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Relative Formula Mass (Mr) Calculator

Relative formula mass is the sum of the relative atomic masses of all the atoms in a formula: Mr = Σ k·Ar, where k is the number of atoms of each element. For H₂SO₄, Mr = 2 × 1 + 32 + 4 × 16 = 98, so its molar mass M is 98 g/mol.

Relative formula mass formula: Mr = Σ k·Ar

M = Σ k·Ar
M
molar mass, g/mol
Mr
relative formula mass
Ar
relative atomic mass
k
number of atoms

The legend lists the base units: g, mol, dm³ and g/mol. You can enter mg, kg, cm³ and other units; the calculator converts them and shows the conversion as a step. Relative atomic masses are rounded as in the GCSE periodic table, for example Cl = 35.5 and Cu = 63.5.

Fe₂O₃

Each element's contribution to the relative formula mass
ElementAtomsArMass in MrShare
Fe256112 70 %
O31648 30 %
Mr(Fe₂O₃)
160
M(Fe₂O₃)
160 g/mol
Mr(Fe₂O₃): 160. M(Fe₂O₃): 160 g/mol
Ball-and-stick model of Fe₂O₃, with the atoms coloured as in the periodic table. The bar shows each element's share of the molar mass, 160 g/mol; hover over an atom to highlight its part.

Step-by-step solution

  1. FormulaMr(Fe₂O₃) = 2·Ar(Fe) + 3·Ar(O)
  2. SubstituteMr(Fe₂O₃) = 2·56 + 3·16 = 160
  3. AnswerMr(Fe₂O₃) = 160
Find the number of moles of Fe₂O₃ from its mass

Relative formula mass examples

  1. Example 1

    Calculate the relative formula mass of calcium carbonate, CaCO₃.

    Given:CaCO₃
    1. FormulaMr(CaCO₃) = Ar(Ca) + Ar(C) + 3·Ar(O)
    2. SubstituteMr(CaCO₃) = 40 + 12 + 3·16 = 100
    3. AnswerMr(CaCO₃) = 100

  2. Example 2

    Calculate the relative formula mass of magnesium hydroxide, Mg(OH)₂. Take care with the bracket.

    Given:Mg(OH)₂
    1. FormulaMr(Mg(OH)₂) = Ar(Mg) + 2·Ar(O) + 2·Ar(H)
    2. SubstituteMr(Mg(OH)₂) = 24.3 + 2·16 + 2·1 = 58.3
    3. AnswerMr(Mg(OH)₂) = 58.3

  3. Example 3

    Ammonium sulfate, (NH₄)₂SO₄, is used as a fertiliser. Calculate its relative formula mass.

    Given:(NH₄)₂SO₄
    1. FormulaMr((NH₄)₂SO₄) = 2·Ar(N) + 8·Ar(H) + Ar(S) + 4·Ar(O)
    2. SubstituteMr((NH₄)₂SO₄) = 2·14 + 8·1 + 32 + 4·16 = 132
    3. AnswerMr((NH₄)₂SO₄) = 132

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What is relative formula mass?

Relative formula mass, Mr, tells you how heavy one formula unit of a substance is compared with one twelfth of the mass of a carbon-12 atom. To find it, add up the relative atomic masses, Ar, of every atom in the formula. The Ar values come from the periodic table: H = 1, C = 12, O = 16, Cl = 35.5. Mr has no unit, because it is a ratio of two masses.

Mr is the starting point for almost every calculation in quantitative chemistry. The mass of one mole of a substance in grams is numerically equal to its Mr, so water, with Mr = 18, has a molar mass of 18 g/mol. You need Mr to convert between mass and moles, to find the percentage by mass of an element and to work out concentrations in mol/dm³. In a balanced equation, the total Mr of the reactants, counting the balancing numbers, equals that of the products, which shows that mass is conserved.

Brackets need care. In Ca(OH)₂ the 2 applies to everything inside the bracket, so there are 2 O and 2 H: Mr = 40 + 2 × (16 + 1) = 74. A hydrate such as CuSO₄·5H₂O also contains five water molecules, so its Mr = 159.5 + 5 × 18 = 249.5.

Common mistakes

  • Giving Mr a unit. Mr has no unit; the molar mass M has the same number and is measured in g/mol.
  • Ignoring the number after a bracket: Ca(OH)₂ has 2 oxygen and 2 hydrogen atoms, not one of each.
  • Leaving out the water of crystallisation in a hydrate: in CuSO₄·5H₂O the water adds 5 × 18 = 90.
  • Including the balancing number from an equation: in 2H₂O the Mr of water is still 18; the 2 only tells you there are two molecules.
  • Using precise values such as 35.45 for chlorine when the GCSE periodic table gives 35.5. Use the values on your exam's periodic table.

More chemistry formulas

MolesPercentage by massAvogadro constantPeriodic tableAll chemistry equations

Frequently asked questions

Add up the relative atomic masses of all the atoms in the formula. For CO₂: Mr = 12 + 2 × 16 = 44.

Ar is the relative atomic mass of one element, read from the periodic table. Mr is the relative formula mass of a compound or molecule: the sum of the Ar values of all its atoms.

No. Mr is a ratio, so it has no unit. The molar mass, the mass of one mole, has the same value in g/mol.

18: two hydrogen atoms (2 × 1) plus one oxygen atom (16).

Chlorine is a mixture of two isotopes, chlorine-35 and chlorine-37, in a ratio of about 3 : 1. The relative atomic mass is the average mass, weighted by how common each isotope is.