Table of Contents
Area of Quadrant Formula
A circle is a closed curved shape with all points equidistant from a central point called the center. It is one of the fundamental shapes in geometry and has various properties, including its circumference, diameter, radius, and area.
A quadrant, on the other hand, is a specific section of a circle. It is formed by drawing two perpendicular lines that intersect at the center of the circle, dividing the circle into four equal parts. Each of these parts is a quadrant. In geometry, a quadrant covers 90 degrees of the circle’s total 360degree angle.
The area of a quadrant is calculated using the formula (π * r²) / 4, where “r” represents the radius of the circle. This formula finds the area of one of the four equal sections created by the intersecting lines, or onefourth of the total circle’s area. Quadrants are often used in geometry and trigonometry to calculate angles and areas in circular shapes.
What is Quadrant?
A quadrant is a subdivision of a plane. It is a foursided figure with four right angles.
The coordinated frame system has four quarters or segments in it and these quarters or segments are known as the quadrants. These quadrants are all equal in size and area. With respect to a circle, the quarter of a circle is known as a quadrant, which is a segment of 90 degrees. Let us consider four such quadrants attached together. What does it make? It forms a circle. Let’s understand this better with the help of the image given below. You can see that the circle has been divided into four equal parts. Now, these parts are known as quadrants. Each of these quadrants is equal in size and at the midpoint or the center O, they all make a 90degree right angle.
How to Calculate the Area of a Quadrant of Circle?
Before we go ahead and learn how to calculate the area of a quadrant of a circle, there are a few things you must know. Stated below are the key factors you must keep in handy before you solve the problem.
In order to find the area of a quadrant of a circle, you first need to know the area of the circle. Here’s a list of things you need to know.

The Center of a Circle: All the points of the circle are at an equal distance from the center of the circle. Hence, this is known as the center.

The Radius of a Circle: The distance from the center of the circle to any point on the circle, is known as the radius of the circle. It is denoted by the letter R.

The Diameter of a Circle: The diameter is twice the radius of the circle. It is denoted by the letter D.

The Circumference of a Circle: The distance around the edge of the circle is called the circumference of the circle.

The formula of the circumference of Circle: Circumference = 2πr

The Area of a Circle: The total amount of sq units occupied by a circle is known as the area of the circle.

The formula of Area of Circle: Area = π x radius x radius or Area of circle = πr2
How to Calculate the Area of a Quadrant of Circle?
The area of a quadrant of a circle can be found by using the following equation: A = πr²
Methods to Calculate the Area of a Quadrant
There are a few ways to calculate the area of a quadrant. One way is to use the formula for the area of a triangle, which is onehalf the base multiplied by the height. Another way is to use the formula for the area of a rectangle, which is the base multiplied by the height.
The Formula for The Perimeter of a Quadrant
The perimeter of a quadrant is the distance around the four sides of the quadrant. To find the perimeter of a quadrant, multiply the length of each side by 4.
Related Links:
 Area of Square
 Area of Triangles with 3 Sides
 Area of A Sector of A Circle
 Area of an Octagon
 Area of a Pentagon
 Area of Trapezium
 Area of a Prism
Frequently Asked Questions (FAQs) on Area of Quadrant
What is the area of a quadrant formula?
The formula for the area of a quadrant is (π * r²) / 4, where r is the radius of the circle.
How is the area of a quadrant calculated?
To calculate the area of a quadrant, square the radius, multiply it by π (pi), and then divide by 4.
What does the formula (π * r²) / 4 represent?
The formula represents the area of onefourth of a circle, which is the area of a quadrant.
Why is the area of a quadrant important?
The area of a quadrant is used in geometry to find the space enclosed by a quartercircle, helping in various calculations and applications.
Can the area of a quadrant be used for a full circle?
No, the formula calculates the area of onefourth of a circle. To find the area of the full circle, you would use the formula π * r².
How does the radius affect the area of a quadrant?
The area of a quadrant increases with the square of the radius. As the radius grows, the area of the quadrant becomes larger.
What units are used for the area of a quadrant?
The units for the area of a quadrant are determined by the units used for the radius. For example, if the radius is in meters, the area will be in square meters.
What is the significance of a quadrant in geometry?
A quadrant is a quarter of a circle, and its area and angles are important for various calculations involving circular shapes and angles.