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Density: formula, units and how to measure it

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Density is the mass per unit volume of a substance: how tightly its mass is packed.

ρ=mV\rho = \frac{m}{V}

where ρ\rho is density (kg/m³), mm is mass (kg) and VV is volume (m³). A block of lead and a block of wood the same size have very different masses because lead is far denser. Try the density calculator to check your working.

Key takeaways

  • Density = mass ÷ volume.
  • 1 g/cm³ = 1,000 kg/m³; water is about 1,000 kg/m³.
  • Measure irregular volumes by displacement.
  • Less dense than the liquid: it floats.

Worked examples

  1. A metal block has a mass of 2.7 kg and a volume of 0.001 m³. ρ=2.7÷0.001=2,700\rho = 2.7 \div 0.001 = 2{,}700 kg/m³ (that's aluminium).
  2. A stone has a mass of 60 g and a volume of 24 cm³. ρ=60÷24=2.5\rho = 60 \div 24 = 2.5 g/cm³, which is 2,500 kg/m³.
  3. What is the mass of 2 m³ of water? m=ρ×V=1000×2=2,000m = \rho \times V = 1000 \times 2 = 2{,}000 kg.

Units

UnitUsed when
kg/m³SI unit; large objects and most exam questions
g/cm³Small samples measured in a lab

To convert g/cm³ to kg/m³, multiply by 1,000. This works because 1 kg = 1,000 g and 1 m³ = 1,000,000 cm³.

Measuring density

Regular solid: measure length, width and height with a ruler, multiply for the volume, and find the mass on a balance.

Irregular solid: fill a displacement (eureka) can to the spout, lower the object in, and collect the water that overflows in a measuring cylinder. That volume equals the object's volume.

Liquid: put an empty measuring cylinder on a balance and zero it, pour in a measured volume of liquid, and read the mass.

Repeating the measurements and finding a mean makes the result more reliable.

Density and the particle model

Solids and liquids are usually denser than gases because their particles are much closer together. When a substance changes state, its mass stays the same but its volume changes, so its density changes. Water is unusual: ice is slightly less dense than liquid water, which is why ice floats.

Floating and sinking

An object floats if its overall density is less than the liquid's and sinks if it's greater. A steel ship floats because its shape includes a lot of air, so its average density is less than water's. A liquid with a lower density floats on a denser one, which is why oil floats on water.

Common mistakes

  • Dividing volume by mass.
  • Forgetting to convert cm³ to m³ (divide by 1,000,000) when the answer is wanted in kg/m³.
  • Reading a measuring cylinder at the top of the meniscus instead of the bottom.

Approximate densities of common materials

MaterialDensity (kg/m³)
Air (room temperature)about 1.2
Iceabout 920
Waterabout 1,000
Aluminiumabout 2,700
Ironabout 7,900
Goldabout 19,300

Values change slightly with temperature. Use the data your question gives.

Practice questions

  1. A 0.4 kg block has a volume of 0.0002 m³. What is its density?
  2. A liquid has a density of 0.8 g/cm³. What is the mass of 250 cm³ of it?
  3. An object with a density of 1,200 kg/m³ is placed in water. Does it float or sink?

Answers: 2,000 kg/m³; 200 g; it sinks, because it's denser than water.

Frequently asked questions

Does density change if you cut an object in half?

No. Both the mass and the volume halve, so the density stays the same. Density is a property of the material.

What is the density of water?

About 1,000 kg/m³, or 1 g/cm³.

How do you find the volume of an irregular object?

By displacement: put it in water and measure how much water it pushes out (or how much the level rises).

Why does ice float?

Ice is slightly less dense than liquid water, because its particles are held in an open arrangement.

Sources

  1. GCSE Physics (8463) specification: subject content. AQA.
  2. Cambridge IGCSE Physics 0625 syllabus for 2026, 2027 and 2028. Cambridge International.

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