# Circle Sector and Segment

## Slices

There are two main "slices" of a circle:

- The "pizza" slice is called a
**Sector**. - And the
**Segment**, which is cut from the circle by a "chord" (a line between two points on the circle).

## Try Them!

Sector | Segment |
---|---|

images/circle-prop.js?mode=sector |
images/circle-prop.js?mode=segment |

## Area of a Sector

You can work out the Area of a Sector by comparing its angle to the angle of a full circle.

*Note: we are using radians for the angles.*

This is the reasoning:

^{2}

**instead of**2π so its Area is : \frac{θ}{2π} × πr

^{2}

^{2}

Area of Sector = \frac{θ}{2} × r^{2} *(when θ is in radians)*

Area of Sector = \frac{θ × π}{360} × r^{2} *(when θ is in degrees)*

## Area of Segment

The Area of a Segment is the area of a sector minus the triangular piece (shown in light blue here).

There is a lengthy reason, but the result is a slight modification of the Sector formula:

Area of Segment = \frac{θ − sin(θ)}{2} × r^{2} *(when θ is in radians)*

Area of Segment = ( \frac{θ × π}{360} − \frac{sin(θ)}{2}) × r^{2} *(when θ is in degrees)*

## Arc Length

The arc length (of a **Sector or Segment**) is:

L = θ × r *(when θ is in radians)*

L = θ × \frac{π}{180} × r *(when θ is in degrees)*