Area of a Sector Calculator

Introduction of Area of Sector

Area of the sector is a sector like a ‘pizza slice’ in round-shaped pizza. This sector consists of a region confined by an arc bounded between two radii. It is a fraction of the area of the circle. If its central angle is bigger, the area of the sector will also be larger accordingly. In other words, we may say the area of sector is proportional to the central angle.

What is an Area of Sector Calculator?

Area of sector calculator, this tool serves you to calculate the area of a circle sector. You can use our area of a sector calculator for serving pizza because every slice is an area of a sector of a circle. Area of a sector calculator will also be useful to measure the sector area of the circle of the skirt. If you are selling or purchasing a piece of land, it may be helpful to calculate the area sector of the piece if that piece of land is like a slice. Apart from routine life examples, it must be helpful in mathematical geometry problems etc.

Area of a Sector Formula

Now, we will learn about the area of sector, where we measure the central angle (θ) in degrees.

As, the area of a circle=r² and the angle of a full circle = 360°

Thus, the formula of the area of a sector will be:

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

$$\frac{Area\;of\;Sector}{πr^2}\;=\;\frac{0}{360°}$$

$$\text{Area of Sector}\;=\;\frac{0}{360°} * πr^2 $$

r = radius of the circle

This formula supports us to find anyone of the values if the other two values are given.

But, if we measure the angle of a circle in radians, the area of sector formula will be

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

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

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

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

r = radius of the circle

This formula helps us to find anyone of the values if the other two are given.

Semicircle Area:

To know the area of the half of a circle, this formula will be applicable.

$$\text{Semicircle area}\;=\;\frac{πr^2}{2} $$

Divide the area of the circle by 2.

Quadrant Area:

To know the area of a quarter of a circle, this formula will be applied.

$$\text{Quadrant area}\;=\;\frac{πr^2}{4} $$

Sectors

Before using these formulas in examples, let’s understand “Sectors”.

You are familiar with the area of a circle, but we have to calculate just shaded area. In the first figure, shaded area just covers half the circle. So the area will be ½ multiplied by πr². Next circle is divided into four equal parts.

What will be the area of the shaded part?

It will be ¼ πr². Now, look at last figure.

What will be the area of the shaded region in this case?

This area of a sector is proportional to the angle that the arc subtends at the center. In this area, the angle is 30 degrees. Then the area of the sector will be 30/360.In this equation, πr² is the area of the circle whereas 30/360 tells us how much of the circle is covered. To generalize the formula for a sector, we can say that if the sector angle is. Then the area of sector will be θ/360° * πr². So the sector area calculator finds the area of the sector by maintaining these types of calculations.

Note: In above all circles, the shaded area is called sector of a circle.

Arc Length

Area of a sector of a circle and arc length is little different calculations but related to a circle. As, if you again look at this circle, the area bounded between two radii and 1 is the area of sector whereas length from one point to another along a section of the curve is called arc length as in figure the distance from point “A” to “B” is arc length.

Arc length is calculated by this formula.

$$\text{Arc Length}\;=\;r\theta$$

Here “r” is radius and theta is the central angle of the circle.

Example

Find the area for the sector of a circle.

r = 10 cm

π = 3.14

θ = 300

A =?

As we know the full inside a circle is:

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

We have 300/360 of the full circle

$$\text{Area of Sector}\;=\;\frac{300}{360°} * πr^2$$

$$\text{Area of Sector}\;=\;2.62cm^2$$

Thus, here the area of sector is 262 cm².

Area of sector calculator works according to these calculations.

How to Use Area of a Sector Calculator?

Our area of a sector calculator is easy to understand and reliable. You can get your required area of the section by just putting radius value and angle. As we calculated above example, we can look at the same example at the calculator like this.

Hopefully, this tool will be proved easy to use as well as helpful for academically and routine- life too.
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