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Percentage by Mass Calculator: Element in a Compound

The percentage by mass of an element in a compound is (Ar × number of atoms of that element) ÷ Mr × 100: w = k·Ar / Mr × 100 %. In magnesium oxide, MgO (Mr = 40), magnesium makes up 24 ÷ 40 × 100 = 60% of the mass.

Percentage by mass formula

w = k·ArMr · 100 %
w
percentage by mass, %
k
number of atoms of the element
Ar
relative atomic mass
Mr
relative formula mass

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
O31648
w(Fe) in Fe₂O₃
70 %

Click an element in the table or the model to see how its percentage is worked out.

w(Fe) in Fe₂O₃: 70 %
Model of Fe₂O₃: the bar shows each element's share of the mass. Fe makes up 70 %; click another part to see its calculation.

Step-by-step solution

  1. Relative formula massMr(Fe₂O₃) = 2·56 + 3·16 = 160
  2. Formulaw(Fe) = 2·Ar(Fe)Mr(Fe₂O₃) · 100 %
  3. Substitutew(Fe) = 2·56160 · 100 %
  4. Answerw(Fe) = 70 %
Relative formula mass of Fe₂O₃, step by step

Percentage by mass examples

  1. Example 1

    Calculate the percentage by mass of carbon, C, in carbon dioxide, CO₂.

    Given:CO₂
    1. Relative formula massMr(CO₂) = 12 + 2·16 = 44
    2. Formulaw(C) = Ar(C)Mr(CO₂) · 100 %
    3. Substitutew(C) = 1244 · 100 %
    4. Answerw(C) ≈ 27.3 %

  2. Example 2

    Ammonium nitrate, NH₄NO₃, is used as a fertiliser. Calculate the percentage by mass of nitrogen, N, in it.

    Given:NH₄NO₃
    1. Relative formula massMr(NH₄NO₃) = 2·14 + 4·1 + 3·16 = 80
    2. Formulaw(N) = 2·Ar(N)Mr(NH₄NO₃) · 100 %
    3. Substitutew(N) = 2·1480 · 100 %
    4. Answerw(N) = 35 %

  3. Example 3

    Iron is extracted from iron(III) oxide, Fe₂O₃, in a blast furnace. Calculate the percentage by mass of iron, Fe, in the oxide.

    Given:Fe₂O₃
    1. Relative formula massMr(Fe₂O₃) = 2·56 + 3·16 = 160
    2. Formulaw(Fe) = 2·Ar(Fe)Mr(Fe₂O₃) · 100 %
    3. Substitutew(Fe) = 2·56160 · 100 %
    4. Answerw(Fe) = 70 %

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What is percentage by mass?

Percentage by mass tells you what share of a compound's mass comes from one element. Multiply the element's relative atomic mass by the number of its atoms in the formula, divide by the compound's relative formula mass and multiply by 100. In water, H₂O (Mr = 18), oxygen contributes 16, so it is 16 ÷ 18 × 100 = 88.9% of the mass, and hydrogen is the other 11.1%.

It is used to compare fertilisers, to see which supplies the most nitrogen per kilogram, and to choose the best ore for extracting a metal. Working backwards, chemists use measured percentages to find an empirical formula. Because it depends only on the formula, the percentage is the same for a gram or a tonne of the compound.

A worked intuition: in magnesium oxide, MgO (Mr = 40), magnesium accounts for 24 of the 40 units of mass, so it is 60% by mass and oxygen is 40%. The percentages of all the elements in a compound add up to 100%; if yours come to 99.9% or 100.1%, that is just rounding.

Common mistakes

  • Forgetting the number of atoms: nitrogen appears twice in NH₄NO₃, so use 2 × 14 = 28, not 14.
  • Dividing by the Ar of the element instead of the Mr of the whole compound.
  • Mixing a decimal and a percentage: 0.6 and 60% are the same share, but 0.6% is not.
  • Using the Mr of a different compound, such as FeO instead of Fe₂O₃. Check the formula before you start.
  • Worrying when the percentages add up to 99.9% or 100.1%. Rounding causes this, and it is not an error.

More chemistry formulas

Relative formula massConcentrationMolesPeriodic tableAll chemistry equations

Frequently asked questions

Multiply the element's Ar by the number of its atoms, divide by the Mr of the compound and multiply by 100. For carbon in CH₄: 12 ÷ 16 × 100 = 75%.

88.9%: oxygen contributes 16 to water's Mr of 18, and 16 ÷ 18 × 100 = 88.9%.

Yes. Percentage composition lists the percentage by mass of every element in a compound, and together they add up to 100%.

Because each one is rounded. Totals such as 99.9% or 100.1% are normal; keep more decimal places if you need an exact total.