◆ Free Download

The complete GCSE Maths formula sheet.

Every formula you need for AQA, Edexcel and OCR — in one printable PDF. Download it, pin it to your wall, and never forget a formula again.

Browse topic sheets Summary PDF

Quick Reference

Every formula, at a glance.

The key formulas from the sheet. Download the full PDF above for the complete list with diagrams.

Area & Perimeter

✦Area of rectangle = length × width

✦Area of triangle = ½ × base × height

✦Area of parallelogram = base × height

✦Area of trapezium = ½(a + b) × h

✦Area of circle = πr²

✦Circumference = 2πr = πd

II.

Volume & Surface Area

✦Volume of cuboid = l × w × h

✦Volume of prism = area of cross-section × length

✦Volume of cylinder = πr²h

✦Volume of sphere = ⁴⁄₃πr³

✦Volume of cone = ⅓πr²h

✦Surface area of sphere = 4πr²

III.

Algebra

✦Quadratic formula: x = (−b ± √(b²−4ac)) / 2a

✦Difference of two squares: a² − b² = (a+b)(a−b)

✦Gradient = (y₂ − y₁) / (x₂ − x₁)

✦Equation of a line: y = mx + c

✦nth term (arithmetic): a + (n−1)d

IV.

Trigonometry & Pythagoras

✦Pythagoras: a² + b² = c²

✦sin θ = opposite / hypotenuse

✦cos θ = adjacent / hypotenuse

✦tan θ = opposite / adjacent

✦Sine rule: a/sin A = b/sin B = c/sin C

✦Cosine rule: a² = b² + c² − 2bc cos A

✦Area of triangle = ½ab sin C

Probability & Statistics

✦Probability = favourable outcomes / total outcomes

✦P(A or B) = P(A) + P(B) − P(A and B)

✦P(not A) = 1 − P(A)

✦Mean = sum of values / number of values

✦Compound interest: A = P(1 + r/100)ⁿ

VI.

Compound Measures

✦Speed = distance / time

✦Density = mass / volume

✦Pressure = force / area

How to use this formula sheet

Print it out and stick it on your bedroom wall or inside your revision folder.

Test yourself — cover the right side and try to recall each formula from memory.

In the exam, some formulas are given on the front page (area of trapezium, volume of prism, etc.) but many are not. Learn the ones that are NOT given.

Use our practice questions to apply each formula in exam-style contexts.

Which formulas are given in the exam?

AQA, Edexcel and OCR all provide a formula sheet on the front page of the exam paper.

✓ Given in the exam

✦ Area of trapezium

✦ Volume of prism

✦ Quadratic formula (Higher)

✦ Sine rule, Cosine rule (Higher)

✦ Area = ½ab sin C (Higher)

✦ Volume of cone and sphere (Higher)

✕ Must memorise

— Area of circle, triangle, parallelogram

— Circumference of a circle

— Pythagoras' theorem

— SOH CAH TOA

— Speed = distance / time

— Density = mass / volume

— Compound interest formula

— y = mx + c

Know the formulas? Now apply them.

Practise exam-style questions with AI marking — get instant feedback on your working and method marks.

Start practising free →Download PDF again

Related resources