How do you calculate density?
Short answer
Density = mass ÷ volume, written ρ = m ÷ V. With mass in kilograms and volume in cubic metres, density is in kg/m³; with grams and cm³, it is in g/cm³. An object floats in water if its density is less than that of water, 1 g/cm³ or 1000 kg/m³.
Step by step
- Measure the mass on a balance.
- Find the volume: for a regular shape, length × width × height; for an irregular object, the volume of water it displaces.
- Divide the mass by the volume.
- Give the units, matching the units you used.
Worked example
A stone has a mass of 270 g and displaces 100 cm³ of water
- ρ = 270 ÷ 100
- ρ = 2.7 g/cm³
- That is denser than water, so the stone sinks
Common mistakes
- Mixing units, such as grams with m³.
- Dividing volume by mass.
- Thinking a heavier object is always denser. A large log is heavy but floats.
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