# Circumference of a Circle

## What is the Circumference of a Circle

The circumference of a circle is the distance around the boundary of the circle. It is the same as calculating the perimeter of any polygon such as triangle, square, and rectangle. The circumference of a circle is measured in units of meters, kilometers, inches, etc.

The diagram below shows the circumference of a circle.

## Formulas

There are two ways to get the circumference of a circle. The first method uses a radius of the circle, while the second one involves the diameter to calculate the circumference. But, it is important to know that both give the same result.

### How to Find the Circumference of a Circle with Radius

When the radius of a circle is known, the formula to determine the circumference is given below:

Let’s solve some examples to understand the concept better.

Solved Examples

Find the circumference of the circle with a radius of 10 inches.

Solution:

As we know,
Circumference (C) = 2πr, here r = 10 inches, π = 3.141
= 2 × 3.141 × 10
= 62.82 inches

Calculate the radius of the circle with circumference 12 inches.

Solution:

As we know,
Circumference (C) = 2πr, here C = 12 inches, π = 3.141
12 = 2 × 3.141 × r
r = 12/2 × 3.141
= 1.91 inches

### How to Calculate the Circumference of a Circle with Diameter

When the diameter of the circle is given, formula to get the measure of circumference is given below:

Derivation

The above formula can be obtained from the standard formulas A = 2πr …..(1)

As we know,

Diameter (d) = 2 × radius (r)

r = d/2

Putting the value of r in equation (1) we get,

A = 2 × π × d/2

A = πd

Let’s solve some examples to understand the concept better.

Find the exact circumference of the circle with diameter 6 inches in terms of π?

Solution:

As we know,
A = πd, here d = 6 inches
= (π× 6) inches
= 18.84π inches

What is the approximate circumference of the given circle?

Solution:

As we know,
A = πd, here π = 3.141, d = 8 inches
= (3.141 × 8) inches
= 25.12 inches

The circumference of a circle is 220 yards. Find the diameter and radius of the circle.

Solution:

As we know,
Circumference (C) = 2πr, here C = 220 inches, π = 3.141
220 = 2 × 3.141 × r
r = 220/6.282 yards
r = 35.02 yards
Now, since
Diameter (d) = 2 × radius (r)
d = (2 × 35.02) yards
d = 70.04 yards

Find the area and circumference of a circle with a radius of 4 inches.

Solution:

As we know,
Circumference (C) = 2πr, here π = 3.141, r = 4 inches
= (2 × 3.141 × 4)
= 25.12 inches
Now,
A = πr2, here π = 3.141, r = 11 inches
= 3.141 × (11)2
= 380.06 inches2