What Is a Sector of a Circle?
A sector of a circle is a portion or part of a circle that is composed of an arc and its two radii. You can compare the sector of a circle to the shape of a pizza slice. A sector is formed when two radii of the circle meet at both ends of the arc. An arc is simply a portion of the circumference of the circle.

Sector of a Circle Definition
The definition of the sector of a circle in geometry can be given as the part of the circle enclosed by two radii and an arc of the circle. The arc of the circle is a part of the boundary/circumference of the circle.

Two radii meet at the center of the circle to form two sectors.
- Minor sector
- Major sector
Minor Sector
A sector of a circle is called the minor sector if the minor arc of the circle is a part of its boundary. It is the sector with a smaller area. The angle of a minor sector is less than 180 degrees.
Major Sector
A sector is called the major sector if the major arc of the circle is a part of its boundary.
It is the sector with the greater area. The angle of a major sector is greater than 180 degrees.

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Sector of a Circle Formulas
Let’s learn how to find the area of a sector of a circle. The formula for determining the area of a sector is given in two ways, with an angle and without an angle.
Area of a Sector Formula: When Angle Is Given
If the radius of a circle is given as “r” and the angle of the sector is given as . This angle is made by the two radii at the center.

As we know, for a complete circle, the angle made at the center is equal to 2 or
- If is measured in degrees, then “the area of a sector of a circle formula” is given by
Area of sector
- If is measured in radians, then “the area of a sector of a circle formula” is given by
Area of sector
- Perimeter of sector
Area of Sector Formula: When Angle Is Not Given
How can we find the area of a sector of a circle when the central angle is not given? Let’s find out.
If l is the length of the arc, r is the radius of the circle and θ is the angle subtended at the center, then the angle is expressed in terms of l and r as
If the angle of the sector
Similarly, for the angle
Thus, for the angle , area of the sector
- Area of the sector without an angle
.
- Perimeter of sector
Arc Length of a Sector Formula

The length of the arc “l” of the sector with angle is given by:
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Facts about Sector of a Circle
- A section or part of a circle involved by two radii with a central angle
is called a quadrant.
- A section or part of a circle involved by two radii with a central angle of
is called a semicircle.
- The combination of any two hands (minute hands and hour hands or hour hands and second hands or minute hands and second hands) of a circular analog clock form sectors.
Conclusion
In this article, we learned about the sector of a circle, minor and major sector, the sector formula for area, perimeter and arc length with and without angle. Now, let us look at some solved examples and practice questions.
Solved Examples On Sector of a Circle
- Calculate the area of the sector.

Solution:
The radius of sector
Angle of sector
The area of sector
- Find the area of a sector of a circular region whose central angle is 3 radians with a radius of 5 feet.
Solution:
The radius of sector
Angle of sector
If is measured in radians, then
The area of the sector
- Find the central angle of a sector (in degrees) which has a 25 sq. yard area and a radius of 4 yards. Use $\pi = 3.14$.
Solution:
Radius of sector
Area of sector
If is measured in degrees, then
Area of the sector
- Find the perimeter of the sector shown below.

Solution:
The radius of sector
Angle of sector
The perimeter of sector
- Find the area and perimeter of a sector with a radius of 10 feet and an arc length of 12.56 feet.
Solution:
The radius of sector
Arc length
Area of the sector without an angle
Perimeter of sector
- Find the arc length of a sector having a radius of 5 feet and a central angle of
.

Solution:
The radius of sector
Angle of sector
The length of the arc “l” of the sector with angle is given by;
Practice Problems On Sector of a Circle
Sector of a Circle: Definition, Formula, Area, Perimeter, Examples
The sector of a circle is formed by two ____ and an arc.
The sector of a circle is formed by two radii and an arc.
The central angle of the minor sector is _________.
The central angle of the minor sector is less than 180 degrees.
For the quadrant of a circle, the central angle is _________.
The quadrant of a circle can be a sector of a circle with a central angle of
If is measured in radians, then the formula for the area of a sector of a circle is equal to ____________.
If
Area of sector
The area of the quadrant of a circle is equal to _____ of that of the circle.
The area of the quadrant of a circle is equal to one-fourth, i.e.,
Frequently Asked Questions On Sector of a Circle
What is the difference between a sector and an arc?
Arc represents the part of the circumference. The sector of a circle is a part of the circle that is enclosed by two radii and an arc of the circle as a part of its boundary.
What is the area of the sector of a circle composed of?
The area of the sector of a circle is the area of the part of a circle composed of an arc and two radii.
What is the formula for the perimeter of a sector of a circle?
The perimeter of a sector is formed by two radii and an arc.
Perimeter of the sector
How many types of sectors are in a circle?
There are two types of a sector, which can be categorized as a minor or a major part.
What is the formula for the area of a sector without an angle?
Area of the sector without an angle
How to find the arc length of a sector of a circle?
The arc length of a sector of a circle can be found using the formula: