Arc length formula: l = rθ
The arc length formula is arc length l = rθ, with θ in radians.
What each letter means
- \(l\) the length of the arc
- \(r\) the radius
- \(\theta\) the angle at the centre, in radians
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).
AI SL works in degrees: arc length = θ/360 × 2πr.
Worked example
A sector has radius 6 cm and angle 1.2 radians. Find the arc length and the perimeter.
- \(l=6\times1.2\)
- Perimeter \(=7.2+2\times6=19.2\) cm
Answer: \(l=7.2\) cm
Common mistake
Putting θ in degrees into l = rθ. Convert first: θ in radians = θ° × π/180.
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 arc length formula?
The arc length formula is arc length l = rθ, with θ in radians. l: the length of the arc; r: the radius; θ: the angle at the centre, in radians.
Is the arc length 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.
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 IB Math Revision. Not produced or endorsed by the International Baccalaureate Organization.