# Length of an Arc of a Circle

## Description

Circular arc is a segment of a circle, or of its circumference (boundary) if the circle is considered to be a disc. Central angle is an angle whose apex (vertex) is the center of a circle and whose legs (sides) are radii intersecting the circle in two distinct points and thereby subtending an arc between those two points whose angle is (by definition) equal to that of the central angle itself. It is also known as the arc segment’s angular distance.. Arc lengths are denoted by s, since arcs “subtend” an angle. The length of an arc of a circle can be calculated multypling the central angle (measure in degrees) with π and the radius of the circle, dividing by 180 degrees (the semiperimeter of the circle).

Related formulas## Variables

s | The arc's length (m) |

π | pi |

r | The circle's radius (m) |

a | The angle that corresponds to the arc (The angle which the arc subtends at the centre of the circle) (degree) |

hc | Half circle (180°) |