Circumference of a Circle: Definition, Formula, Properties, and Examples


The circumference of a circle gives the length of the outer border of a circular shape. It is similar to the perimeter of any other two-dimensional figure. The term perimeter is specifically referred to as circumference in the case of a circle.

The circumference is an important measurement since it is directly related to the size of any circle. It is essential for anyone studying geometry or any field that involves circular objects.

In this blog, we will discuss the definition of the circumference with an explanation. We will explain both the mathematical formula and properties of the circumference. We will include examples for our readers in the example section to clarify this concept.

What is the Circumference of a Circle?

The circumference of a circle is the distance of its outside boundary. It measures the entire length of the border of the circle. Let's learn this concept through real-life examples. Imagine a girl running around a circular park and completing a single rotation.

circumference of a park

The distance covered by her in this circular track in one trip is called the circumference of the park.

The circumference of a circle is a basic concept in geometry. We can apply it in our daily life to compute the perimeter of a circular racetrack, determine the belt length required to encircle a pulley or calculate the distance traveled by a wheel during one complete round.

Explanation of Circumference of Circle

The circumference of a circle can be defined as the length of the boundary that encloses a 2D circular shape. If we cut a circle and create a straight line, the total length of this line would be the circumference of a given circle.

circle's circumference

Circle circumferences are measured in length units such as feet, inches, centimeters, meters, miles, or kilometers. Let’s learn about a few important terms associated with circles to understand how to find the circumference of a circle.

Center of Circle

A circle is a set of all points that are a constant distance from a fixed point, known as the center of the circle.


The diameter is a straight-line segment that passes through the center of the circle and connects two points on the boundary of the circle.


The radius of a circle is the distance from the center of the circle to any point on its circumference. The radius (r) is equivalent to half of the diameter (i.e. r = d/2).

components of a circle

Formula for Calculating Circumference of Circle

The circumference measures the overall length of the outer border of the circle. It can be evaluated using the formula:

C = 2 π r

In this formula:

  • C expresses the circumference or perimeter of a circle.
  • π (pi) is a mathematical constant approximately equal to 22/7 (or 3.14159 in decimal).
  • r denotes the radius of the circle which is the distance from the center of the circle to the point on its outer edge.

We can also calculate the Circumference using the diameter with the following formula:

C = π d


  • C is the Circumference.
  • π (Pi) is a constant.
  • d expresses the diameter of the circle

Note that the choice of the formula depends on the given data.

Properties of Circumference of Circle

The circumference has the following essential characteristics:

  • The circumference of a circle is directly proportional to its radius or diameter. The perimeter will also be doubled if the radius or diameter is doubled.
  • The ratio of the circumference of a circle to its diameter is referred to as pi (i.e. π = C/d).
  • The circumference of a circle always gives a positive value.
  • The unit of the determined circumference of a circle is the same as the unit of radius or diameter.

Steps to Find the Circumference of Circle

The Circumference of any 2D circular shape can be evaluated in a few simple steps:

  1. Find the measurement of the radius or diameter of the circular shape.
  2. Substitute the measured radius or diameter into the general formula.
  3. Calculate the circumference by multiplying the appropriate value (2πr or πd) with the measured radius or diameter.
  4. The result of the calculation is the circumference of the circle.
  5. Write down the appropriate unit of measurement with the final answer.

Examples of Circumference of a Circle

The following examples illustrate how to calculate the circumference of a circle manually.

Example 1:

If the circle has a radius of 7 cm, find its circumference.


Given Data:

Radius (r) = 7cm

∴ π ≈ 3.14

The circumference of a circular shape can be calculated using the following formula.

C = 2πr

Substitute these given values in the above formula, we get

C = 2 × 3.14 × 7

Circumference = 43.96 cm

Example 2:

Calculate the length of fabric required to make a 36-inch-radius round dining tablecloth.



r = 36 inches

An estimated value of pi (π) is 3.14.

C = 2πr

Substitute the given values into the formula:

Circumference = 2 (3.14) (36)

C = 226.08 inches

The tablecloth requires around 226.08 inches of fabric.

Example 3:

Calculate the circumference for the circular region with a 10-meter diameter.



Diameter = d = 10

∴ π ≈ 3.14

The formula for the circumference when d is given:

C = πd

Put the value of d and pi in the formula of circumference.

C = 3.14 × 10 m

Circumference = 31.43 m

Thus, the circumference with a radius of 10m is approximately 31.43m.

To solve problems of calculating the circumference of a circle, Use our circumference calculator for precise results quickly.