Density is a measure of how much mass is packed into a given volume. A small, heavy object can have a much greater density than a large, light one. Understanding density — and the formula that links mass, volume, and density — is a core part of KS3 physics, typically covered in Year 7 or Year 8.
What is density?
Density is defined as the mass per unit volume of a substance. In plain terms, it tells you how tightly matter is packed together. A piece of lead and a piece of polystyrene of the same size have very different masses: the lead is far denser because its atoms are heavier and more closely packed.
The formula for density is:
density = mass ÷ volume
Written using symbols:
ρ = m ÷ V
Where:
- ρ (the Greek letter rho) = density, measured in kilograms per cubic metre (kg/m³) or grams per cubic centimetre (g/cm³)
- m = mass, measured in kilograms (kg) or grams (g)
- V = volume, measured in cubic metres (m³) or cubic centimetres (cm³)
Units: at KS3, g/cm³ is common in practical work because it gives convenient numbers. 1 g/cm³ = 1000 kg/m³.
How do you rearrange the density formula?
The density triangle is a useful memory aid. Write D (density) on top, M (mass) on the bottom left, and V (volume) on the bottom right:
- To find density: D = M ÷ V
- To find mass: M = D × V
- To find volume: V = M ÷ D
Densities of common materials
Knowing some typical values helps you reason about everyday situations:
| Material | Density (g/cm³) | Notes |
|---|---|---|
| Air | 0.0013 | Very low; gas particles far apart |
| Wood (pine) | 0.5 | Less than water — floats |
| Water (liquid) | 1.0 | The reference point |
| Ice | 0.92 | Slightly less than liquid water — ice floats |
| Aluminium | 2.7 | Light metal |
| Iron | 7.8 | Heavy metal |
| Lead | 11.3 | Very dense metal |
| Gold | 19.3 | Extremely dense |
Notice that water has a density of 1.0 g/cm³. Any substance with a density less than 1.0 g/cm³ will float in water; any substance denser than 1.0 g/cm³ will sink.
Why do objects float or sink?
An object floats if its average density is less than the density of the fluid it is placed in. This explains several everyday observations:
- Ice floats on water — ice (0.92 g/cm³) is slightly less dense than liquid water (1.0 g/cm³). This happens because water molecules in ice form a hexagonal lattice that is more spread out than in liquid water. This is unusual — most solids are denser than their liquids.
- A steel ship floats — a solid block of steel sinks (density ~7.8 g/cm³), but a ship is hollow. The ship's hull displaces a volume of water. If the average density of the ship (steel + air inside) is less than water, the upward force (upthrust) equals the ship's weight and it floats.
- Submarines dive and surface — by flooding or emptying ballast tanks with water, a submarine changes its average density relative to seawater, allowing it to sink or rise.
Worked example: calculating density
Question: A block of wood has a mass of 120 g and a volume of 200 cm³. What is its density? Will it float in water?
Working:
ρ = m ÷ V ρ = 120 g ÷ 200 cm³ ρ = 0.6 g/cm³
Conclusion: The density (0.6 g/cm³) is less than the density of water (1.0 g/cm³), so the block will float.
Question: A rock has a density of 2.5 g/cm³ and a volume of 40 cm³. What is its mass?
Working:
m = D × V m = 2.5 g/cm³ × 40 cm³ m = 100 g
How do you measure density in the lab?
For a regular solid (e.g. a rectangular block)
- Measure the mass using a balance (in grams).
- Measure the length, width, and height with a ruler (in cm).
- Calculate volume: V = length × width × height (in cm³).
- Calculate: ρ = m ÷ V.
For an irregular solid (e.g. a stone)
- Measure the mass on a balance.
- Part-fill a measuring cylinder with water and record the volume (e.g. 50 cm³).
- Carefully lower the solid into the water on a piece of string and record the new volume (e.g. 72 cm³).
- Volume of solid = new volume − original volume = 72 − 50 = 22 cm³.
- Calculate: ρ = m ÷ V.
This method is called displacement (or the Eureka method, named after the Greek mathematician Archimedes, who allegedly discovered the principle in around 250 BCE while stepping into a bath).
The Department for Education's Science Programmes of Study for Key Stage 3 requires pupils to calculate density using the formula, and relate density to the particle model of matter. BBC Bitesize KS3 Physics covers the density formula, calculations, and the practical method for measuring the density of regular and irregular objects.
Frequently asked questions
What are the units of density and how do you convert between them?
At KS3, density is most often measured in grams per cubic centimetre (g/cm³) in lab work, and in kilograms per cubic metre (kg/m³) in SI units. To convert from g/cm³ to kg/m³, multiply by 1000. So water at 1.0 g/cm³ is the same as 1000 kg/m³. When doing calculations, it is essential to use consistent units throughout: if mass is in grams and volume is in cm³, your density answer is in g/cm³. If mass is in kg and volume is in m³, your density answer is in kg/m³.
Why does ice float on water when most solids sink in their own liquid?
Most solids are denser than their liquid form because, when a substance cools and solidifies, the particles lose energy, slow down, and pack more closely together. Water is a famous exception: when water freezes into ice, the molecules form a hexagonal (six-sided) arrangement held together by hydrogen bonds. This structure is actually slightly less closely packed than liquid water, so ice has a lower density (0.92 g/cm³) than liquid water (1.0 g/cm³). This property is vital for life: lakes freeze from the top down, and the floating ice layer insulates the liquid water below, allowing aquatic organisms to survive winter.
How do ships made of steel float if steel is denser than water?
A solid block of steel (density ~7.8 g/cm³) placed in water will sink because it is much denser than water (1.0 g/cm³). A steel ship floats because the ship is not solid steel — it is mostly air inside a steel hull. The relevant density is the average density of the whole ship (steel + air + contents). By making the hull the right shape and size, naval architects ensure that the ship displaces a volume of water whose weight equals the weight of the ship. At that point, the upthrust (buoyancy force) balances the ship's weight and it floats. If the ship floods with water and the air is replaced, its average density rises above water's, and it sinks.
How do you measure the density of a liquid?
To find the density of a liquid, measure a known volume using a measuring cylinder (e.g. 50 cm³), then measure its mass by weighing the cylinder before and after adding the liquid (and subtracting the mass of the cylinder itself). Divide mass by volume to get density. For example, if 50 cm³ of cooking oil has a mass of 46 g, its density = 46 ÷ 50 = 0.92 g/cm³. This is less than water (1.0 g/cm³), which is why oil floats on water.
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