What Is the Equation for Arc Length?


Quick Answer

The length of an arc of a circle is equal to the angle subtended by the arc, in radians, times the radius of the circle. For an angle measured in degrees, the arc length is the angle, in degrees, times the radius times pi divided by 180.

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Full Answer

An arc is a portion of a circle along its circumference. Drawing lines from the endpoints of the arc to the center of the circle creates an angle, also known as the subtended angle. For most purposes, angles are measured in degrees or radians, with 180 degrees being equal to pi radians. The length of the arc is proportional to the radius of the circle. The larger the circle, the greater the length of the arc. Likewise, the greater the subtended angle, the greater the length of the arc.

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