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.
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.
