Do you want to **calculate the area of a circular sector**? Use our online calculator and you will get the area of the sector automatically as well as its arc length and perimeter.

All you need is **to know the radius of the circle (r) and the number of degrees (α)** that the circular sector occupies. When you have it, press the calculate button and you will get the result immediately.

Article sections

## What is a circular sector?

When we want to calculate the area of a circle, we do it taking into account its entire surface. However, we may only be interested in **a portion of the circle** . Therefore, we refer to this portion as the circular sector.

If we look at the figure above these lines, the circular sector would correspond to the part colored in turquoise.** It is formed by the rotation of the radius** a given number of degrees or radians.

## Area of a circular sector

Now that we know what a circular sector is, we are going to learn **how to calculate its area**. To do so, we will use the following mathematical formula:

In this formula we have two unknowns that we must know:

- r is the radius of the circle
- α is the angle in degrees of the sector

If we were given the **sector angle expressed in radians** we have two options. The first is to switch from radians to degrees while the second option is to apply this other formula:

**Remember**this second one **formula for calculating the area of the circular sector** we will use it if we are given the angle expressed in radians.

## Arc length

If we are asked to **calculate the arc length of the circular sector**, it refers to the distance from point A to point B. We will have to calculate the length of that arc by applying the following formula:

## Calculate the perimeter of a circular sector

In the case that we want to **calculate the perimeter of the entire circular sector**, we must add to the length of the arc 2 times the radius, that is to say:

Circular sector perimeter = arc length + 2r

If we express it mathematically, the formula to calculate the perimeter of the circular sector is:

## Circular sector exercises

To put into practice everything we have learned so far, we are going to do a solved exercise in which we are asked for **calculate the area, arc length and perimeter of a circular sector** whose radius is 6cm and α=90º.

We will start with the area since it is the first formula we have seen in the theory:

Remember that **area units are squared**. If you do not leave it indicated, you may be deducted points in the grade of the exercise.

Next we will calculate the arc of the circular sector:

With the arc already calculated, the perimeter is obtained in a very simple way since we only have to add twice the length of the radius. The complete process to calculate it would be as follows:

If you have any questions or have any problems solving an exercise, leave us a comment and we will help you solve it.

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