Calculate the arc length, sector area, and chord length of a circle from radius and central angle.
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Geometry
The arc length calculator finds the length of a circular arc from the radius and central angle. It also computes the sector area and the straight-line chord length across the arc.
The arc length is the portion of the circumference subtended by the central angle. In radians: arc = r * theta. In degrees: arc = r * theta * pi / 180.
The chord length — the straight line connecting the arc endpoints — is 2r * sin(theta/2). This is always shorter than the arc itself.
Arc = r * theta
Theta in radians. Multiply degrees by pi/180 first.
Chord = 2r sin(theta/2)
Straight-line distance between arc endpoints.
The calculator handles arcs up to a full circle (360 degrees). For angles beyond 360 degrees, the arc length continues to increase but the chord length cycles.
Frequently asked questions
For a semicircle (180 degrees), the arc length is pi * r — exactly half the circumference.
Always shorter. The chord is the straight-line distance; the arc curves along the circle. They are equal only when both are zero.
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