Arc length formula: arc length = θ/360 × 2πr
The arc length formula is arc length = (θ/360) × 2πr, with θ in degrees.
What each letter means
- \(r\) the radius
- \(\theta\) the angle at the centre, in degrees
When to use it
To find the curved edge of a sector or part of a circle, for example the perimeter of a sector (arc length + 2r).
Worked example
A sector has radius 9 cm and angle \(140^\circ\). Find the arc length, to 2 decimal places.
- \(\dfrac{140}{360}\times2\pi\times9=7\pi\)
Answer: 21.99 cm
Common mistake
Forgetting the two radii when the question asks for the perimeter of the sector.
On your course
| Course | In the exam |
|---|---|
| Edexcel 4MA1 (Higher) | Not given: learn it |
| Cambridge 0580 | Not given: learn it |
From our own IGCSE Maths formula sheets, in our words. Official: Pearson's 4MA1 specification (PDF, Appendix 5) · Cambridge's 0580 syllabus (PDF).
Practise and revise
Questions
What is the arc length formula?
The arc length formula is arc length = (θ/360) × 2πr, with θ in degrees. r: the radius; θ: the angle at the centre, in degrees.
Is the arc length given in the exam?
Edexcel 4MA1 (Higher): not given: learn it. Cambridge 0580: not given: learn it. This comes from our own IGCSE Maths formula sheets; your teacher has the official booklet.
How do I find the perimeter of a sector?
Add the arc length to the two straight edges: perimeter = arc length + 2r.
Our own wording, examples and card, checked by IGCSE Math Revision. Not produced or endorsed by Pearson Edexcel.