Circle arc

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 \theta (measured in radians) with the circle center — i.e., the central angle — equals \theta r . This is because


Substituting in the circumference

\frac{L}{2\pi r}=\frac{\theta}{2\pi}

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

L=\theta r

An angle of \alpha degrees has a size in radians given by


and so the arc length equals

L=\frac{\pi}{180}\alpha r

See also

External links

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