Density measures how much mass is packed into a volume: density = mass ÷ volume, usually in g/cm³ or kg/m³. Pressure measures how concentrated a force is: pressure = force ÷ area, in N/m² (pascals). Both formulae rearrange in the same way, so if you know two of the three quantities you can always find the third.
Density and pressure
- Density = mass ÷ volume
- Mass = density × volume; volume = mass ÷ density
- Pressure = force ÷ area
- Force = pressure × area; area = force ÷ pressure
- 1 g/cm³ = 1000 kg/m³
Density
Density compares mass with volume. A block of mass 270 g and volume 30 cm³ has density 270 ÷ 30 = 9 g/cm³, meaning each cubic centimetre has a mass of 9 grams. Denser materials have more mass in the same volume. The units of density come from the units used: grams and cm³ give g/cm³.
Using a formula triangle
A formula triangle puts mass at the top and density and volume at the bottom. Cover the quantity you want: covering mass leaves density × volume, and covering volume leaves mass ÷ density. The same triangle works for pressure, with force at the top and pressure and area at the bottom.
Pressure
Pressure compares a force with the area it acts on: pressure = force ÷ area. A force of 360 N on 1.5 m² gives a pressure of 240 N/m². The same force on a smaller area gives a greater pressure, which is why a sharp knife cuts more easily than a blunt one.
Checking units
Make sure the units match before calculating. If the mass is in kilograms and the volume in cm³, convert one of them first. Converting density from g/cm³ to kg/m³ multiplies by 1000, so 1.2 g/cm³ is 1200 kg/m³.
Problems with mixtures and shapes
Some questions combine density with the volume of a shape, or ask for the density of a mixture. Work out each mass separately using mass = density × volume, add the masses and the volumes, then divide total mass by total volume.
Worked examples
Example 1. A metal block has mass 270 g and volume 30 cm³. Work out its density.
- Density = mass ÷ volume = 270 ÷ 30.
Answer: 9 g/cm³.
Example 2. A piece of iron has density 7.8 g/cm³ and volume 40 cm³. Work out its mass.
- Mass = density × volume = 7.8 × 40.
Answer: 312 g.
Example 3. Aluminium has density 2.7 g/cm³. Work out the volume of 810 g of aluminium.
- Volume = mass ÷ density = 810 ÷ 2.7.
Answer: 300 cm³.
Example 4. A force of 360 N acts on an area of 1.5 m². Work out the pressure.
- Pressure = force ÷ area = 360 ÷ 1.5.
Answer: 240 N/m².
Example 5. A crate exerts a pressure of 150 N/m² on a floor area of 2.4 m². Work out the force.
- Force = pressure × area = 150 × 2.4.
Answer: 360 N.
Common mistakes
- Dividing the wrong way round. Density is mass ÷ volume, not volume ÷ mass.
- Mixing units. Convert so that mass and volume units match the density units.
- Forgetting units in the answer. Give density in g/cm³ or kg/m³, and pressure in N/m².
- Multiplying instead of dividing. Use the formula triangle to check the operation.
- Using area for pressure in cm² with N/m². Convert the area to m² first if the answer is in N/m².
How density and pressure are examined
Density and pressure are compound measures tested on Foundation and Higher papers of Edexcel GCSE (1MA1); density also appears in the 4MA1 International GCSE. Typical questions:
- work out a density, mass or volume
- work out a pressure, force or area
- use the volume of a shape before finding a mass
- combine two materials and find the density of the mixture
The compound measures worksheet includes density and pressure questions with answers. The GCSE proportion revision engine provides more.
Related compound measures are speed, distance and time and rates such as pay and flow.
Frequently asked questions
How is density calculated?
Density = mass ÷ volume.
What is the formula for pressure?
Pressure = force ÷ area.
How do you convert g/cm³ to kg/m³?
Multiply by 1000.