The density formula
Density = mass ÷ volume. Using the formula triangle: Mass = Density × Volume, with mass at the top, and density and volume on the bottom.
Cover the letter you want to find — whatever's left shows the calculation to use.
Worked Example 1
A block has a mass of 180g and a volume of 20cm³. Find its density.
1
Cover "density" in the triangle: this leaves mass ÷ volume
2
Substitute the values: 180 ÷ 20 = 9
Answer9g/cm³
Converting density units
Density is usually measured in g/cm³ or kg/m³. Since 1cm³ of water weighs 1g, and 1m³ of water weighs 1000kg, the conversion factor between the two units is always 1000.
Worked Example 2
Convert a density of 2.5g/cm³ to kg/m³.
1
Recall the conversion: 1g/cm³ = 1000kg/m³
2
Multiply by 1000: 2.5 × 1000 = 2500
Answer2500kg/m³
Finding volume by water displacement
For an irregular object like a rock, its outer dimensions can't be measured directly with a ruler. Instead, submerge it in water and measure how much the water level rises — that rise in volume equals the object's own volume.
The rise in water level exactly equals the volume of the submerged object, however irregular its shape.
Worked Example 3
A rock is lowered into a measuring cylinder, and the water level rises from 150cm³ to 210cm³. The rock has a mass of 156g. Find its density.
1
Find the volume displaced: 210 − 150 = 60cm³
2
Use the density formula: 156 ÷ 60 = 2.6
Answer2.6g/cm³
Mixing substances of different densities
Worked Example 4
40cm³ of metal A (density 11g/cm³) is mixed with 60cm³ of metal B (density 7g/cm³). Assuming the volumes simply add, find the density of the alloy.
1
Find the mass of each metal: A = 40 × 11 = 440g, B = 60 × 7 = 420g
2
Find the total mass and total volume: 440 + 420 = 860g, 40 + 60 = 100cm³
3
Divide total mass by total volume: 860 ÷ 100 = 8.6
Answer8.6g/cm³
Practice questions
Work through each question before checking the answers.
Foundation (Grade 3–5)
Q1A block has a mass of 180g and a volume of 20cm³. Find its density.Foundation
Q2A liquid has a volume of 40cm³ and a mass of 32g. Find its density.Foundation
Q3A metal cube has a density of 8g/cm³ and a volume of 15cm³. Find its mass.Foundation
Q4A substance has a density of 2.5g/cm³. Find the volume of 50g of the substance.Foundation
Q5An object has a mass of 300g and a volume of 60cm³. Find its density.Foundation
Higher (Grade 5–7)
Q6Convert a density of 3g/cm³ to kg/m³.Higher
Q7Convert a density of 2500kg/m³ to g/cm³.Higher
Q8A rock is submerged in a measuring cylinder. The water level rises from 120cm³ to 165cm³. If the rock has a mass of 108g, find its density.Higher
Q9A metal sphere has a density of 7.5g/cm³ and a mass of 300g. Find its volume.Higher
Q10An irregular object is submerged in water, and the water level rises by 35cm³. The object has a density of 4g/cm³. Find its mass.Higher
Higher — Hard (Grade 8–9)
Q11A cube of ice has a mass of 125g and a density of 1g/cm³. Find the length of one side of the cube.Grade 8–9
Q12300cm³ of liquid A (density 0.9g/cm³) is mixed with 200cm³ of liquid B (density 1.4g/cm³). Find the density of the mixture, assuming the volumes simply add.Grade 8–9
Q13A solid sphere has a volume of 300cm³ and floats in a liquid with density 0.8g/cm³, with exactly half the sphere submerged. Find the mass of liquid displaced by the submerged half.Grade 8–9
Q1440cm³ of metal A (density 11g/cm³) is mixed with 60cm³ of metal B (density 7g/cm³). Find the density of the alloy, assuming the volumes simply add.Grade 8–9
Q15A statue is made from a metal with density 8.4g/cm³. The statue has a mass of 6.3kg. Find its volume, in cm³.Grade 8–9
Answers
Foundation (Q1–Q5)
Q19g/cm³
Q20.8g/cm³
Q3120g
Q420cm³
Q55g/cm³
Higher (Q6–Q10)
Q63000kg/m³
Q72.5g/cm³
Q82.4g/cm³(volume = 165 − 120 = 45cm³, 108 ÷ 45)
Q940cm³(300 ÷ 7.5)
Q10140g(35 × 4)
Higher — Hard (Q11–Q15)
Q115cm(volume = 125 ÷ 1 = 125cm³, cube root of 125)
Q121.1g/cm³(mass = 270g + 280g = 550g, volume = 500cm³, 550 ÷ 500)
Q13120g(submerged volume = 150cm³, 150 × 0.8)
Q148.6g/cm³(mass = 440g + 420g = 860g, volume = 100cm³, 860 ÷ 100)
Q15750cm³(6.3kg = 6300g, 6300 ÷ 8.4)
Common mistakes
Common Mistake 1
Using the object's outer dimensions instead of displaced volume
For irregular shapes, don't try to estimate volume from measurements with a ruler — always use the volume of water displaced, which is exact.
Common Mistake 2
Using the wrong conversion factor between g/cm³ and kg/m³
The conversion factor is always 1000 (multiply g/cm³ by 1000 to get kg/m³, or divide kg/m³ by 1000 to get g/cm³) — not 100 or 10,000.
Common Mistake 3
Forgetting to convert kg to g (or m³ to cm³) before calculating
If a mass is given in kg but the density is in g/cm³, convert the mass to grams first — mixing units gives a meaningless result.
Common Mistake 4
Averaging densities instead of using total mass ÷ total volume
When mixing substances, the density of the mixture is not the average of the two densities — find the total mass and total volume separately first.
Exam tips
💡 Exam Tip 1
Draw the M/D/V triangle every time
Sketching the triangle and covering the unknown removes any doubt about whether to multiply or divide, especially under exam pressure.
💡 Exam Tip 2
For displacement questions, subtract the readings first
Always calculate "after minus before" as a clear first step to find the displaced volume, before applying the density formula.
💡 Exam Tip 3
Remember 1g/cm³ = 1000kg/m³
This single conversion fact covers almost every density unit question at GCSE — it's worth memorising directly.
💡 Exam Tip 4
For mixtures, always find totals before dividing
List each substance's mass and volume, add them separately, then divide — never divide or average partway through the working.
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