Maths Formulas

Circle Formula

We may have come across many objects in our daily life which is round in shape. Some objects of this shape are wheels of a vehicle, bangles, dials of clocks, coins, etc. In a clock, we have observed that the second’s hand goes around the dial of the clock. It is making a round path around the fixed pivot. This pivot is known as a circle. This path traversed by the tip of the second’s hand is called a circle. In this article, we will discuss circles, some other related terms and circle formula with examples. Let’s start learning!

Circle Formula

What is a circle?

A circle is a particular shape of the objects. A circle is a type of closed shape. It is the set of all points in a plane that are at a given distance from a given point. So, it is the curve traced out by a point that moves in a plane in such a way so that its distance from the given point is constant.

It is defined as the set of points in a plane placed at the equal distance from a single pivot point, called the center of the circle. It is a fact that the circle represents a two-dimensional plane. Its three-dimensional figure is known as a sphere. In this shape, no vertex or edge exists.

Some terms related to this shape are as follows:

  1. Center: It is a point as a pivot in the circle. It is used to draw the circle.
  2. Circumference: It is the set of points that are at equal distance around the center of the circle.
  3. Radius: It is the distance from the center to any point on the circumference.
  4. Diameter: It is the distance between any two points on the circumference measured through the center. It is double in the length that the length of the radius.
  5. Area: Area of the circle describes the amount of space covered by the circle. So, it will give the coverage of circle as a two-dimensional plane.


circle formula



r the radius of the circle.
d the diameter of the circle.
C circumference of the circle.

Circle Formula:

  1. The diameter of the Circle is computed as,

D = 2 × R


D The diameter of a Circle
R Radius of circle


  1. Circumference of the circle is computed as,

C = 2 × \(\pi\) × R


C Circumference of circle
R Radius of circle


  1. Area of the circle is computed as,

A = \(\pi\) × R2


A Area of circle
R Radius of circle

Solved Examples on Circle Formula 

Q. A circular ground has a diameter of 800 m. Calculate the area of the circle.


First we have to find radius of the circle as,

R = \(\frac{D}{2}\)

i.e R = \(\frac{800}{2}\)

R = 400 m


Area of circular ground,

A = \(\pi\) × R2

= \(\pi\) × (400)2

=  \(\frac{22}{7}\) × 400 × 400

= 502857.14 sq m

  1. Find the area of the circle with length of circumference as 440 cm.


First find the radius of the circle as,

C= 2 × \(\pi\) × R

i.e. R = \(\frac{C}{2 × \(\pi\)}\)

= \(\frac{440}{2 × 7}{22}\)

= 70 cm

Now, find the area of the circle as,

A = \(\pi\) × R × R

= \frac{22}{7} × 70 × 70

=15400 sq cm.

Share with friends

Customize your course in 30 seconds

Which class are you in?
Get ready for all-new Live Classes!
Now learn Live with India's best teachers. Join courses with the best schedule and enjoy fun and interactive classes.
Ashhar Firdausi
IIT Roorkee
Dr. Nazma Shaik
Gaurav Tiwari
Get Started

One response to “Equation Formula”

  1. KUCKOO B says:

    I get a different answer for first example.
    I got Q1 as 20.5
    median 23 and
    Q3 26

Leave a Reply

Your email address will not be published. Required fields are marked *

Download the App

Watch lectures, practise questions and take tests on the go.

Customize your course in 30 seconds

No thanks.