Circle: arc, sector and segment

A circle has these main slices: arc, sector and segment. In this article we will show how to calculate these parts.

The arc

The arc is any part of a circle. It can be the part of section or segment. The arc length can be calculated by this formula below:

$$L=\frac{\pi R}{180}\cdot \theta$$

The sector

The sector of a circle is region bounded by two radius of equal length with a common center. The sector area can be calculated by this formula below:

$$A=\frac{\pi R^2}{360}\cdot \theta$$

The segment

The segment of a circle is a region bounded by a chord and one of the arcs connecting the chords endpoints. The area of a segment is the area of a sector minus the triangular. The segment area can be calculated by this formula below:

$$A=\frac{\pi R^2}{360}\cdot \theta-\frac{R^2 \sin\theta}{2}$$

2021-08-30