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Sector Area Calculator

Introduction

Welcome to our Sector Area Calculator! which will help you calculate the sector’s area quickly and accurately. A sector is a portion of a circle formed by an arc on the circle and the arc’s endpoints being connected to the center of the circle.

The simplest example of the sector certainly has to be a slice of a pizza or a slice of a cake, as seen from the top.

The space occupied by the sector on a two-dimensional plane is called the area of the sector. The smaller area in the circle is called the minor sector, whereas the larger area is the major sector.

How to use the Sector Area Calculator?

Using the Sector Area Calculator, you can calculate the area of the sector by inputting the value for the circle’s radius and the included angle forming the arc and the sector.

The variables in the Sector Area Calculator include

Radius (r) The distance from the center to the circle.

Angle (θ) The angle made by the arc at the center of the circle.

Area of the sector (A) The area of the sector is calculated using the following formula

A=θ360×π×r2\text{A} = \normalsize \dfrac{θ}{360} \times \pi \times r^2

Where,

r = Radius of the circle

θ = Angle made by the arc at the center of the circle

What is the Sector of the Circle?

A sector is a two-dimensional shape formed by an arc on the circle along with the radii, so that the lines connecting the ends of the arc, meet at the center of the circle.

The size of a sector is generally described using the measure of the central angle formed by the two radii. The central angle is the included angle formed at the circle’s center, measured in degrees.

When the arc forms a sector, the smaller area is called the minor sector, and the larger area is called the major sector.

How is the area of the sector calculated?

The space occupied by the sector on a two-dimensional plane is called the area of the sector. It could also be thought of as the number of square units required to fill the region inside the sector. Hence the measurement will be in square units.

The area of the sector is calculated using the following formula.

A=θ360×π×r2 \text{A} = \normalsize \dfrac{θ}{360} \times \pi \times r^2

Where,

r = Radius of the circle

θ = Angle made by the arc at the center of the circle

Examples

Let’s say an arc forms a sector on a circle, making an angle of 45 degrees at the center. The radius of the circle is 7cm. What is the area of the sector?

The area of the sector can be calculated using the following formula

A=θ360×π×r2=45360×π×r2=19.24  cm2\begin{aligned} \text{A} &= \normalsize \dfrac{θ}{360} \times \pi \times r^2 \\[10pt]&= \normalsize \dfrac{45}{360} \times \pi \times r^2 \\[10pt] &= 19.24 \; cm^2 \end{aligned}

As shown above, in the example, we can see that the area of the sector is 19.24 sq cm.

Author

hexacalculator design team

Our team blends expertise in mathematics, finance, engineering, physics, and statistics to create advanced, user-friendly calculators. We ensure accuracy, robustness, and simplicity, catering to professionals, students, and enthusiasts. Our diverse skills make complex calculations accessible and reliable for all users.

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