The Arc Length Calculator finds the distance along part of a circle. It uses the circle's radius and the central angle to determine how much of the circumference is represented by the arc.
Arc Length Formula
When the central angle θ is in radians, arc length is s = rθ. When the angle is in degrees, the equivalent formula is s = (θ ÷ 360) × 2πr.
How to Use the Calculator
- Enter the circle's radius.
- Enter the central angle.
- Confirm whether the angle is supplied in degrees or radians.
- Calculate the arc length and check the resulting unit.
Example
For a radius of 10 cm and a central angle of 90 degrees, the arc is one quarter of the circle. Its length is (90 ÷ 360) × 2π × 10 = 5π cm, approximately 15.71 cm.
Angle Units Matter
The formula s = rθ requires radians. If an angle is given in degrees, convert it to radians or use the degree-based formula. Mixing these forms without conversion produces an incorrect result.