Sector Area Calculator

Sector Area Calculator

Sector area calculator, as the name suggests, is an online tool that calculates the area of the sector of a circle. All it needs is; the radius and angle to find the area of sector.

This tool can be used to solve geometry problems related to circle. Moreover, it can be used to measure the land in sectors, and some cool things such slice of pizza or cake.

In this article, we will provide you a detailed explanation on sector of circle, how to use sector area calculator, sector definition, formula for sector of circle, how to find the area of a sector of a circle, and much more.

How to use Area of a Sector Calculator?

Area of a sector calculator provides an elegant and interactive interface to the users. To calculate sector area using this calculator, follow the steps below:

• Select the value for which you want make sector calculation.
• Choose the given set of parameters from the list.
• Enter the radius in the given input box.
• Enter the angle in the next input box.
• Hit the Calculate button to get the sector area.

You will instantly get the area of sector with the step by step demonstration of the calculation. It also shows the formula that it used to find the sector of circle. Sector area calculator only finds the inner portion of circle. If you want to calculate the circumference of circle, you can use our circumference calculator anytime.

What is a Sector of a Circle?

A circle sector or circular sector is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger is the major sector. As you can see in the image below, θ is the central angle in radians, "\(\displaystyle L\)" is the arc length of the minor sector, and "\(\displaystyle r\)" is the radius of the circle, and. Wikipedia

Formula to Find Sector Area of a Circle

The formula for finding the sector area of a circle is a simple equation that can be expressed as:

Area of sector of circle = πr² × (θ / 360)

In this equation:

• r represents the radius of the circle,
• θ is the angle between sector arcs, and
• π is a mathematical constant.

How to Find the Sector Area of a Circle?

If you are pondering how to find the area of a sector, don’t exhaust yourself. We are here for you. The above area of sector calculator finds the circular sector area in no time and there is no doubt that. But, you should also be able to calculate it yourself, especially, if you are a student.

To find the area of a circular sector, follow the below steps:

• Write down the radius of circle and angle between arcs.
• Write down the sector area formula.
• Substitute the values and calculate the area of a sector of a circle.

Example:

Find the area of a sector of a circle having a radius of 12 cm and an angle of 45°.

Solution:

Step 1: Write down the radius of circle and angle between arcs.

r = 12 cm, θ = 45°

Step 2: Write down the sector area formula.

Area of sector of circle = πr² × (θ / 360)

Step 3: Substitute the values and calculate the area of a sector of a circle.

Area = 3.1415 × (12)² × (45° / 360)

Area = 3.1415 × 144 × (45° / 360)

Area = 3240 cm²

So, the sector area of a circle having a 12 cm radius and 45° angle will be 3240 cm² approximately.

Area of a Circle Sector – Real World Example

What will be the size of the pizza slice if the radius of the pizza is 20 cm and its central angle is 30°?

Solution:

Step 1: Write down the radius of pizza and central angle.

r = 20 cm, θ = 30°

Step 2: Write down the sector area formula.

Area of sector of circle = πr² × (θ / 360)

Step 3: Substitute the values and calculate the area of slice of pizza.

Area = 3.1415 × (20)² × (30° / 360)

Area = 3.1415 × 400 × (30° / 360)

Area = 6000 cm² or 930 sq. inch

So, the sector area of a pizza slice having 20 cm radius and 30° angle will be 6000 cm² approximately. You can use our area of a sector calculator to quickly find the area of a sector of a circle with steps and avoid manual calculations.

FAQs

How to find the area of a sector?

To find the area of a sector,

• Get the radius and central angle.
• Substitute the values in the area of sector formula, Area = πr²× (θ / 360).
• Solve the equation after placing the values to get the sector area.
• Or use the Sector Area Calculator to get the area of a sector.

How do you find the area of a sector using online calculator?

To find the area of a sector of the circle using an online calculator, follow the steps below:

• Go to the Area of a Sector Calculator.
• Select the set of parameters that is given.
• Enter the given values in the respective input boxes. i.e., radius, angle, etc.
• Press the Calculate

Bingo! You have got the area of a sector of a circle without getting engaged in complex equations.

What is the formula for the area of a sector of a circle?

The formula for the area of a sector of a circle can be stated as:

Area of sector of circle = πr² × (θ / 360)

Where, r represents the radius of the circle, θ is the angle between sector arcs, and π is a mathematical constant.

How do you find the area of a shaded sector?

The area of a shaded sector can be calculated by the same method we calculate the area of a sector. To find the area of a shaded sector:

• Get the radius and central angle.
• Substitute the values in the area of a sector formula, Area = πr²× (θ / 360).
• Solve the equation after placing the values to get the sector area.

What is a minor sector?

A minor sector of a circle is a sector that has the central angle of less than 180°. The measurement of the central angle of the minor sector cannot exceed 180°.