Segment in a Circle Calculator: 

Segment: A segment in a circle is a region bounded by two radii and an arc of the circle. There are two types of segments in a circle: minor segments and major segments. A minor segment is a segment that is enclosed by a smaller arc, while a major segment is a segment that is enclosed by a larger arc.

A chord is a line segment that connects two points on the circumference of a circle. A secant is a line that intersects a circle at two points. A segment can be defined as the region between a chord and the circumference of the circle that it intersects.

The area of a circle segment can be calculated using the formula A = (1/2) * r^2 * (θ - sin(θ)), where r is the radius of the circle and θ is the central angle of the segment in radians. The length of the arc can be calculated using the formula L = r * θ.

Segments in a Circle Calculator

Segments in a Circle Calculator

Radius of Circle (r):

Length of Chord (d):



Area of Segment:

Length of Arc:

There are two types of segments in a circle:

1. Minor segment: A minor segment is a segment that is enclosed by a smaller arc and is created when a chord of the circle is less than or equal to the diameter of the circle.
2. Major segment: A major segment is a segment that is enclosed by a larger arc and is created when a chord of the circle is greater than the diameter of the circle.

Both minor and major segments can be defined as the region between a chord and the circumference of the circle that it intersects.

Here is an example to illustrate both types of segments in a circle:

Consider a circle with radius r and a chord of length d that intersects the circumference of the circle at two points.

1. Minor segment: If the length of the chord d is less than or equal to the diameter of the circle (2r), then a minor segment is created. The central angle θ of the minor segment can be calculated using the formula θ = 2 * sin^-1(d / (2r)).
2. Major segment: If the length of the chord d is greater than the diameter of the circle (2r), then a major segment is created. The central angle θ of the major segment can be calculated using the formula θ = 360° - 2 * sin^-1(d / (2r)).

In both cases, the area of the segment can be calculated using the formula A = (1/2) * r^2 * (θ - sin(θ)) and the length of the arc can be calculated using the formula L = r * θ.

Example with solution

Consider a circle with radius r = 5 and a chord of length d = 7. We want to find the area and the length of the arc of the major segment created by the chord.

1. First, we find the central angle θ of the major segment using the formula θ = 360° - 2 * sin^-1(d / (2r)). Substituting the values we get:
   • θ = 360° – 2 * sin^-1(7 / (2 * 5))
   • = 360° – 2 * sin^-1(7 / 10)
2. Now we can calculate the area of the segment using the formula A = (1/2) * r^2 * (θ - sin(θ)). Substituting the values we get:
   • A = (1/2) * 5^2 * (θ – sin(θ))
   • = (1/2) * 25 * (θ – sin(θ))
3. Finally, we can calculate the length of the arc using the formula L = r * θ. Substituting the values we get:
   • L = 5 * θ