Circumference of Circle – Definition, Perimeter Formula, and Examples

The circumference of a circle is the distance around its boundary, much like the perimeter of any other shape. It is a key concept in geometry, particularly when dealing with circles in real-world applications such as measuring the distance traveled by wheels or calculating the boundary of round objects.

To calculate the circumference of a circle, we use simple formulas that involve the circle’s radius or diameter.

Here are some important terms related to circle :

Circumference of Circle Formula

The circumference of a circle is equal to the length of its boundary, but the circle is a curved shape, its circumference can’t be measured with a ruler. The correct way to find the perimeter of a circle is to calculate it using the formula C = 2π × r. If the diameter or radius of a circle is known circumference of the circle can be easily calculated. 

Circumference to Diameter

The ratio of Circumference to the Diameter of a circle is always a constant and that is π. Using this fact we can calculate the formula for circumference.

Circumference/Diameter = π
Circumference = π×Diameter

Circumference to Radius

As the Diameter of a circle is two times the circle’s radius, the ratio of Circumference to the radius of a circle is also always a constant, which is 2π. Using this fact we can also calculate the formula for the circumference.

Circumference/Radius =2π
Circumference = 2π×Radius

How to Find Circumference of Circle?

Perimeter of a circle is found using any of the two approach added below,

Approach 1: Due to its curved nature, directly measuring the length of a circle with a ruler or scale isn’t feasible as it is for polygons like squares, triangles, and rectangles. However, you can determine the circumference of a circle using a thread. By tracing the circle’s path with the thread and marking points along it, you can measure this length using a standard ruler.

Approach 2: A precise method to ascertain a circle’s circumference involves calculation. To do this, the circle’s radius must be known. The radius of a circle is the distance from its center to any point on its circumference. In the illustration below, a circle with radius R and center O is depicted. The diameter, twice the radius of the circle, is also shown.How to Find the Circumference of a Circle?

Circumference of Semicircle

Semicircle is the half of the circle and its image is added below,

Semi circle 

If a circle is split into two equal parts it is called a semi-circle. The circumference of a Circle is defined as the overall length of its boundary, which is given by :

Circumference of Semi – Circle = πr + d

Where,

• r is Radius of Circle
• d is Diameter of Circle

Area of Semicircle

Area of a semi-circle is calculated by taking half of the area of the circle. i.e. the area of a semi-circle is ½ × the area of a circle. Formula for area of semi circle is given by :

Area of semi – circle =  ½ × πr²

where, r is Radius of Circle

Area of Circle Formula

Area enclosed by the circumference of a circle is known as the Area of a Circle. In other words, all the area inside the boundary of the circle is considered its area and it is calculated using the formula,

A = πr²

Where,

• r is Radius of Circle
• π is Constant (π = 22/7 or 3.14)

Difference Between Circumference and Area

The differences between Area and Circumfernce between of a circle is added in the table below,

Related :

• Radius of Circle
• Segment of a Circle
• Equation of a Circle
• What is a Circle?
• Area of a Circle
• Sector of a Circle

Solved Examples on Circumference of Circle

Some examples on Circumference of a circle are,

Example 1: What is the circumference of a circle with a diameter of 2 cm?

Solution:

Given, diameter = 2 cm

By using formula of circumference of a circle,

C = π × d
C = 3.14 × 2
C = 6.28 cm

Example 2: What is the circumference of a circle with a radius of 3 cm?

Solution: 

Given, radius = 3 cm

C = 2 × π × r 
C = 2 × 3.14 × 3
C = 18.84 cm

Example 3: What is the circumference of a circle with a diameter of 14cm?

Solution: 

Given, diameter = 14 cm

C = π × d
C = 3.14 × 14
C = 43.96 cm.

Example 4: What is the circumference of a circle with a radius of 10 cm?

Solution:

Given, radius = 10 cm

C = π × 2r 
C = 3.14 × 2(10)
C = 62.8 cm.

Practical Applications of the Circumference of a Circle

The concept of circumference extends far beyond academic problems. In the real world, calculating the circumference helps in:

• Wheels and Gears: To determine how far a wheel or gear moves in one full rotation, we calculate the circumference. This is critical in automotive design, bike manufacturing, and machinery.
• Astronomy: Scientists often calculate the circumference of planets to better understand their size and rotation. For example, the Earth’s circumference is approximately 40,075 kilometers at the equator.
• Construction and Engineering: When building structures such as circular columns, pools, or roundabouts, the circumference is necessary for calculating material usage.

Understanding the circumference is not only a key math concept but also a practical tool in various industries.

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