Calculate the area of a sector using the radius of an arc and the rotation angle. This area uses units of degrees for the angle and any unit of distance for the radius.

Area of a sector formula

The area of a sector or arc can be calculated with the following formula:

Area of a sector formula
  • Where PI is approximately 3.14519
  • r is the radius of the arc/sector
  • the angle is the degrees of rotation of that arc/sector

Area of Sector Definition

The area of a sector refers to the portion of a circle enclosed by two radii and an arc. To calculate the area of a sector, we need to know the measure of the central angle that the sector encompasses and the radius of the circle.

The area of a sector is significant in various fields, such as mathematics, physics, engineering, and architecture. It allows us to determine the proportion of a circle’s total area that a sector occupies. This knowledge is essential for various applications and calculations.

In mathematics, understanding the area of a sector is crucial for geometry and trigonometry.

It helps us analyze and solve problems involving circular shapes, such as finding the area of a segment, determining the length of an arc, or calculating the angle subtended by an arc.

By utilizing the area of a sector, mathematicians can explore the relationships between different parts of a circle and make precise calculations.

How to calculate a sector area

Since a sector is also known as some percentage of a circle, the area itself is also a portion of the area of a circle. The formula for finding the area of a circle is pi*r*r, where r is the radius. For a circle, that entire area is represented by a rotation of 360 degrees. For a sector, the area is represented by some other angle.

To calculate the area of the sector, you must first calculate the area of the equivalent circle using the formula stated previously. Then, you must multiply that area by the ratio of the angles, which would be theta/360 since the circle is 360, and theta is the angle of the sector.


What is the area of a sector?

The area of a sector along an arc is also known as the circular sector. It’s a percent or portion of a disk that is enclosed by that arc and two equal radii. To understand how to calculate the area of such a sector, it’s important to understand the formula that it uses, which is given above.

area of a sector calculator