The perimeter of any figure defines the path or the boundaries that enclose the figure. The perimeter of a circle is also called the circumference and it tells us the length of the path around the circle. This length can be calculated using the constant *π* and the diameter or radius of the circle.

Here, we will learn more about the perimeter or circumference of the circle. We will learn about its formula and find out where it comes from. Also, we will explore the origin of the constant *π*. Finally, we will use the circumference formula to calculate the length around various circles.

## What is the formula to find the perimeter of a circle?

The perimeter of a circle, also known as the circumference, is the distance around the circle. We can calculate the length of the perimeter using the length of its diameter or its radius and the constant pi.

The value of pi is approximately 3.141592… and we use the Greek letter *π* (pronounced pi) to represent this number.

Let’s consider the following circle:

We see that the distance around the circle is the perimeter of the circumference. The diameter is the distance across the circle and through the center. π shows the ratio of the perimeter of the circle to the diameter.

Therefore, when we divide the circumference by the diameter of any circle, we get the value π. This relationship can be expressed by the following formula:

$latex \frac{C}{d}=\pi$

where C indicates the length of the circumference and *d* represents the length of the diameter of the circle. We can also write the formula as follows:

$latex C=\pi d$ |

### Perimeter of a circle using the radius

To find the perimeter of a circle if we only know the length of the radius, we can use the relationship $latex d = 2r$. Therefore, rewriting the perimeter formula, we have:

$latex C=2\pi r$ |

## Perimeter of a circle – Examples with answers

With the following examples, you can practice applying the formulas for the perimeters of circles. Each example has its respective solution, but it is recommended that you try to solve the problems yourself before looking at the solution.

**EXAMPLE 1**

If a circle has a diameter of 6 m, what is its perimeter?

##### Solution

To calculate the perimeter or circumference, we use the value $latex d=6$ in the first formula:

$latex C=\pi d$

$latex C=\pi (6)$

$latex C=18.8$

The perimeter is equal to 18.8 m.

**EXAMPLE 2**

What is the perimeter of a circle that has a diameter of 15 cm?

##### Solution

We use the value $latex d=15$ in the first formula for the perimeter:

$latex C=\pi d$

$latex C=\pi (15)$

$latex C=47.1$

The perimeter is equal to 47.1 cm.

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**EXAMPLE 3**

If a circle has a radius of 8 m, what is the length of its perimeter?

##### Solution

In this case, we have the radius of the circle instead of the diameter, so we use the value $latex r = 8$ in the second formula:

$latex C=2\pi r$

$latex C=2\pi (8)$

$latex C=50.3$

The perimeter is equal to 50.3 m.

**EXAMPLE 4**

What is the perimeter of a circle that has a radius of 13 m?

##### Solution

We have to use the value $latex r=13$ in the second formula for the perimeter. Therefore, we have:

$latex C=2\pi r$

$latex C=2\pi (13)$

$latex C=81.7$

The perimeter is equal to 81.7 m.

**EXAMPLE 5**

What is the diameter of a circle that has a perimeter of 100 m?

##### Solution

In this case, we have the perimeter of the circle and we want to find the diameter, so we use the value $latex C=100$ in the formula and solve for *d*:

$latex C=\pi d$

$latex 100=\pi d$

$latex d=\frac{100}{\pi}$

$latex d=31.8$

The length of the diameter is equal to 31.8 m.

## Perimeter of a circle – Practice problems

Practice using the formulas for perimeters of circles to solve the following problems. If you need help with this topic, you can look at the solved examples above.

## See also

Interested in learning more about circles? Take a look at these pages:

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