Arc Length Calculator
Calculate the arc length of a circle from radius and central angle in degrees.
How it works
- 1Enter the circle’s radius and the central angle in degrees.
- 2The arc length s is computed as s = r·θ, where θ = angle × π ÷ 180 converts degrees to radians.
- 3The result is also expressed as a percentage of the full circumference (angle ÷ 360 × 100).
Use cases
- Engineering and machining: calculating the length of curved cuts or bends on a circular workpiece.
- Architecture: finding the length of a curved wall segment or arch given its radius and sweep angle.
- Education: verifying the radian-based arc-length formula s = r·θ with concrete numeric examples.
Frequently asked questions
What is the formula for arc length?
Arc length s = r·θ, where r is the radius and θ is the central angle in radians. Equivalently, s = 2πr·(angle ÷ 360) when the angle is in degrees.
Why convert degrees to radians first?
Radians define angle as the ratio of arc length to radius, so s = r·θ holds directly in radians. Degrees are a different unit — multiplying by π ÷ 180 performs the conversion.
What does fraction of circumference mean?
It tells you what percentage of the full circumference the arc occupies. A 90° arc covers 90 ÷ 360 = 25% of the circumference, regardless of radius.
Related tools
See all →Calculate the area and perimeter of a rectangle from its width and height, with a labeled diagram.
Calculate the area and circumference of a circle from its radius, with a labeled diagram.
Calculate the area (Heron’s formula) and perimeter of a triangle from its three sides.
Calculate the area and perimeter of a trapezoid from its two parallel sides, height, and legs.