# How to Calculate the Circumference of a Circle

In the previous post, we have learned about the basic terminologies about circles. We continue this series by understanding the meaning of circumference of a circle. The circumference of a circle is basically the distance around the circle itself. If you want to find the circumference of a can, for example, you can get a measuring tape and wrap around it.

The animation below shows, the meaning of circumference. As we can see, the circle with diameter 1 has circumference $\pi$ or approximately $3.14$.

Note: If you want to know where $\pi$ came from, read Calculating the Value of Pi.

Example 1

What is the perimeter of a circle with diameter 1 unit?

Solution

The formula of finding the circumference of a circle is with circumference$C$ and diameter $d$ is $C = \pi d$. So,

$C = \pi d = \pi(1) = \pi$.

Example 2

Find the circumference of a circle with radius 2.5 cm.

Solution

The circumference $C$ of a circle with radius $r$ is

$C = 2 \pi r$

So, $C = 2(3.14)(2.5) = 15.7$

Therefore, the circumference of a circle with radius 2.5 cm is 15.7 cm.

Example 3

Find the radius of a circle with a circumference 18.84 cm. Use $\pi = 3.14$.

Solution

$C = 2 \pi r$

$18.84 = 2 (3.14) r$

$18.84 = 6.28 r$

Dividing both sides by 6.28, we have

$3 = r$.

Therefore, the radius of a circle with circumference 18.84 cm is 3 cm.

Example 4

Mike was jogging in circular park. Halfway completing the circle, he went back to where he started through a straight path. If he traveled a total distance of 514 meters, what is the total distance if he jogged around the park once? (Use $\pi = 3.14$).

Solution

The distance traveled by Mike is equal to half the circumference of the circular park and its diameter. Since the circumference of a circle is $2 \pi r$ and the diameter is equal to $2r$, the distance traveled by Mike is

So, $D = \frac{1}{2}(2 \pi r) + 2r$.

Substituting, we have $514 = \pi r + 2r$.

Factoring out $r$, we have $514 = r( \pi + 2)$

$514 = r(3.14 + 2)$

$514 = r (5.14)$.

Dividing both sides by 5.14, we get

$r = 100$.

Now, we are looking for the distance around the park (cirumfrence of the circle). That is,

$C = 2 \pi r = 2 (3.14)(100)$

$C = 628$ meters.

In the next post, we will discuss how to calculate the area of a circle.