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How to Find the Circumference of a Circle (Mathematics Lesson)

How to Find the Circumference of a Circle

The circumference of a circle is found using the formula:



In the formula, d is the diameter of the circle. The image below shows what we mean by diameter:

A Real Example of How to Find the Circumference of a Circle

An Example Question

What is the circumference of a circle with a diameter of 10 cm, as shown below?

Step 1
Start with the formula:
Circumference = πd
Don't forget: π is pi (≈ 3.14) and πd = π × d

Step 2
Substitute the diameter into the formula. In our example, d = 10.
Circumference = π × 10 = 31.4 cm
The circumference of the circle with a diameter of 10 cm is 31.4 cm.

Another Real Example of How to Find the Circumference of a Circle

The slider below shows another real example of how to find the circumference of a circle:

How to Find the Circumference of a Circle Using the Radius

The circumference of a circle can be found using the radius rather than the diameter.

The circumference of a circle, using the radius, is found using the formula:



In the formula, r is the radius of the circle. The image below shows what we mean by radius:



Read more about finding the circumference of a circle using the radius

Curriculum
Geometry Lessons
Interactive Test
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Here's a second test on finding the circumference of a circle.
Here's a third test on finding the circumference of a circle.
Note

What Is a Circle?

A circle is a shape containing a set of points that are all the same distance from a given point, its center.

Radius and Diameter

The radius of a circle is half the length of its diameter.

If you are given the radius of a circle, double it to find the diameter and put this in the formula.

Alternatively, use the formula containing radius.

What Is Pi?

π is the symbol for pi.

π is how many times longer a circle's circumference is than its diameter. It is the circumference divided by the diameter



π is the same for all circles, and is approximately equal to 3.14.

A Note on Units

The circumference of a circle is a length. Whatever the units of the diameter is, that is the units of the circumference.

If the diameter is in cm, the circumference is in cm. If it is inches, the circumference is in inches.