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!

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 = θ2 × r²   (when θ is in radians)

Area of Sector = θ × π360 × r²   (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 = θ − sin(θ)2 × r²   (when θ is in radians)

Area of Segment = ( θ × π360 − sin(θ)2) × r²   (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 × π180 × r   (when θ is in degrees)