# How to Find the Area and Perimeter of a Circle?

Contents

## 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.

### Radius

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.

### Diameter

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 covered by one complete cycle of the radius of the circle on a two-dimensional plane is known as the area of 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 perimeter of the Circle**

A perimeter of the circle is defined as the length of its boundary or border. When it comes to circles, the perimeter is given a new name. It is also called the circumference of the circle. This circumference or perimeter is the length of the border of the circle. If we cut open the circle to form a straight line, then the length of the straight line is the perimeter. To define the circumference of the circle, understanding a term known as ‘pi’ is required.

## The perimeter of a Circle Formula

The Circumference or perimeter of a circle has a standard formula = 2πR

Where, R is the radius of the given circle, π is the mathematical constant with an approximate standard estimated value of 3.14.

Pi (π) is a special geometrical constant, it is the ratio of circumference to diameter of any particular circle.

## The radius of a Circle

The distance from the center to the border or outer line of the circle is known as a radius. It is the most significant quantity of the circle based on which the formulas for the area and perimeter of the circle are derived. Twice the radius of a circle is known as the diameter of the circle. The diameter cuts the circle into two halves, which is called a semi-circle.

Conclusion

Circles help in the basics of geometry. Geometry deals with shapes, graphs, and many such interesting things. You can learn more about circles using some of the interesting learning tools. Cuemath is an online learning platform that enables you to understand the concept of circles in the most interesting way. These points discussed above show us the importance of circles and their formulas. Circles can be very easy to master and is a very scoring topic for children.