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Maths Formulas

Circumference Formula

Our earth is like a sphere, and if we sliced it in half, we’d end up with a circle. Similarly, in our day to day life, we may find many objects in similar shapes. Circle and sphere both represent the 2-dimensional and 3- dimensional shape of the round objects. The circumference is the distance that surrounds a circle. We can measure the circumference of the earth by measuring the distance that we will have to walk all the way around the world. To understand circumference, this article will help a lot. Here we will discuss the circumference formula with examples. We also have to understand the meaning of diameter and radius. Let us begin!

Circumference Formula

What is Circumference?

Circumference of the circle is like the perimeter of the circle. So, it is the measurement of the boundary across any two-dimensional circular shape like a circle. To measure the circumference we need the radius or diameter of the circle.

As we know that the diameter is the distance between two points on the edge of the circle across the center of the circle. And, the radius is the distance from the center to the edge of a circle. It is the most important quantity of the circle through it we can compute the area and circumference of the circle.

The double value of the radius of a circle is called the diameter of the circle. Also, we can say that the diameter cuts the circle into two equal parts, which is called as a semi-circle.

Therefore the circumference of a closed curve or circular object is the linear distance around its edge. The circumference of a circle always has a lot of importance in geometry as well as trigonometry.

Formula to Find Circumference

The circumference formula of a circle is obtained by multiplying the diameter with a constant π.  The Circumference Formula will require either the radius or the diameter of the circle for its calculation.

The mathematicians have evolved a relationship between circumference and diameter of the circle. This ratio is a constant known as π.

i.e.  \(\frac{C}{d}\) = π

Where C indicates circumference and d indicates diameter.

Circumference of a Circle,

C= 2 \(\pi r = \pi d\)


C Circumference of the circle.
D The diameter of the circle.


R The radius of the circle.


Solved Examples

Q.1: What is the circumference of the circle with area\( 4 \pi square\) cm?

Solution: First we have to apply formula for area of a circle to get value of radius of the circle. Since area of circle,

A= πr²

i.e r = \(\sqrt{\frac{A}{\pi}}\)

i.e. r = \(\sqrt{\frac{4\pi}{\pi}}\)

i.e. r = \(\sqrt {4}\)

i.e. r = 2 cm

Therefore, Circumference of the Circle,

C= \(2\pi r\)

i.e. C= \(2\pi 2\)

Thus  C  = 12.56 cm.

Thus circumference length is 12.56 cm.

Q.2: Find the radius of the circle having circumference C =  50 cm.


It is given that circumference C is 50 cm.

As per the formula,

C= 2π r

i.e r=\(\frac{c}{2\pi}\)

i.e. r=\(\frac{50}{2\pi}\)

i.e. r = \(\frac{25}{3.14}\)

This implies, that

r =  7.96 cm

Therefore, the radius of the circle is 7.96 cm.

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