Density of materials: density, ρ, in kilograms per metre cubed, kg/m³

The idea

Density is represented by the Greek letter ρ (rho) and its SI unit is the kilogram per cubic metre, written kg/m³. This unit means the mass in kilograms contained in one cubic metre of material. For example, water has a density of about 1000 kg/m³, so 1 m³ of water has a mass of about 1000 kg. A smaller unit, g/cm³, is often used in laboratory work; 1 g/cm³ = 1000 kg/m³. To convert g/cm³ to kg/m³, multiply by 1000; to convert kg/m³ to g/cm³, divide by 1000. Using the correct unit matters because a numerical answer without the correct unit does not fully communicate the density.

What earns the marks

• State that ρ is the symbol for density and that its SI unit is kg/m³.
• Interpret kg/m³ as kilograms of mass per cubic metre of volume.
• Convert between g/cm³ and kg/m³ using the factor 1000.
• Use the correct unit consistently in calculations and final answers.
• Compare densities of materials using values in the same unit.

Common mistakes and how to put them right

• Writing kg/m² instead of kg/m³.

  Put it right: Density involves volume, so the length unit must be cubed.

• Treating g/cm³ and kg/m³ as interchangeable without converting.

  Put it right: 1 g/cm³ equals 1000 kg/m³, not 1 kg/m³.

• Omitting the unit or using kg.

  Put it right: A density value must include both a mass unit and a volume unit.

Exam tips

• Write the unit as kg/m³ or kg m⁻³ and keep it with the numerical value throughout.
• When converting, multiply by 1000 to go from g/cm³ to kg/m³ and divide by 1000 for the reverse.
• Use the symbol ρ only if the question uses it; otherwise write density to avoid confusion.