Area of a Sector Calculator
Use this Area of a Sector calculator to easily and quickly calculate the area of a sector given its radius and angle .
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About Area of a Sector Calculator
The “Area of Sector Calculator” tool can be used to calculate the area of a circle. It helps in engineering, geometry and many other subjects. Users enter the field angle and the radius of the circle. After processing this data and converting the units as necessary, the calculator uses the appropriate mathematical formula to determine the location of the field. The results are expressed in square meters. This simple calculation improves the accuracy of geometry calculations by providing a fast and accurate method of calculating the area of the field without the need for tedious calculations
Table of Contents
Area of a Sector Formula
Here on this page we will learn to calculate the area of an sector and understand how to calculate it. This is very simple and easy. Let’s start by understanding what a sector is. A sector is like a slice of pizza or a piece of pie from a whole circle. To find the area of this sector, we use a simple
Formula:
Area of a Sector = (θ/360) × π × r²
If you are not given the radius, and the diameter is given, you can use the formula given below. But it is important to know that radius is always half the diameter. And the diameter is always double the radius. Meaning if the radius is 50 then the diameter is 100. And if the diameter is 60 then the radius is 30.
Radius = Diameter / 2
diameter=Radius * 2
Area of a Sector = (angle / 360) x π x (diameter / 2)2.
Here –
θ is the angle of the sector (in degrees).
π is a mathematical constant (approximately 3.14159).
r is the radius of the circle.
Now, let’s understend the steps to calculate the area of a sector using the formula:
Measure the angle (θ) of the sector.
Divide the angle by 360.
Multiply the result by π (pi).
Square the radius (r).
Multiply all these values together.
Here’s the simplified
Formula: Area = (θ/360) × π × r²
Calculation Example - Find the Area of a Sector
Here on this page we will learn to calculate the area of a Sector and understand how to calculate it. Imagine you have a pizza with a radius of 8 , and you cut out a sector with an angle of 60 degrees. Let’s find the area.
θ = 60 degrees
(60/360) = 1/6
Multiply by π: 1/6 × π
Square the radius: 8² = 64
Multiply all together: (1/6) × π × 64 ≈ 33.51 square inches
So, the area of the sector is approximately 33.51 square inches.
Using this easy guide, you can quickly calculate the area of any sector. Just remember to measure the angle, divide by 360, multiply by π, and square the radius. Now you must have understood well.