Density formula: ρ = m/V
Density = mass ÷ volume, written ρ = m/V. The Greek letter ρ (say rho) is density in kilograms per cubic metre (kg/m³), m is mass in kilograms (kg) and V is volume in cubic metres (m³). All six GCSE physics and combined science specifications list it for recall, and the sheet in your exam prints it anyway.
Equation
ρ = m ÷ V
| Symbol | Quantity | Unit |
|---|---|---|
ρ | density | kg/m³ |
m | mass | kg |
V | volume | m³ |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Recall | ρ = m/V |
| AQA Combined Science (8464) | Recall | ρ = m/V |
| Edexcel Physics (1PH0) | Recall | ρ = m/V |
| Edexcel Combined Science (1SC0) | Recall | ρ = m/V |
| OCR Gateway Physics A (J249) | Recall | ρ = m/V |
| OCR Twenty First Century Physics B (J259) | Recall | ρ = m/V |
Calculator: ρ = m ÷ V
What density tells you
Density tells you how much mass is packed into each cubic metre of a material. Lead is dense, so a lead fishing weight feels heavy for its size. Polystyrene is the opposite: a big block barely registers on the scales.
Density belongs to the material, whatever the size of the piece. A steel paperclip and a steel girder have the same density. The girder simply has more mass and more volume, in the same ratio.
An object floats in water if its average density is less than the density of water, which is about 1000 kg/m³. A steel ship floats because its hull holds a lot of air, so the ship as a whole has a low average density.
How the boards write it
AQA, Edexcel and OCR all print this one in the same way: ρ = m/V. It sits on the recall list of AQA 8463 and 8464, Edexcel 1PH0 and 1SC0, OCR Gateway J249 and OCR Twenty First Century J259.
Recall is the word each specification uses for its own list. In the exam hall it makes no difference, since every board has printed all its equations on a sheet in the paper since 2025. The physics equation sheet page explains how that works, and the Edexcel equation list shows the Edexcel version.
Rearranging and changing units
You can make mass or volume the subject:
- m = ρ × V
- V = m ÷ ρ
Lab data usually comes in grams and cubic centimetres. You have two choices. Work in g/cm³ and convert at the end, or convert first. One g/cm³ equals 1000 kg/m³, so water is 1 g/cm³ or 1000 kg/m³.
Converting volume trips people up. A cube 1 m on each side is 100 cm × 100 cm × 100 cm, which is 1 000 000 cm³. So divide cm³ by one million to get m³.
Density also appears inside other equations. You need it for the pressure in a liquid, where deeper and denser liquids push harder. Once you know a mass, the weight equation gives the pull of gravity on it.
You can practise these conversions on our sister site too, in the Density Mass Volume game, which also asks which objects float.
Worked examples
ρ
- Change the mass to kilograms: 540 g = 0.54 kg
- Change the volume to cubic metres: 200 cm³ = 0.0002 m³
- ρ = m ÷ V
- ρ = 0.54 ÷ 0.0002
- ρ = 2700 kg/m³
2700 kg/m³
m
- m = ρ × V
- m = 750 × 0.05
- m = 37.5 kg
37.5 kg
V
- V = m ÷ ρ
- V = 1.5 ÷ 920
- V = 0.00163 m³ (to 3 significant figures)
0.00163 m³
Common mistakes
- Dividing cm³ by 100 to get m³. Volume has three dimensions, so the factor is 100 cubed, which is one million.
- Mixing grams with cubic metres. Pick one set of units for mass and volume and stick to it, or the answer is off by a factor of 1000.
- Writing V = ρ ÷ m after rearranging. Test it on water: 2 kg at 1000 kg/m³ fills 0.002 m³, which is 2 ÷ 1000, while 1000 ÷ 2 gives a silly 500.
- Thinking a bigger piece of a material is denser. Cutting a block in half halves the mass and the volume, so the density stays the same.
You can drill ρ, m and V as the subject in the Equation Rearranger.
Questions people ask
How do you measure the volume of an odd shape?
Lower it into a measuring cylinder or a eureka can full of water. The volume of water it pushes aside equals the volume of the object. Then weigh it and divide.
Why does ice float on water?
Water expands as it freezes. The same mass takes up more room, so ice has a lower density than liquid water, at about 920 kg/m³.
Which boards include the density equation?
All three. AQA, Edexcel and OCR list it in all six specifications on this site, with the same symbols.