Perimeter of Circles
2026-02-28 01:06 Diff
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Last updated on October 7, 2025

The perimeter of a shape is the total length of its boundary. The perimeter of a circle is known as its circumference. It is used in various practical applications such as designing circular tracks, calculating the length of material needed for circular objects, and more. In this topic, we will learn about the perimeter of a circle.

What is the Perimeter of a Circle?

The perimeter of a circle is called its circumference. It is the total distance around the circle.

The formula for the circumference of a circle is 𝐶 = 2πr, where r is the radius of the circle.

For instance, if a circle has a radius of r = 5, then its circumference is C = 2π(5) = 10π.

Formula for Perimeter of Circle - 𝐶 = 2πr.

Let’s consider another example of a circle with a radius of r = 7. So the circumference of the circle will be: 𝐶 = 2πr = 2π(7) = 14π.

How to Calculate the Perimeter of Circle

To find the perimeter of a circle, we just need to apply the given formula and multiply the radius by 2π. For instance, if a given circle has a radius of r = 4. Perimeter = 2πr = 2π(4) = 8π.

Example Problem on Perimeter of Circle -

For finding the circumference of a circle, we use the formula, 𝐶 = 2πr.

For example, let’s say, r = 3 cm.

Now, the circumference = 2π(3) = 6π cm.

Therefore, the circumference of the circle is 6π cm.

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Tips and Tricks for Perimeter of Circle

Learning some tips and tricks makes it easier for children to calculate the circumference of circles. Here are some tips and tricks given below:

  • Always remember that a circle's circumference is simply the diameter times π, or 2π times the radius. For that, use the formula, 𝐶 = 2πr.
  • Calculating the circumference of a circle starts by determining the radius or diameter. The radius is half the diameter.
  • To reduce confusion, make sure to identify whether you are given the radius or diameter before applying the formula.
  • To avoid mistakes when calculating the circumference, ensure the radius or diameter is measured accurately and consistently for applications like crafts and construction.
  • If you are given the diameter, simply divide it by 2 to find the radius, and then use the formula for the circumference.

Common Mistakes and How to Avoid Them in Perimeter of Circle

Did you know that while working with the perimeter of a circle, children might encounter some errors or difficulties? We have many solutions to resolve these problems. Here are some given below:

Problem 1

A circular garden has a circumference of 62.8 meters. If the diameter of the garden is 20 meters, verify the circumference.

Okay, lets begin

The circumference is correct.

Explanation

Given diameter = 20 meters. Radius r = diameter/2 = 10 meters. Using formula: C = 2πr = 2π(10) = 20π ≈ 62.8 meters. Therefore, the given circumference is correct.

Well explained 👍

Problem 2

A circular track has a diameter of 50 meters. Find the length of the perimeter of the track.

Okay, lets begin

The perimeter is 50π meters.

Explanation

Given diameter = 50 meters. Radius r = diameter/2 = 25 meters. Using formula: C = 2πr = 2π(25) = 50π meters. Therefore, the length of the perimeter of the track is 50π meters.

Well explained 👍

Problem 3

Find the circumference of a circle with a radius of 8 cm.

Okay, lets begin

16π cm

Explanation

Circumference of circle = 2πr C = 2π(8) = 16π Therefore, the circumference of the circle is 16π cm.

Well explained 👍

Problem 4

Sarah is planning to put a fence around her circular swimming pool. The pool has a radius of 6 meters. How much fencing material should Sarah buy?

Okay, lets begin

Sarah will need 12π meters of fencing material.

Explanation

The circumference of the pool is the amount of fencing material needed. Using the formula: C = 2πr C = 2π(6) = 12π meters.

Well explained 👍

Problem 5

Find the perimeter of a circular walking path with a radius of 15 meters.

Okay, lets begin

Perimeter = 2π(15) = 30π meters.

Explanation

The perimeter of the circular path is calculated using the formula for circumference. By multiplying the radius by 2π, the entire distance around the path is 30π meters.

Well explained 👍

FAQs on Perimeter of Circles

1.Evaluate the circle’s circumference if its radius is 3 cm.

Circumference of circle = 2πr, Hence C = 2π(3) = 6π cm.

2.What is meant by a circle’s perimeter?

The total length around a circle’s boundary is its perimeter, also known as the circumference.

3.What are the types of circles?

There is only one type of circle, defined by its center and radius, but circles can be described in terms of their size (e.g., small, large) or in terms of their position (e.g., concentric circles).

4.What value is used for π in calculations?

Common values used for π in calculations are 3.14 or 22/7, depending on the required precision.

5.How does the diameter relate to the circumference of a circle?

The circumference of a circle is the diameter multiplied by π: C = πd.

Important Glossaries for Perimeter of Circles

  • Circumference: The perimeter or total length around a circle.
  • Radius: The distance from the center of a circle to any point on its boundary.
  • Diameter: The distance across a circle, passing through the center; it is twice the radius.
  • π (Pi): A mathematical constant approximately equal to 3.14159, used in calculations involving circles.
  • Formula for circumference: The mathematical expression used to calculate the perimeter of a circle is 𝐶 = 2πr.

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Seyed Ali Fathima S

About the Author

Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.

Fun Fact

: She has songs for each table which helps her to remember the tables