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 = πr^{2}, here π = 3.141, r = 11 inches = 3.141 × (11)^{2} = 380.06 inches^{2}