Segment Area Calculator

Calculate the area and height of a segment by entering the central angle and radius in the calculator below.

Results:

Segment Area

 

Segment Height (h)

 

Arc Length (s)

 

Chord Length (a)

 


How to Calculate the Area of a Segment

A segment is a part of a circle separated by a chord connecting two points of a circle. Think of a segment as a part of a circle sliced off using a straight line.

diagram of a circular segment showing the radius, central angle, chord length, height, and arc length

In addition to area, a segment is defined by its height, chord length, and arc length. The area of a segment can be found using a simple formula.

Segment Area Formula

The area can be found using the segment area formula:

segment area = r² × (θ – sin(θ))2

Thus, a segment’s area is equal to the radius r squared, times the central angle θ in radians minus the sine of θ, divided by 2.

For example, find the area of a segment with a radius of 17 and a central angle of 1.25 radians.

segment area = 17² × (1.25 – sin(1.25))2
segment area = 289 × (1.25 – 0.021815)2
segment area = 289 × 1.22819)2
segment area = 354.94552
segment area = 177.47275

Thus, the segment area is 177.47275.

How to Find the Height of a Segment

The following formula defines the height of a segment.

segment height = r × (1 – cos(12θ))

The height of a segment is equal to the radius r times 1 minus the cosine of the central angle θ in radians divided by 2.

How to Find the Arc Length of a Segment

The arc of a segment is the rounded outer portion of the circle that connects the two radii. The arc length can be found using the formula:

arc length (s) = radius (r) × central angle (θ)

The arc length s of a segment is equal to the radius r times the central angle θ in radians.

You might also be interested in our sector area calculator for solving the parts of a sector.