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

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 | |

- Circle definition
- Radius of a circle
- Diameter of a circle
- Circumference of a circle
- Parts of a circle (diagram)
- Semicircle definition
- Tangent
- Secant
- Chord
- Intersecting chords theorem
- Intersecting secant lengths theorem
- Intersecting secant angles theorem
- 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)

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

- 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

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