Calculate the area of a sector using the radius of an arc and the angle of rotation. 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:
- 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
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.
How to calculate a sector area
Since a sector is also known as some percentage of a circle, then 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.
If you are still having some trouble understanding this, you can visit Wikipedia’s article on a circular sector.