A circular sector is shaded in green. Its curved boundary of length L is a circular arc.

In geometry, an arc is a closed segment of a differentiable curve in the two-dimensional plane; for example, a circular arc is a segment of the circumference of a circle. If the arc segment occupies a great circle (or great ellipse), it is considered a great-arc segment.

The length of an arc of a circle with radius r and subtending an angle (measured in radians) with the circle center — i.e., the central angle — equals . This is because

Substituting in the circumference

and solving for arc length, L, in terms of yields

An angle of α degrees has a size in radians given by

and so the arc length equals

See also

• Arc length
• Other meanings of arc
• Circular-arc graph

External links

• Definition and properties of a circular arc With interactive animation
• A collection of pages defining arcs and their properties, with animated applets Arcs, arc central angle, arc peripheral angle, central angle theorem and others.
• Eric W. Weisstein, Arc at MathWorld.

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