Arc Length Calculator - Circle Arc Formula
Calculate the arc length of a circle from radius and central angle. Shows the formula, step-by-step solution, and sector area for any circular arc.
Formula
L = 2πr(θ/360°)
Arc length is the circumference (2πr) multiplied by the fraction of the circle (θ/360).
Worked Examples
Example 1: Quarter Circle
Problem:r=10, angle=90°
Solution:2π(10)(90/360) = 20π(0.25) = 5π
Result:15.71
Example 2: Semicircle
Problem:r=5, angle=180°
Solution:2π(5)(180/360) = 10π(0.5) = 5π
Result:15.71
Frequently Asked Questions
What is Arc Length?
Arc length is the distance along the curved line making up an arc. It is a portion of the circumference of a circle.
What is the formula for Arc Length?
If the angle is in degrees: L = 2πr × (θ/360). If in radians: L = r × θ.
How is it different from chord length?
The arc length measures the curve. The chord length measures the straight-line distance between the two endpoints of the arc.
Can arc length be infinite?
No, for a finite radius and angle, the length is finite. However, fractal curves can have infinite length in a finite space.