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
In today’s article, we will learn about the area of a sector and the length of an arc. What is the area of the sector, and how can we find its area? First, let us understand what a sector is. We have given the photo below, which has a drawing of the sector. You can understand this example by looking at the drawing of that sector.
A sector is the area enclosed between two radii and an arc. So the sector is the area between two radii and R, as shown in the photo; here A is an arc and P is our radius; the area in between is called the sector. So this portion between radius and R is our sector. The remaining portion here is also a sector. So we will call it a major sector, and the smaller one is our minor sector.
Now if we want to find the area of a sector, then its formula is that we have Area of a Sector = Theta / 360 * pi r square. Now, what is Theta? The angle formed between these two radii is our theta, and here APB is the arc, so the formula to find it is the length of an arc; its formula will be theta upon 360 * 2 pi r. So these are two formulas. The first formula is to find our area of a sector; okay, the second is to find the length of an arc.
Let’s take an example. Find the area of a sector of a circle with a radius of 7 cm and an angle of 30 degrees. So here we have a circle, and a sector is formed in the middle of it whose radius has been given to us, which is 7 cm, and the angle formed between both the radii is 30 degrees, so our r is 7 cm and theta is 30 degrees. So if we want to find the area of a sector, its formula is the formula of area of a sector: area = theta / 360*pi r square. So here we put the value; our r is 30. In our case, 30 / 360 * 5 is 22 / 7, and our radius is 7, so 7 * 7. area = 11 * 7. So if we multiply 11 by 7, it will become 77. Area = 77 / 6. Here, 77 divided by 6 is 12.83 square cm. So this is the area of our sector.
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Area of a Sector Formula
Here on this page, we will learn how to size an area and understand how it is calculated. This is very simple and easy. Let’s start by understanding what the field is. The area looks like a slice of pizza or like a slice of pie from a full circle. We use Simple to find the location of this field
Ingredients:
Area of a field = (θ/360) × π × r2
If you are not given a radius and you are given a diameter, you can use the formula below. However, it should be noted that the radius is always half the circumference. and its circumference is always twice the radius. That is, if the radius is 50, the circumference is 100 and if the circumference is 60, 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.
Calculation Example - Find the Area of a Sector
On this page, we will learn how to calculate the area of a sector. Imagine you have a pizza with a radius of 8 and 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. remember to measure the angle, divide by 360, multiply by π, and square the radius. Now, you must have understood well.