Density, mass & volume

Density, mass and volume are connected by a formula triangle. Density is a measure of how much mass is packed into a given volume.

Revising density, mass & volume the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Density, mass & volume GCSE” on the site for the complete guide.

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Key facts to remember

1Density = Mass ÷ Volume
2Mass = Density × Volume
3Volume = Mass ÷ Density
4SI units: density in g/cm³ or kg/m³; mass in g or kg; volume in cm³ or m³.
5A denser material has more mass per unit volume.
6Water has a density of 1 g/cm³ — objects less dense than water float.

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Formulas

Density

D = M / V

Mass

M = D × V

Volume

V = M / D

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Worked examples

Example 1

A metal block has mass 540 g and volume 60 cm³. Find its density.

Working

Density = Mass ÷ Volume
D = 540 ÷ 60 = 9 g/cm³

Answer9 g/cm³

Example 2

A liquid has density 1.2 g/cm³ and mass 300 g. Find its volume.

Working

Volume = Mass ÷ Density
V = 300 ÷ 1.2 = 250 cm³

Answer250 cm³

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Common mistakes

✗Dividing mass by density to get density, or confusing which quantity to divide.

✗Using inconsistent units — ensure mass and volume units match the density units.

✗Forgetting to state the units in the answer.

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Exam tips

✓Use the formula triangle: cover the quantity you want, and the remaining two show whether to multiply or divide.

✓Always check your units — if density is in g/cm³, mass must be in g and volume in cm³.

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