Arc Length Calculator in Degrees or Radians
Enter the radius and the angle at the centre, in degrees or radians. You get the arc length, the straight chord across it and the sector values.
- Nothing you type is stored
- Free
- No signup
Arc length
21.9911cm
- Chord length
- 21 cm
- Sector area
- 230.9071 cm²
- Sector perimeter
- 63.9911 cm
- Angle in radians
- 1.0472 Radians
Show working
- l = (θ / 360°) × 2πr
- l = (60 / 360) × 2 × π × 21 = 21.9911 cm
- θ = 60° = 1.0472 rad
- chord = 2r × sin(θ/2) = 21 cm
How to use
- Enter the radius.
- Enter the central angle and choose degrees or radians.
- Read the arc length, chord and sector area.
Good to know
In degrees: arc length l = (θ/360°) × 2πr, the formula in NCERT Class 10 "Areas Related to Circles". In radians it is simply l = rθ, from Class 11 "Trigonometric Functions", where 1 radian is the angle whose arc equals the radius.
The chord is the straight line joining the ends of the arc: 2r sin(θ/2). For a 60° arc the chord equals the radius.
With π = 22/7, a 60° arc of radius 21 cm is exactly 22 cm long. Useful for curved paths, the length of a pendulum swing and bending bars into an arc.
Questions
What is the formula for arc length?
l = (θ ÷ 360°) × 2πr for θ in degrees, or l = r × θ for θ in radians.
How do I convert degrees to radians?
Multiply by π/180. 60° = π/3 ≈ 1.0472 rad.
What is the difference between an arc and a chord?
The arc is the curved part of the circle; the chord is the straight line between its ends. The arc is always longer.
How far does a pendulum tip travel?
Enter the pendulum length as the radius and the swing angle; the arc length is the distance along the curve.
Is anything I enter stored?
No. The calculation runs in your browser and nothing is sent to a server.