Density is a measure of the mass in a given volume of a substance. It can be calculated using the equation:

density = \frac{mass}{volume}

This is when:

  • density is measured in kilograms per metre cubed (kg/m³)
  • mass is measured in kilograms (kg)
  • volume is measured in metres cubed (m³)

Example 1

A piece of aluminium has a mass of 200 kg and a volume of 0.074 m3. Calculate its density in kg/m3, to two significant figures.

density = \frac{mass}{volume}

density = \frac{200}{0.074}

= 2,700 \: kg/m^3

The units for density

The kilogram (kg) is the standard unit for mass. The cubic metre (m3) is the standard unit for volume. However, in many laboratory situations mass will be measured in grams (g) and volume in cubic centimetres (cm3).

Example 2

A piece of iron has a mass of 100 g and a volume of 12.7 cm3. Calculate its density in g/cm3.

density = \frac{mass}{volume}

density = \frac{100}{12.7}

= 7.87 \: g/cm^3

Converting between units

To convert between units:

  • kg/m3 to g/cm3, divide by 1,000
  • g/cm3 to kg/m3, multiply by 1,000
1 g/cm3 = 1,000 kg/m3

Example 3

The density of air at 20 °C is 0.00120 g/cm3. Give its density in kg/m3.

density = 0.00120 × 1,000

= 1.20 kg/m3