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Moles Calculator: How to Calculate Moles

To calculate moles, divide the mass by the relative formula mass: moles = mass ÷ Mr, or n = m / M with m in g and M in g/mol. For a gas at room temperature and pressure, n = V / 24 with V in dm³; from a number of particles, n = N / (6.02 × 10²³).

Moles formula: n = m / M

From mass
n = mM
n = mMm = n·MM = mn
From gas volume
n = VVm
n = VVmV = n·Vm
From number of particles
n = NNA
n = NNAN = n·NA
n
number of moles, mol
m
mass, g
M
molar mass, g/mol
V
gas volume, dm³
Vm
molar gas volume, dm³/mol
N
number of particles
NA
Avogadro constant, mol⁻¹

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.

Fe₂O₃M(Fe₂O₃) = 160 g/mol

0.306 mol
g/mol
nnumber of moles
0.306 mol
number of moles: 0.306 mol
The scales hold 49 g of Fe₂O₃ (M = 160 g/mol), which is 0.306 mol; each heap below is one mole.

Step-by-step solution

  1. Molar massM(Fe₂O₃) = 2·56 + 3·16 = 160 g/mol
  2. Formulan = mM
  3. Substituten = 49 g160 g/mol
  4. Answern ≈ 0.306 mol
How many particles is that? n = 0.3063 mol → number of particles N

Moles calculation examples

  1. Example 1

    A beaker contains 9 g of water, H₂O. Calculate the number of moles of water.

    Given:H₂Om = 9 g
    1. Molar massM(H₂O) = 2·1 + 16 = 18 g/mol
    2. Formulan = mM
    3. Substituten = 9 g18 g/mol
    4. Answern = 0.5 mol

  2. Example 2

    Calculate the mass of 0.2 mol of calcium carbonate, CaCO₃.

    Given:CaCO₃n = 0.2 mol
    1. Molar massM(CaCO₃) = 40 + 12 + 3·16 = 100 g/mol
    2. Formulam = n·M
    3. Substitutem = 0.2 mol · 100 g/mol
    4. Answerm = 20 g

  3. Example 3

    A reaction produces 48 dm³ of hydrogen gas at room temperature and pressure. One mole of any gas occupies 24 dm³/mol at RTP. Calculate the number of moles of hydrogen.

    Given:V = 48 dm³Vm = 24 dm³/mol
    1. Formulan = VVm
    2. Substituten = 48 dm³24 dm³/mol
    3. Answern = 2 mol

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What is a mole?

A mole is the chemist's way of counting particles. One mole of any substance contains 6.02 × 10²³ particles (atoms, molecules or ions), a number called the Avogadro constant. The mass of one mole in grams equals the substance's relative formula mass, so one mole of carbon (Ar = 12) has a mass of 12 g and one mole of water (Mr = 18) has a mass of 18 g.

The key formula is moles = mass ÷ Mr. Rearranged, mass = moles × Mr, which is how you find the mass of product a reaction makes. For gases there is a shortcut: at room temperature and pressure (RTP, 20 °C and 1 atmosphere), one mole of any gas occupies 24 dm³, so moles = volume in dm³ ÷ 24. The type of gas does not matter, only the number of molecules.

A worked intuition: 36 g of water is 2 × 18 g, so it is 2 mol, or 1.204 × 10²⁴ molecules. Mole ratios from balanced equations let you move from one substance to another: in 2H₂ + O₂ → 2H₂O, 2 mol of hydrogen react with 1 mol of oxygen. Most GCSE reacting-mass questions take three steps: mass to moles, use the ratio, then moles back to mass.

Common mistakes

  • Using the Ar of one atom instead of the Mr of the whole formula: for CO₂ use 44, not 12.
  • Mixing cm³ and dm³ in gas calculations. Divide cm³ by 1000 to get dm³ before dividing by 24, or divide cm³ by 24 000 directly.
  • Using 24 dm³/mol for a liquid or a solid. The molar gas volume only works for gases.
  • Dividing the wrong way round: it is mass ÷ Mr, not Mr ÷ mass. If 36 g of water gives 0.5 mol, the fraction is upside down.
  • Entering the mass in kg. In chemistry the mass goes in grams, so that it matches M in g/mol.

More chemistry formulas

Relative formula massAvogadro constantMolarityPeriodic tableAll chemistry equations

Frequently asked questions

Divide the mass in grams by the relative formula mass: moles = mass ÷ Mr. For example, 88 g of CO₂ (Mr = 44) is 2 mol.

At room temperature and pressure, divide the volume in dm³ by 24: moles = volume ÷ 24. If the volume is in cm³, divide by 24 000.

Multiply the moles by Mr: mass = moles × Mr. For example, 0.5 mol of NaCl (Mr = 58.5) has a mass of 29.25 g.

The amount of substance that contains 6.02 × 10²³ particles. Its mass in grams equals the relative formula mass.

Both values are used. GCSE uses 24 dm³/mol at room temperature and pressure (20 °C); 22.4 dm³/mol applies at standard temperature and pressure (0 °C). Use the value given in the question.