Area of a Sector of a Circle Formula
The area of a sector of a circle formula is used to find the area of the sector formed by an arc and two radii of the circle. The sector of a circle is a part of a circle that is formed inside two radii and arc of a circle. Let us see more about the area of a sector of a circle formula along with the solved examples in the next section.
What is the Area of a Sector of a Circle Formula?
Area of a sector of a circle with radius r is:
When angle is given in radians:
\[\begin{align}\text{Area of a sector} &= \dfrac {\theta}{2 \pi} \times \pi \times r^2 \\ &= \dfrac {\theta}{2} \times r^2 \end{align}\]
When angle is given in degrees:
\[\begin{align}\text{Area of a sector} &= \dfrac {\theta}{360} \times \pi \times r^2 \end{align}\]
Where,
 θ is the angle subtended by the arc at the center,
 r is the radius of the circle.
Let's take a quick look at a couple of examples to understand the sector of a circle formula, better.
Solved Examples using Area of a Sector of a Circle Formula

Example 1:
Find the area of a sector of a circle with a radius of 7 units and the angle formed at the center by the sector is 60°.
Solution:
Given, r = 7 units, and θ = 60°.
Using area of a sector of a circle formula,
\[\begin{align}\text{Area of a sector} &= \dfrac {\theta}{360} \times \pi \times r^2 \\ &= \dfrac {60}{360} \times \pi \times 7^2 \\ &= \dfrac{22 \times 7}{6} \\ \text{Area of a sector} &= 25.67\end{align}\]Answer: Hence the area of a sector is 25.67 sq.units.

Example 2:
Find the area of a sector of a circle with a radius of 12 units and the angle formed at the center by the sector is 22 radians.
Solution:
Given, r = 12 units, and θ = 22 radians.
Using area of a sector of a circle formula,
\[\begin{align}\text{Area of a sector} &= \dfrac {\theta}{2} \times r^2 \\ &= \dfrac {22}{2} \times 12^2 \\ &= 11 \times 144 \\ \text{Area of a sector} &= 1584 \end{align}\]Answer: Hence the area of a sector is 1584 sq.units.