a unit.
Use the AQA GCSE periodic table to find the Ar values used in the examples. Values on your own data sheet may be printed differently, so follow the numbers in your question. The calculator does not use bracketed mass numbers or elements with no printed Ar.
Ar and Mr: what is the difference?
Ar describes one element. Mr describes the whole formula, including every atom in it. For water, H₂O, you use the Ar of hydrogen twice and the Ar of oxygen once.
A formula can describe an ionic compound as well as a molecule. Calcium hydroxide, Ca(OH)₂, is an ionic compound, so relative formula mass is the useful term for its formula.
The Periodic Table Challenge helps you find elements and their properties.
Using formula mass in chemistry
Count the atoms in the formula before you calculate. In balancing equations, a number in front of a formula counts whole formula units. It does not change the Mr of that formula.
Once you can calculate Mr, try Mole Ratio Rush to practise the ratios in chemical equations.
Relative formula mass is a GCSE calculation. At KS3, pupils meet chemical symbols and formulae, which are useful preparation for counting the atoms here.
AQA Chemistry 8462 section 4.3.1.2, Edexcel Chemistry 1CH0 point 1.43 and OCR Gateway Chemistry A J248 point C2.1c include Mr calculations.
Worked examples
Relative formula mass of H₂O
- There are 2 H atoms and 1 O atom.
- Using Ar values H = 1 and O = 16, calculate (2 × 1) + 16.
18
Relative formula mass of CO₂
- There is 1 C atom and 2 O atoms.
- Using Ar values C = 12 and O = 16, calculate 12 + (2 × 16).
44
Relative formula mass of Ca(OH)₂
- The 2 outside the brackets gives 2 O atoms and 2 H atoms. There is 1 Ca atom.
- Using Ar values Ca = 40, O = 16 and H = 1, calculate 40 + 2 × (16 + 1).
74
Common mistakes
- Missing an atom when there is no small number after its symbol: the count is one.
- Multiplying only the last element inside brackets. The number outside applies to the whole group.
- Using atomic number instead of relative atomic mass, or adding a unit to Mr.
The chemistry hub brings together more explanations and practice.
Questions people ask
What is relative formula mass?
It is the sum of the relative atomic masses of every atom shown in a chemical formula. It has no unit.
How do you calculate relative formula mass with brackets?
Multiply the count of each atom inside the brackets by the number after the closing bracket, then add the relative atomic masses of all the atoms in the formula.
What is the relative formula mass of CO₂?
Using Ar values C = 12 and O = 16, the Mr is 12 + (2 × 16) = 44.
Is relative formula mass measured in grams?
No. Relative formula mass is a ratio and has no unit. A mass measured in grams is a different quantity.