Calculate the area, arc length, and perimeter of a circular sector from radius and central angle.
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Also in Circles
Geometry
The circle sector calculator finds the area, arc length, and perimeter of a sector from its radius and central angle. Enter the angle in degrees or radians.
A sector is a "slice" of a circle defined by two radii and an arc. The area is half the radius squared times the angle in radians. The arc length is the radius times the angle in radians. The perimeter of the sector is the arc length plus twice the radius (the two straight edges).
Area = (1/2) r^2 theta
Theta in radians.
Arc = r * theta
Arc length in the same linear unit as the radius.
The calculator handles sectors with angles from 0 to 360 degrees. For angles beyond 360 degrees, the result wraps around the full circle.
Frequently asked questions
For a quarter circle (90 degrees), the sector area is one-quarter of the full circle area: pi*r^2/4.
Multiply degrees by pi/180. For example, 90 degrees = 90 * pi/180 = pi/2 radians. The calculator does this conversion automatically.
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