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.
AI SL works in degrees: area of a sector = θ/360 × πr².
Worked example
A sector has radius 5 cm and angle 0.8 radians. Find its area.
- \(A=\tfrac12\times5^2\times0.8\)
Answer: \(A=10\text{ cm}^2\)
Common mistake
Using degrees in ½r²θ. Convert to radians first, or use the degree version.
On your course
| Course | In the exam |
|---|---|
| AA SL | In the IB formula booklet |
| AI SL | In the IB formula booklet |
| AA HL | In the IB formula booklet |
| AI HL | In the IB formula booklet |
From our own IB Maths formula sheets, in our words. The IB gives its booklet to schools, so we checked against our own copy: your teacher has the official one. Official: IB DP Mathematics page.
Practise and revise
- Practise AA SL radians questions
- Practise AI SL arcs and sectors questions
- Revise The unit circle (AA SL)
- Revise AA SL revision notes
- Print AA SL 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?
AA SL: in the IB formula booklet. AI SL: in the IB formula booklet. AA HL: in the IB formula booklet. AI HL: in the IB formula booklet. This comes from our own IB 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 IB Math Revision. Not produced or endorsed by the International Baccalaureate Organization.