Circumference of a Circle

The circumference of a circle is the distance around the edge of the circle. It is like the perimeter of a square or rectangle. But for a circle, we call it the circumference. This concept is used in many parts of daily life. Knowing how to calculate the circumference is important.

1.0What Is the Circumference?

The circumference is the total length around the outer boundary of a circle. If you were to walk around a circular track once, the distance you walk is the circumference.

2.0Formula for Circumference

There is a simple formula for circumference to calculate the circumference of a circle. This formula uses π (pi) and either the diameter or radius of the circle. There are two common forms of the formula for circumference:

• C = π × d

(Where C is circumference and d is diameter)

• C = 2 × π × r

(Where r is the radius of the circle)

3.0Relation with Radius and Pi(π)

π (pi) is a special mathematical constant. It is approximately equal to 3.14159. Pi represents the ratio of the circumference of a circle to its diameter. That is:

π = Circumference ÷ Diameter

So, we can say:

Circumference = π × Diameter

Since the diameter is 2 × radius, we can also write:

Circumference = 2 × π × Radius

This shows the circumference’s relation with radius and pi very clearly.

4.0Circumference vs Diameter

Let’s now look at the circumference vs diameter comparison. These two are closely related. The diameter is the distance across the circle, passing through its centre.

Here is a table that shows the difference between circumference and diameter:

From the table, we can see how circumference and diameter are different but related. Both depend on the radius and are tied to the value of pi.

5.0Calculating Circumference

Now, let’s look at how we go about calculating circumference. The steps are simple. You just need the radius or the diameter and the value of π.

Let’s go through a few examples.

Example 1: Find the circumference of a circle with a diameter of 10 cm. 

Solutions: Using the formula:

C = π × d

C = 3.14 × 10

C = 31.4 cm

So, the circumference is 31.4 cm.

Example 2: Suppose the radius of a circle is 7 cm. Find its circumference.

Solution: Use the formula:

C = 2 × π × r

C = 2 × 3.14 × 7

C = 43.96 cm

So, the circumference is 43.96 cm.

Example 3: If the radius of a circle is 14 cm. what is the circumference?

Use the fraction 22/7 for π. 

Solution: C = 2 × π × r

C = 2 × (22/7) × 14

C = 88 cm

Here, the circumference is 88 cm.

6.0Real-Life Examples

Understanding circumference helps in daily activities. Let’s explore some real-life examples:

Bicycle Wheels

When you ride a bike, the wheels turn. The circumference of the wheel tells you how far the bike moves in one full turn. If the wheel has a diameter of 70 cm, then:

C = π × d = 3.14 × 70 = 219.8 cm

Every rotation moves the bike about 220 cm forward.

Circular Tracks

Running tracks or playgrounds often have circular areas. If a track has a radius of 20 meters, then:

C = 2 × π × r = 2 × 3.14 × 20 = 125.6 m

A runner covers 125.6 meters in one full lap.

Pots and Pans

The size of round pans and pots is measured across the top (diameter). If the pan’s diameter is 30 cm, then:

C = π × d = 3.14 × 30 = 94.2 cm

This is the edge length of the pan that touches the lid.

Fencing Around Circular Gardens

You may want to put a fence around a circular garden. Suppose the garden has a radius of 10 meters.

C = 2 × π × 10 = 62.8 m

So, you’ll need about 63 meters of fencing material.

Circular Tables

If a round table has a radius of 0.5 meters:

C = 2 × π × 0.5 = 3.14 m

That is the edge length around the tabletop.

7.0Why Learn About Circumference?

Learning the formula for circumference helps in:

• Measuring distances around circular areas
• Designing round objects
• Estimating materials like ribbons, wires, or pipes
• Solving geometry problems in school

It’s a practical skill in both daily life and academics.

8.0Practice Problems

Try calculating the circumference for the following:

1. A circle with a diameter of 15 cm.
2. A circle with a radius of 12 cm.
3. A round clock with a diameter of 25 cm.
4. A circular pool with a radius of 5 meters.
5. A coin with a radius of 1.5 cm.

The circumference of a circle is more than just a math concept. It connects math to the real world. Learning the circumference of a circle will help you solve many practical problems.