Area of a sector formula: A = ½r²θ
The area of a sector formula is area of a sector A = ½r²θ, with θ in radians.
What each letter means
- \(A\) the area of the sector
- \(r\) the radius
- \(\theta\) the angle at the centre, in radians
When to use it
To find the area of a 'slice' of a circle. Subtract the triangle ½r² sin θ to get the area of a segment.
Worked example
A sector of a circle of radius 5 cm has area \(15\text{ cm}^2\). Find the angle of the sector.
- \(15=\tfrac12\times25\times\theta\)
- \(\theta=\dfrac{30}{25}\)
Answer: \(\theta=1.2\) radians
Common mistake
Using degrees in ½r²θ. Convert to radians first, or use the degree version.
On your course
| Course | In the exam |
|---|---|
| Edexcel A Level (9MA0) | Not in the Edexcel booklet: learn it |
| Edexcel International A Level | Not in the booklet: learn it |
| AQA or OCR A Level | Check your board’s formula booklet: AQA formulae booklet (PDF) · OCR A Level Maths assessment page |
From our own A Level Maths formula sheets, in our words. Official: Pearson's formulae booklet (PDF) · Pearson's IAL formulae booklet (PDF).
Practise and revise
- Practise A Level Maths practice
- Revise Trigonometry
- Revise IAL P1 trigonometry
- Print Edexcel A Level (9MA0) one-page formula sheet
Questions
What is the area of a sector formula?
The area of a sector formula is area of a sector A = ½r²θ, with θ in radians. A: the area of the sector; r: the radius; θ: the angle at the centre, in radians.
Is the area of a sector given in the exam?
Edexcel A Level (9MA0): not in the Edexcel booklet: learn it. Edexcel International A Level: not in the booklet: learn it. AQA or OCR A Level: check your board’s formula booklet. This comes from our own A Level Maths formula sheets; your teacher has the official booklet.
What is the difference between a sector and a segment?
A sector is bounded by two radii and an arc, like a slice of pizza. A segment is bounded by a chord and an arc: sector area minus the triangle.
Our own wording, examples and card, checked by A Level Math Revision. Not produced or endorsed by Pearson Edexcel, AQA or OCR.