Area of a Circle Segment Given the Central Angle

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.

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.

Other circle topics

General

• Circle definition
• Parts of a circle (diagram)
• Semicircle definition
• Tangent
• Secant
• Chord
• Intersecting chords theorem
• Intersecting secant lengths theorem
• Intersecting secant angles theorem
• Radius of a circle
• Diameter of a circle
• Area of a circle
• Concentric circles
• Annulus
• Area of an annulus
• Sector of a circle
• Area of a circle sector
• Segment of a circle
• Area of a circle segment (given central angle)
• Area of a circle segment (given segment height)

Equations of a circle

• Basic Equation of a Circle (Center at origin)
• General Equation of a Circle (Center anywhere)
• Parametric Equation of a Circle

Angles in a circle

• Inscribed angle
• Central angle
• Central angle theorem

Arcs

• Arc
• Arc length
• Arc angle measure
• Adjacent arcs
• Major/minor arcs
• Intercepted Arc
• Sector of a circle
• Radius of an arc or segment, given height/width
• Sagitta - height of an arc or segment