Arc Length Calculator
Find the length of a circular arc from its radius and angle, or find the angle or radius from the other two.
Arc length
10.471976
- Radius
- 5
- Angle in degrees
- 120.0000°
- Angle in radians
- 2.094395
- Chord length
- 8.660254
The arc is 10.472 long.
Calculation breakdown
| Step | Formula | Result |
|---|---|---|
| Arc length | 5 × 2.0944 radians | 10.471976 |
How it works
Choose what to find, then enter the other two values.
Worked example
A circle of radius 5 and a 120° arc:
- Angle in radians: 120 × π ÷ 180 = 2.0944
- Arc length: 5 × 2.0944 = 10.472
- That is a third of the circumference, 31.416. The chord is 8.6603
Sources
Frequently asked questions
What is the formula for arc length?
With the angle in radians, the arc length is the radius times the angle, s = rθ. With degrees, it is the angle divided by 360, times the circumference 2πr. A radius of 5 and an angle of 120° give an arc of 10.47.
How do I find the angle from the arc length?
Divide the arc length by the radius to get the angle in radians, then multiply by 180 ÷ π for degrees. An arc of 10 on a circle of radius 5 spans 2 radians, or 114.59°.
How do I find the radius from the arc length?
Divide the arc length by the angle in radians. An arc of 10 spanning 120° (2.0944 radians) belongs to a circle with radius 4.77.
What is the chord of an arc?
The chord is the straight line joining the two ends of the arc. Its length is 2r sin(θ/2), which is always shorter than the arc.
What is the longest possible arc?
The whole circle, a full 360° or 2π radians, where the arc equals the circumference 2πr. The calculator rejects anything longer.