Circumference Of A Circle

The concept of the circumference of a circle is covered here along with the definition of the circumference of a circle, circumference formula (or perimeter of a circle formula) and method to know the circumference of a circle by using formula and physical method.

Introduction to the Circumference of a Circle

A circle is defined as a shape with all points at equidistant from a point at the center. The circle below is called as a circle A, because the center lies at point A. When you calculate the distance around a circle divided by the distance across a circle through its center, you will come close to a specific value based on the precision of your measuring technique. The value is approximately 3.1415926535897… and we use a Greek letter π (pronounced as Pi) to describe this number. The value π is a non-terminating value.

Definition of the Circumference of a Circle

What is meant by the circumference of a circle? It is the one-dimensional linear measurement of the boundary across any two-dimensional circular surface. It follows the same principle behind finding the perimeter of any polygon which is why calculating the circumference of a circle is the same as finding its perimeter.

For circle A (as given above), the circumference will be-

In other words, the distance surrounding a circle is known as the circumference of circle. The diameter is the distance across a circle through the center. π shows the ratio of the circumference of a circle to the diameter. Therefore, when you divide the circumference by the diameter for any circle, you obtain a value close enough to π. This relationship can be explained by the formula mentioned below.

C/d = π

Where, C indicates circumference and d indicates diameter. A different way to put up this formula is C = π × d. This formula is mostly used when the diameter is mentioned and the circumference needs to be calculated.

Measurement of Circumference

Since it is a curved surface, we can’t physically measure the length of a circle using a scale or ruler. But this can be done for polygons like squares, triangles and rectangles. Instead, we can measure the circumference of a circle using a thread. Trace the path of the circle using the thread and mark the points on the thread. This length can be measured using a normal ruler and you have the circumference of the circle.

An accurate way of knowing the circumference of a circle is to calculate it. For this, the radius of the circle has to be known. The radius of a circle is the distance from the centre of the circle and any point on the circle itself. The figure below shows a circle with radius R and center O. The diameter is twice the radius of the circle.

Perimeter of a Circle Formula (Circumference Formula)

The perimeter of a circle = 2πR

where,

R is the radius of the circle

π is the mathematical constant with an approximate (upto two decimal points) value of 3.14

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

where,

C is the circumference of the circle

D is the diameter of the circle

Sample Question on Circumference

Question: What is the circumference of the circle with diameter 4 cm?

Solution:

Since the diameter is known to us, we can calculate the radius of the circle,

Therefore, Circumference of the Circle = 2 x 3.14 x 2 = 12.56 cm.

Circumference of a Circle Questions

1. Calculate the perimeter of a circle whose diameter is 8 cm.
2. What will be the diameter of a circle if its circumference is 10 cm?
3. If the perimeter of a circle is 12 cm, what will be its radius?
4. What is the circumference of a 16 inch circle?
5. What is the circumference of a 6 mm circle?

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Practise This Question

Which of the following number gives a more accurate value of π?