Sector of a Circle
A sector of a circle is a pieshaped part of a circle made of the arc along with its two radii. A portion of the circumference (also known as an arc) of the circle and 2 radii of the circle meet at both endpoints of the arc formed a sector. The shape of a sector of a circle looks like a pizza slice or a pie. In geometry, a circle is one of the most perfect figures. The shape of a sector of a circle is the simplest shape in geometry. It has various parts of its own. Such as diameter, radius, circumference, segment, sector. In this article, we will learn about what is a sector of a circle, formulas related to the sector of a circle along with solving a few examples on the sector of a circle.
1.  What is Sector of a Circle? 
2.  Formulas of Sector of a Circle 
3.  FAQs on Sector of a Circle 
What is Sector of a Circle?
A sector is a portion of a circle that can be defined based on the four points mentioned below:
 A portion of a circle is covered by two radii and an arc.
 A circle is divided into two sectors and the divided parts are known as minor sectors and major sectors.
 The large portion of the circle is the major sector whereas the smaller portion is the minor sector.
 In the case of semicircles, the circle is divided into two equalsized sectors.
The 2 radii meet at the part of the circumference of a circle known as an arc, formed a sector of a circle.
Look at the following figure to distinguish between the minor sector and major sector.
The portion OAPB of the circle is called the minor sector and the portion OAQB of the circle is called the major sector.
The semicircle is also a sector with an angle of 180 degrees.
Formulas of Sector of a Circle
Area of a Sector of a Circle
The area of a sector of a circle is the amount of space occupied within the boundary of a sector of a circle. A sector always initiates from the center of the circle. The semicircle is also a sector of a circle, in this case, a circle is having two sectors of equal size. Let's learn about how to calculate the area of a sector. If the radius of the circle is (r) and the angle of the sector is (θ) is given, then the formula used to calculate the area of the sector is of :
Area of sector (A) = (θ/360°) × πr^{2}
 θ is the angle in degrees.
 r is the radius of the circle.
Length of the Arc of Sector Formula
Similarly, the length of the arc of the sector with angle θ is given by;
l = (θ/360) × 2πr or l = (θπr) /180.
Area of a Sector of a Circle Without an Angle Formula
When the angle of the sector is not given and the length of the arc of a sector of a circle is given we can calculate the area of the sector of a circle by using length. Assuming the length of an arc, 'l' and radius of a circle is 'r'. According to the radian definition angle of the sector of a circle is equal to the ratio of the length of an arc of a sector of a circle to the radius of a circle.
θ = l/r, where θ is in radians.
Area of a sector of a circle = (l × r)/2
Perimeter of a Sector of a Circle Formula
The following are the formulas for the perimeter of a sector of a circle.
Perimeter of sector = 2 radius + arc length
Arc length is calculated as, Arc length = l = (θ/360) × 2πr
Therefore, Perimeter of a Sector = 2 Radius + ((θ/360) × 2πr )
Related Articles on Sector of a Circle
Check out these interesting articles to know more about Sector of a Circle and its related topics.
Sector of a Circle Example

Example 1: What is the length of the sector of a circle if the radius of the circle is 7 units and the angle of the sector is 40°?
Solution: Area of sector = (θ/360°) × πr^{2}
= (40°/360°) × (22/7) × 7 × 7
= 154/9 square units
The length of the sector = (θ/360°)× 2πr
l = (40°/360°) × 2 × (22/7) × 7
l = 44/9 units

Example 2: Find the area of the sector of a circle if the radius of the circle is 20 units, and the length of the arc is 8 units.
Solution: Given, radius = 20 units and length of an arc of a sector of circle = 8 units
Area of sector of circle = (lr)/2 = (8 × 20)/2 = 80 square units.

Example 3: Find the perimeter of the sector of a circle whose radius is 8 units and a circular arc makes an angle of 30° at the center. Use π = 3.14.
Solution : Given that r = 8 units,
θ = 30° = 30° × (π/180°) = π/6
Perimeter of sector is given by the formula;
P = 2 r + r θ
P = 2 (8) + 8 ( π/6)
P = 16 + 4π/3
P = 16 + (4 × 3.14)/3 = 20.187 units
Hence, Perimeter of sector is 20.187 units.
FAQs on Sector of a Circle
What is the Formula for the Area of a Sector of a Circle?
To calculate the area of a sector of a circle we have to multiply the central angle by the radius squared, and divide it by 2. Area of a sector of a circle = (θ × r^{2 })/2 where θ is measured in radians. The formula can also be represented as Sector Area = (θ/360°) × πr^{2}, where θ is measured in degrees.
What do you understand by the Sector of a Circle?
The part of a circle covered by 2 radii of a circle and their intercepted arc(the arc coming in that portion) is a sector of a circle. It is also known by the term pieshaped part of a circle.
What is a Perimeter of a Sector of a Circle?
The total length of the circumference of the circle extends within the angle "θ" is a perimeter of a sector of a circle or in other words the sum of the lengths of the arc and the two radii. Formula to calculate the perimeter of a sector of a circle = 2 Radius + ((θ/360) × 2πr )
How do you find the Area of a Sector of a Circle Without an Angle?
We can find an area of a sector of a circle when the angle is missing. An angle of sector of a circle subtended by the arc length(radius of the circle) at the center is equal to one radian also equal to the ratio of the length of an arc of a sector of circle and radius of a circle. Hence, a formula of the area of a sector of a circle without an angle is mentioned below.
Area of a sector of a circle = (l × r)/2
What are Sector and Arc?
An arc is a fraction of the circumference and part of a circle whereas a sector is a pieshaped part of a circle covered with 2 radii.
How Many Sectors Are in a Circle?
There are two sectors in a circle. If the circle is divided into two equal portions that are in semicircles then the sectors are of the same size otherwise in other cases like, if part of a circle is pieshaped then one sector is larger than the other. The larger one is known as the major sector and the smaller one is known as a minor sector of a circle.
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