Arc Length Calculator

Calculate arc length from radius and angle. Free online arc length calculator for circles and sectors.

The Arc Length Calculator finds the length of an arc given the radius and central angle. Whether the angle is in degrees or radians, this tool applies the correct formula to compute the curved distance along a circle's edge. Essential for engineering, design, track layouts, and any application involving circular arcs.

Common use cases

  • Curved road and track design
  • Architectural arches
  • Bent pipe and wire lengths
  • Gear tooth calculations
  • Circular motion distance

How to use

  1. Enter the radius of the circle
  2. Enter the central angle (degrees or radians)
  3. Select the angle unit
  4. Click calculate for arc length
  5. View the formula used

FAQ

What is the arc length formula?

Arc Length = rθ (radians) or Arc Length = (θ/360) × 2πr (degrees), where r is radius and θ is angle.

What's the difference between arc and chord?

Arc is the curved distance along the circle; chord is the straight line connecting the endpoints.

How do I find the full circumference?

Circumference is the arc length for a 360° (or 2π radian) angle: C = 2πr.

Can arc length exceed circumference?

Not for a single arc. Arc length is always ≤ circumference (full 360° gives circumference).