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Concentration Formula and Calculator

At GCSE, concentration = mass of solute ÷ volume of solution, with the mass in g and the volume in dm³, so the concentration is in g/dm³. As a percentage by mass, w = m(solute) / m(solution) × 100 %, where the mass of the solution is the solute plus the water.

Concentration formula

Mass of solution known
w = msolutemsolution · 100 %
w = msolutemsolution · 100 %msolute = w·msolution100 %msolution = msolute·100 %w
Mass ÷ volume (g/dm³)
c = msoluteV
c = msoluteVmsolute = c·VV = msolutec
Solute + water
w = msolutemsolute + mwater · 100 %
w = msolutemsolute + mwater · 100 %msolute = w·mwater100 % − wmwater = msolute·(100 % − w)w
From volume and density
w = msoluteρ·V · 100 %
w = msoluteρ·V · 100 %msolute = w·ρ·V100 %V = msolute·100 %w·ρ
w
percentage by mass of solute, %
msolute
mass of solute, g
msolution
mass of solution, g
c
concentration, g/dm³
V
volume of solution, dm³
mwater
mass of water, g
ρ
density of solution, g/cm³

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.

20 %
wpercentage by mass of solute
20 %
percentage by mass of solute: 20 %
20 g of solute in 100 g of solution gives w = 20 %: the colour and the gauge show how concentrated it is.

Step-by-step solution

  1. Formulaw = msolutemsolution · 100 %
  2. Substitutew = 20 g100 g · 100 %
  3. Answerw = 20 %
Convert w = 20 % to a concentration in mol/dm³

Concentration calculation examples

  1. Example 1

    A solution has a mass of 200 g and contains 10 g of dissolved sugar. Calculate the percentage by mass of sugar in the solution.

    Given:msolute = 10 gmsolution = 200 g
    1. Formulaw = msolutemsolution · 100 %
    2. Substitutew = 10 g200 g · 100 %
    3. Answerw = 5 %

  2. Example 2

    A student dissolves 4 g of sodium hydroxide in water and makes the solution up to 250 cm³. Calculate the concentration of the solution in g/dm³.

    Given:msolute = 4 gV = 250 cm³
    1. Formulac = msoluteV
    2. Converting unitsV = 250 cm³ = 0.25 dm³
    3. Substitutec = 4 g0.25 dm³
    4. Answerc = 16 g/dm³

  3. Example 3

    25 g of salt is dissolved in 100 g of water. Calculate the percentage by mass of salt in the solution.

    Given:msolute = 25 gmwater = 100 g
    1. Formulaw = msolutemsolute + mwater · 100 %
    2. Substitutew = 25 g25 g + 100 g · 100 %
    3. Answerw = 20 %

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What does concentration mean?

Concentration tells you how much solute is dissolved in a given amount of solution. At GCSE it is concentration = mass of solute ÷ volume of solution, measured in g/dm³. Dissolving 10 g of salt to make 0.5 dm³ of solution gives 20 g/dm³. Remember that 1 dm³ = 1000 cm³, so divide a volume in cm³ by 1000 first.

Concentration can also be given as a percentage by mass: the mass of solute divided by the mass of the whole solution, times 100. The mass of the solution is the solute plus the solvent, so 15 g of sugar in 135 g of water makes 150 g of solution at 10%. If you know the volume and density of a solution instead of its mass, mass of solution = density × volume.

Concentration does not depend on how much solution you have. Pour half of a 40 g/dm³ solution into another beaker and both halves are still 40 g/dm³, because the mass and the volume halve together. Adding water dilutes a solution: the mass of solute stays the same, the volume grows and the concentration falls. At Higher tier, concentration is also given in mol/dm³.

Common mistakes

  • Using the mass of water instead of the mass of solution: 10 g of salt in 90 g of water is 10 g out of 100 g, not 10 out of 90.
  • Leaving the volume in cm³. Divide by 1000 first: 500 cm³ is 0.5 dm³.
  • Confusing g/dm³ with mol/dm³. To go from g/dm³ to mol/dm³, divide by the Mr of the solute.
  • Mixing a decimal and a percentage: 0.15 and 15% are the same, but 0.15% is not.
  • Getting a percentage over 100%. The solute can never have more mass than the whole solution, so check which mass is which.

More chemistry formulas

MolarityPercentage by massMolesPeriodic tableAll chemistry equations

Frequently asked questions

Concentration = mass of solute ÷ volume of solution. With the mass in g and the volume in dm³, the answer is in g/dm³.

Divide by 1000, because 1 dm³ = 1000 cm³. For example, 250 cm³ is 0.25 dm³.

Divide the mass of solute by the mass of the solution (solute plus water) and multiply by 100. For 30 g of salt in 270 g of water: 30 ÷ 300 × 100 = 10%.

Divide by the Mr of the solute. Sodium hydroxide (Mr = 40) at 80 g/dm³ is 80 ÷ 40 = 2 mol/dm³.

No. The mass of solute and the volume fall in the same proportion, so the concentration stays the same.