Density of materials: ρ = m / V

The idea

This equation defines density ρ as mass m divided by volume V. To use it, measure mass in kilograms or grams and volume in cubic metres or cubic centimetres, then divide. For example, if m = 0.60 kg and V = 0.00020 m³, then ρ = 0.60 kg ÷ 0.00020 m³ = 3000 kg/m³. Rearranged forms are m = ρV and V = m / ρ, which help find mass or volume when density is known. In calculations, keep units consistent: g with cm³ gives g/cm³, and kg with m³ gives kg/m³. The equation applies to solids, liquids and gases, but gas densities are much lower because particles are far apart. A common task is to identify an unknown material by comparing its calculated density with a table of known values.

What earns the marks

• Identify the symbols ρ, m and V as density, mass and volume respectively.
• Substitute numerical values into ρ = m / V without rearranging incorrectly.
• Rearrange the equation to m = ρV or V = m / ρ when required.
• Keep units consistent and state the final unit, such as kg/m³ or g/cm³.
• Use the calculated density to identify a material from a data table.
• Recognise that density is a material property and is independent of sample size.

Common mistakes and how to put them right

• Dividing volume by mass instead of mass by volume.

  Put it right by checking that ρ = m / V and that the answer has units of mass per volume.

• Mixing units, such as grams with cubic metres, without converting.

  Put it right by converting all quantities to a consistent unit system first.

• Forgetting to cube the side length when finding volume of a cube.

  Put it right by using V = s³ for a cube.

Exam tips

• Write the equation, then substitute values with units before calculating to make method clear.
• Check that the final unit matches the calculation: g ÷ cm³ gives g/cm³, and kg ÷ m³ gives kg/m³.
• For irregular objects, describe displacement method for volume and then use ρ = m / V.