Find arc length, sector area and chord length from radius and angle.
arc length
How to use this tool
The distance from the circle's centre to its edge.
In degrees or radians — pick the unit you have.
All three are shown from the same inputs.
Circumference is shown for scale: a 360° arc is the whole circumference.
Formula & worked example
Radius 10 with a 60° central angle (1.0472 radians): arc length 10.47, sector area 52.36, chord length 10.00.
Limitations — read this before you rely on it
This assumes a perfect circle and a central angle between 0 and 360 degrees (0 to 2π radians). It does not handle ellipses or arcs measured along a curve that is not circular.
Frequently asked questions
Arc length = radius x central angle in radians. With degrees, first convert: radians = degrees x π / 180.
Convert degrees to radians, then multiply by the radius. 60° is π/3 ≈ 1.0472 radians, so radius 10 gives arc 10.47.
The pie-slice region bounded by two radii and the arc. Its area is ½ r² θ.
The straight line joining the arc's two endpoints: 2 r sin(θ/2). For 60°, the chord equals the radius.
The arc (curved) is always longer than the chord (straight) for the same angle, except at 0°.