# 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.