Circle Sector and Segment

circle sector segment

Slices

There are two main "slices" of a circle:

Try Them!

SectorSegment

Common Sectors

The Quadrant and Semicircle are two special types of Sector:

semicircle
Half a circle is
a Semicircle.

quadrant
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.

circular sector area

This is the reasoning:

A circle has an angle of 2π and an Area of:πr2
A Sector has an angle of θ instead of 2π so its Area is : θ2π × πr2
Which can be simplified to:θ2 × r2

 

Area of Sector = θ2 × r2   (when θ is in radians)

Area of Sector = θ × π360 × r2   (when θ is in degrees)

circular segment area

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 × π360sin(θ)2) × r2   (when θ is in degrees)

 

circular sector arc length

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)