Circle Sector and Segment
Slices
There are two main "slices" of a circle:
- A sector is like a slice of pizza, with a radius on two sides.
- A segment is the part of a circle cut off by a "chord" (a line connecting two points on the circle).
Try Them!
Sector | Segment |
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images/circle-prop.js?mode=sector |
images/circle-prop.js?mode=segment |
Area of a Sector

We 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:
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)
Area of Segment

The Area of a Segment is the area of a sector minus the triangular piece shaded blue below:
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)
images/circle-prop.js?mode=arc
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