Explain How to Find the Area of a Circle

By Mitch Rice

The area of circle formula is useful for estimating and measuring the space occupied by a circular field or a shape. Suppose, if the students are given a particular plot to fence it, then the area formula will help the students to check how much fencing is required on that plot. Or suppose if the students have to buy a tablecloth, then how much portion of cloth is needed to cover the tabletop completely.


Consequently, the formulas and concepts revolving around the area of the circle and the perimeter are introduced in Maths and algebra to figure out such day-to-day scenarios and activities. But, one common question that the students often ask is that does a circle have volume? The answer to this particular question is an absolute no. Since a circle is a two-dimensional form, it does not have any volume. A circle has only an area and perimeter. So, the circle does not have the volume of a circle. In this article, let us review and understand in detail the area of circle, surface area, and its circumference with very easy and practical examples.


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What is a Circle?

A circle is a closed plane geometric shape. In scientific terms, a circle is a locus of a point moving around a fixed point at a fixed gap away from the point. A circle is a tight curve with its outer line equidistant from the center point. The determined distance from the point is called the radius of the circle. In real life, a few examples of the circle are wheels, pizzas, a circular ground, etc. In order to calculate the area and circumference of a circle, we first need to understand some of the important terms. Now let us learn, the fundamental terms used in the case of a circle.


The radius of the circle is the important line that joins the center of the circle to the outer boundary. It is usually expressed by ‘r’ or ‘R..’. In the standard formula for the area and perimeter of a circle, radius plays a vital role which we will learn later.


The diameter of the circle is the line that divides the circle into two identical halves. In an obvious way, we can say it is just the double of the radius of the given circle and is expressed by ’d’ or ‘D’. Consequently,

d = 2r or D = 2R

If the diameter of the circle is given to us, we can calculate the radius of the circle, by:

r = d/2 or R = D/2

Area of Circle?

Any curvilinear shape has its area. Here the area is the sphere that is occupied by the shape in a two-dimensional plane. So the area enclosed by one complete cycle of the radius of the circle on a given two-dimensional plane is termed as the area of the circle. Now how do we calculate the area for any circular object given? In this sample, we use the standard and only formula for the circle’s area. Let us learn the formula now.

Derivation of Area of Circle

The area of a circle can be visualized & proved by using two fundamental methods, such as:

  • Determining the circle’s area using rectangular shapes
  • Determining the circle’s area using triangular shapes


The area of the circle holds a very vital place in the concepts of algebra and mathematics. The area of the circle needs a very effective understanding in order for you students to use the concepts very effectively and accurately. Although the concepts of the area of the circle are very simple and easy to understand, the complex subtopics revolving around the circle needs supervision and assistance so that the students do not make any silly mistakes and get the base wrong.