GCSE MATHS • HIGHER TIER
Sector Area Made Simple
Learn how to calculate the area of a sector using the central angle, radius and the area of a full circle.
Clear method
Exam practice
Worked proofs
Sector Area in Four Moves
1
Identify
Identify the radius and central angle of the sector.
2
Full Circle
Calculate the area of the full circle using πr².
3
Fraction
Write the central angle as a fraction of 360°.
4
Calculate
Multiply the full circle area by the angle fraction.
What You’ll Learn
Understand Sectors
Understand that a sector is a region enclosed by two radii and an arc.
Use Circle Vocabulary
Recognise radius, diameter, area, arc, sector and central angle.
Apply the Sector Formula
Use the angle as a fraction of 360° to calculate sector area.
Work with Exact Answers
Give answers in terms of π when required.
Connect Arc Length and Sector Area
Understand that both use the same angle fraction of a full circle.
Key Rules
Sector area formula
Sector Area = (Angle ÷ 360) × πr²
Full circle area
Area of Circle = πr²
Angle fraction
Divide the central angle by 360° to find the fraction of the circle used.
Use the radius
If the diameter is given, halve it first to find the radius.
Square units
Sector area is measured in square units such as cm² or m².
Worked Proof: Sector Area
Step-by-Step Method
- 1. Find the radius.
- 2. Calculate the area of the full circle using πr².
- 3. Find the fraction represented by the angle.
- 4. Multiply the circle area by this fraction.
- 5. Give the answer in exact or decimal form.
More Worked Examples
1
Question: A circle has radius 10 cm and angle 180°.
Full area = 100π cm²
Sector Area = (180/360) × 100π
= 50π cm²
= 50π cm²
2
Question: A circle has diameter 12 cm and angle 60°.
Radius = 6 cm
Area = 36π cm²
Sector Area = (60/360) × 36π
= 6π cm²
Sector Area = (60/360) × 36π
= 6π cm²
3
Question: A circle has radius 8 cm and angle 270°.
Area = 64π cm²
Sector Area = (270/360) × 64π
= 48π cm²
= 48π cm²
4
Question: A circle has radius 5 cm and angle 120°.
Area = 25π cm²
Sector Area = (120/360) × 25π
= 25π/3 cm²
= 25π/3 cm²
- Common GCSE Mistakes
- Diameter vs radius: Halve the diameter before using πr².
- Wrong formula: Use circle area, not circumference.
- Missing angle fraction: Multiply by Angle ÷ 360.
- Wrong units: Sector area needs square units.
- Exam Tips
- Write the formula first: Start with Sector Area = (Angle ÷ 360) × πr².
- Check the radius: Convert from diameter if necessary.
- Keep π exact: Leave π when an exact answer is requested.
- Use the central angle: Make sure the correct angle is used.
- Check units: Use cm², m² or the appropriate square unit.
Skills Used in Sector Area
Circle Area and Circumference
Circumference
Area of Circles
Area of a Sector
Geometry
Compound Shapes
Ready to Practise?
Printable Worksheet
Download and print practice questions with answers.
Interactive Quiz
Test your knowledge with instant feedback and hints.
Exam-Style Questions
Timed questions to build confidence for the real exam.
Watch the Arc Length Tutorial
Step-by-step walkthroughs of Arc Length with clear methods and exam tips.
Frequently Asked Questions
A sector is a region of a circle enclosed by two radii and an arc.
Sector Area = (Angle ÷ 360) × πr².
A full circle contains 360°, so this gives the fraction of the circle represented by the sector.
Divide the diameter by 2 to find the radius before using the formula.
Yes, especially when the question asks for an exact answer.
Both use the central angle as a fraction of 360°.
