✓ Revise Right course
The density formula is ρ = m/V: density = mass ÷ volume, measured in kg/m³. Free GCSE AQA Physics notes with key definitions and 15 questions answered.
Calculating Density is part of Changes of state and the particle model in GCSE AQA Higher Physics.
3 min
Reading time
13
Lessons in this topic
GCSE AQA Higher
Pathway
Reviewed by Revise Right
Content review
The density formula is ρ = m/V: density = mass ÷ volume, measured in kg/m³. Free GCSE AQA Physics notes with key definitions and 15 questions answered.
AQA GCSE Physics mock draft, 26–31 Oct. Draft coverage: Physics Paper 1 (Higher tier). Reviewed for an original-practice sitting; check student availability before registering. Marking and results will follow later, after separate approval. Eligible new accounts receive a five-day Pro trial when signup email verification completes. Previous trials keep their original expiry. After expiry, new papers need Pro unless you have an explicitly confirmed free sitting offer for this event. That offer adds no Pro time or AI learning. Saved attempts and released results remain readable. No card or automatic charge.
Use this lesson to stay inside Changes of state and the particle model while connecting the detail back to the wider Particle model of matter topic.
Read the core explanations from Calculating Density before testing yourself from memory.
Why does ice float on water when it's made of the same stuff? Why do oil spills spread across the ocean surface instead of sinking? The answer lies in a property called density - how tightly packed the particles are in different materials.
Density explains why a small piece of lead feels heavier than a large piece of polystyrene. It's not about size - it's about how much mass is crammed into each cubic metre of space.
This equation can be rearranged to find any of the three quantities. If you know density and volume, you can find mass: $m = \rho \times V$. If you know mass and density, you can find volume: $V = \frac{m}{\rho}$.
The triangle method helps you remember: put density at the top, mass and volume at the bottom. Cover the quantity you want to find, and the triangle shows you the calculation.
Density calculations are straightforward once you master the units. The key is making sure everything is in the correct SI units before you substitute into the formula.
Worked example: Finding the Density of a Metal Block
A metal block has mass 2.4 kg and dimensions 20 cm × 15 cm × 8 cm. Calculate its density. [3 marks]
Answer: 1000 kg/m³
Unit conversion trap: The most common mistake is forgetting to convert centimetres to metres. Remember: 1 cm = 0.01 m, so 20 cm = 0.20 m. If you use cm³ instead of m³, your density answer will be 1,000,000 times too small, so always convert volume carefully before substituting into the formula.
Worked example: Finding Mass from Density
Aluminium has density 2700 kg/m³. What is the mass of 0.5 m³ of aluminium? [2 marks]
Answer: 1350 kg
The displacement method works because when you put an object in water, it pushes away a volume of water equal to its own volume. This is especially useful for irregular solids, where you cannot measure length, width and height accurately. To improve accuracy, make sure the object is fully submerged, read the meniscus carefully, and choose the smallest measuring cylinder that still fits the object so the scale divisions are easier to read.
Density questions are mark-winners if you follow the method systematically. Examiners award marks for showing the formula, correct substitution, and the final answer with units.
Mark-winning language: Use 'displacement method' not just 'put it in water'. Write 'volume of displaced water equals volume of object' to show you understand the principle.
Published by Revise Right. Use the official specification reference to check the requirements for your course. Content updated: 2026-03-20.
Move to the related lessons or back to the topic page when you need the wider sequence before exam-style practice.
The density formula is ρ = m/V: density = mass ÷ volume, with mass in kilograms (kg), volume in cubic metres (m³) and density in kg/m³. It rearranges to m = ρ × V and V = m/ρ.
Mass is found by rearranging the density equation to m = ρ × V. Aluminium has a density of 2700 kg/m³, so 0.5 m³ of aluminium has a mass of 2700 × 0.5 = 1350 kg.
Density is the mass per unit volume of a material, telling us how much matter is packed into a given space. It explains why a small piece of lead feels heavier than a large piece of polystyrene: it is about how much mass is crammed into each cubic metre.
To calculate density, convert to SI units, find the volume, then divide mass by volume. A 2.4 kg metal block measuring 20 cm × 15 cm × 8 cm has a volume of 0.20 × 0.15 × 0.08 = 0.0024 m³, so its density is 2.4 ÷ 0.0024 = 1000 kg/m³.
The density of aluminium is 2700 kg/m³, meaning each cubic metre of aluminium has a mass of 2700 kg. Using m = ρ × V, 0.5 m³ of aluminium has a mass of 1350 kg.
The density triangle has density at the top and mass and volume at the bottom. Covering the quantity to be found shows the calculation: density = mass ÷ volume, mass = density × volume and volume = mass ÷ density.
The displacement method finds the volume of an object by placing it in water: the volume of displaced water equals the volume of the object. It is especially useful for irregular solids, whose length, width and height cannot be measured accurately.
The density of an irregular object is measured using the displacement method: the object pushes away a volume of water equal to its own volume. Make sure it is fully submerged, read the meniscus carefully, and use the smallest measuring cylinder that fits the object.
The density of a block is found by converting its dimensions to metres, multiplying them for the volume, then using ρ = m/V. A 2.4 kg block measuring 20 cm × 15 cm × 8 cm has V = 0.20 × 0.15 × 0.08 = 0.0024 m³, so ρ = 2.4 ÷ 0.0024 = 1000 kg/m³.
Volume must be in m³ for density in kg/m³, and the most common mistake is forgetting to convert centimetres to metres. Since 1 cm = 0.01 m, using cm³ instead of m³ makes the density answer 1,000,000 times too small.
The density equation ρ = m/V rearranges to V = m/ρ to find volume, and to m = ρ × V to find mass. In the triangle method, density goes at the top with mass and volume at the bottom.
The accuracy of the displacement method is improved by making sure the object is fully submerged, reading the meniscus carefully, and choosing the smallest measuring cylinder that still fits the object so the scale divisions are easier to read.
0.5 m³ of aluminium has a mass of 1350 kg. Aluminium has a density of 2700 kg/m³, and m = ρ × V = 2700 × 0.5 = 1350 kg, since kg/m³ × m³ = kg.
A small piece of lead feels heavier than a large piece of polystyrene because lead has a much higher density. Density is about how much mass is crammed into each cubic metre of space, not about size.
Mass is the amount of matter in an object, measured in kilograms (kg), and volume is the amount of three-dimensional space it occupies, measured in cubic metres (m³). Density = mass ÷ volume then gives density in kg/m³.