Circular Segment Area Calculator (from Central Angle)

Find the area of a circular segment from its radius and central angle. Chord length, arc length, and height (sagitta) are calculated too.

Input

Enter a radius and central angle to find the area of a circular segment, the region cut off by a chord. Choose degrees or radians for the angle.

Radius r

Central angle θ

Angle unit

Circular segment area

28.539816

Area

28.539816

Chord length

14.142136

Arc length

15.707963

Height (sagitta)

2.928932

The area unit is the square of the length unit. Lengths share the radius unit, and the area uses its square.

The segment area is (1/2)r²(θ−sinθ), where r is the radius and θ is the central angle in radians.
If you enter the angle in degrees, it is converted with θ (radians) = degrees × π ÷ 180 before calculating.
The chord length is 2r sin(θ/2), the arc length is rθ, and the height (sagitta, from the chord to the top of the arc) is r(1−cos(θ/2)).
The radius must be positive, and the central angle must be greater than 0 and at most a full turn (360 degrees, or 2π radians).
The area unit is the square of the length unit. If the radius is in centimeters, the area is in square centimeters.

Tell us what you think of this calculator.