Area of a Circle Segment Given the Central Angle

Definition: The number of square units it takes to fill a segment of a circle
Try this Drag one of the orange dots that define the endpoints of the segment. Note the number of square units it takes to fill it.

The formula to find the area of the segment is given below. It can also be found by calculating the area of the whole pie-shaped sector and subtracting the area of the isosceles triangle △ACB.

Where:
C is the central angle in DEGREES
R is the radius of the circle of which the segment is a part.
π is Pi, approximately 3.142
sin is the trigonometry Sine function.

If you know the segment height

If you know the segment height and radius of the circle you can also find the segment area. See Area of a Circular Segment given the Segment Height.

Calculator

Use the calculator below to calculate the segment area given the radius and segment's central angle, using the formula described above. Remember: In this version, the central angle must be in degrees.

Radius r
Central angle a (degrees)
Area

Other circle topics

General

Equations of a circle

Angles in a circle

Arcs

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