Segment of a Circle

Definition: The region between a chord of a circle and its associated arc.
Try this Drag one of the orange dots that define the endpoints of the blue arc. The yellow area is a segment of the circle C.

The chord AB in the figure above defines one side of the segment. As you drag the points you will notice that the segment is always the smaller part of the circle. This is a definition of a segment. Its Central Angle is always less than 180°

In fact, if the chord divides the circle exactly in half (becoming a diameter) neither of the two halves are segments. They are semicircles. If you careful with the mouse, you can create this situation in the figure above. Move A or B so that the line AB passes through the center of the circle. No segment is then present.


A segment is defined by the arc and chord that form its outer boundary. See Arc Definition and Chord Definition for more information. The key properties a segment inherits from them are shown below. In the figure above click on "show details" to see these items.

Arc Length The length of the curved arc line. See Arc Length page for more.
Radius The radius of the circle of which the segment is a part.
See Radius of an Arc or Segment for ways to calculate the segment radius when you know other properties of the segment.
Central Angle The angle subtended by the segment to the center of the circle of which it is a part. See Central Angle definition for more.

Area See Area of a Segment of a Circle

Other circle topics


Equations of a circle

Angles in a circle