Arc length formula: l = θ/360° × 2πr
The arc length formula is arc length l = (θ/360°) × 2πr.
What each letter means
- \(l\) the length of the arc
- \(r\) the radius
- \(\theta\) the angle of the sector, 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
Find the length of the arc of a sector of angle \(60^\circ\) in a circle of radius 21 cm. Use \(\pi=\tfrac{22}{7}\).
- \(l=\dfrac{60}{360}\times2\times\dfrac{22}{7}\times21=\dfrac16\times132\)
Answer: \(l=22\) cm
Common mistake
Forgetting the two radii when the question asks for the perimeter of the sector.
On your course
| Course | In the exam |
|---|---|
| Class 10 | Learn it: CBSE gives no formula booklet |
| Class 9 | Learn it: CBSE gives no formula booklet |
From our own CBSE Maths formula sheets, in our words.
Practise and revise
Questions
What is the arc length formula?
The arc length formula is arc length l = (θ/360°) × 2πr. l: the length of the arc; r: the radius; θ: the angle of the sector, in degrees.
Is the arc length given in the exam?
Class 10: learn it: CBSE gives no formula booklet. Class 9: learn it: CBSE gives no formula booklet. This comes from our own CBSE 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 CBSE Math Revision. Not produced or endorsed by CBSE or NCERT.