Area of a Sector Calculator

The area of a sector calculator calculates the central angle of the circle either in degrees or radians. Our area of shaded region calculator makes your calculation quick and effortless and gives 100% fast results.

Area of a Sector:

“The area of a sector is the space inside the circle generated by two radii and an arc”

Its defining characteristic is its central angle. The sector is a region confined by an arc bounded by two radii. It always originates from the center of the circle and can instantly be calculated by using this sector area calculator.

Formula:

The area of a shaded region is a fractional part of the circle. The area of a sector formula is used to measure the central angle. Hence the sector area formula is given below. There are two possibilities for the procedure: 

• If θ is Measured in the Degree

$$ \frac{\text{Area of Sector}}{\text{Area of Circle}}\;=\;\frac{Central\;Angle}{360°} $$

$$ \frac{Area\;of\;Sector}{πr^2}\;=\;\frac{θ}{360°} $$

$$ \text{Area of Sector}\;=\;\frac{θ}{360°} * πr^2 $$

• If θ is Measured in the Radian

$$ \frac{Area\;of\;Sector}{Area\;of\;Circle}\;=\;\frac{Central\;Angle}{2π} $$

$$ \frac{Area\;of\;Sector}{πr^2}\;=\;\frac{θ}{2π} $$

$$ \text{Area of Sector}\;=\;\frac{θ}{2π} * πr^2 $$

$$ \text{Area of Sector}\;=\;\frac{1}{2} * θr^2 $$

Where θ is the angle subtended by the arc at the circle in radians, and r is the radius of the circle.

How to Calculate The Area of a Sector?

No doubt our area of a sector calculator calculates instant outputs, but you also need to get a grip on manual computations. Take a closer look at the example to embellish your concept!

Example:

Let’s suppose that an example is in the form of a shape.

Solution:

In the first figure, a circle is half-shaded, so we know the area of sector formula that is:

= θ/360 * πr^2

= 180/360 * 3.14 * 5 ^ 2 

= 39.25 cm^2

Another way of calculation is that the area will be 1/2

So,

Area of a sector of a circle = 1/2 multiplied by πr^2

In the next figure, 

Area of a sector of a circle = 1/4 multiplied by the πr^2

In the last figure, 

Area of the circle = 1/12 multiplied by the πr^2

Working of an Area of a Sector Calculator:

Our free sector area calculator is the way to determine the authentic results concerning sector area. Let’s know what you need to know!

Input:

• Enter the radius of the circle 
• Now enter the angle of the circle 
• Press the “Calculate” button 

Output:

• Area of a sector of circle in radians and degrees

FAQs:

What Are The Types of the Sector?

A circle is divided into two sectors which are minor and major. The smaller part of the circle is called the minor sector, and the major sector is the largest and significant part of the circle.

How to Find the Area of a Sector Without an Angle?

The area of a sector calculator will find the area of the sector without an angle. The procedure is in the below section:

Area of a sector =  l * r^2 

Where,

l is the arc length, and r is the radius of the circle. 

Is the Sector Angle Same for Every Sector?

Not at all! The sector angle varies with the area of the sector that could be measured with the help of the area of sector formula. Different names are sometimes given to sectors with different central angles.

• Quadrant 45° 
• Sextants 60° 
• Octant 90° 

How Do You Find the Central Angle of the Sector?

To find out the central angle of a sector θ, you can use the following formula:

θ = s / r

In the above-given formula, s is the arc length, and r is the circle's radius.

References:

From the source Wikipedia: Circular sector, Types, Area, Arc length.

From the source Khan Academy: Area of a sector.