Arc Length Calculator
Calculate the length of a circular arc using radius and central angle. Supports both degrees and radians.
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Frequently Asked Questions
What is an arc?
An arc is a portion of the circumference of a circle. It's the curved line connecting two points on the circle.
What is the formula for arc length?
s = rθ (when θ is in radians), or s = (θ/360°) × 2πr (when θ is in degrees), where s is arc length, r is radius, and θ is the central angle.
Why use radians instead of degrees?
The formula s = rθ works only when θ is in radians. Radians provide a natural relationship between angle and arc length, making calculations simpler.
How do you convert degrees to radians?
Multiply degrees by π/180. For example, 90° = 90 × π/180 = π/2 ≈ 1.5708 radians.
What is the arc length of a full circle?
For a complete circle (360° or 2π radians), the arc length equals the circumference: s = 2πr.
What is the arc length of a semicircle?
For a semicircle (180° or π radians), the arc length is half the circumference: s = πr.
Can arc length be negative?
No, arc length is always positive. It represents a physical distance along the circle's edge.
Where is arc length used in real life?
Arc length calculations are used in road design for curves, architecture for arches, manufacturing of curved parts, and anywhere circular motion or curved paths are involved.