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/circleprop.js?mode=sector

images/circleprop.js?mode=segment

Common Sectors
The Quadrant and Semicircle are two special types of Sector:
Half a circle is
a Semicircle.
Quarter of a circle is
a Quadrant.
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:
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)