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Circumference of Circle – Definition, Perimeter Formula, and Examples

Last Updated : 16 Feb, 2024
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Circumference of a Circle is defined as the boundary or the outer path covered by any circle. It is also called its perimeter. Let’s learn about how to find a circle’s circumference using formulas with the help of examples.

Example of circumference

Circumference of Circle Definition

Perimeter of a circle is the curve that runs along the edge of the circle. It is also called its circumference. It is indicated by the letter C and measured in cm, m, or km.

Terms Related to Circle

Here are some important terms related to circle :

Term Definition
Center A fixed point related to a circle such that all points on the boundary of the circle are equidistant from it.
Radius The distance from the center of the circle to any point on its circumference.
Chord A line segment joining any two points on the circumference of a circle.
Diameter A chord of the circle that passes through the center, also the longest chord of the 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,

Circumference of Semicircle Formula

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,

Area vs. Circumference

Area

Circumference

Area is the measure of space occupied by the boundry of any object.

Circumference is the measure of total boundary of the figure. It is also called perimeter in shapes other than circumfernce.

It is the measure in sq. units

It is measured in unit of length

Related :

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.

Practice Questions on Circumference of Circle

Q1. If the circumference of a wheel is 280 cm. Find its radius and diameter.

Q2. What is the circumference of a park if its radius is 42 cm?

Q3. If the radius of a circle is 91 cm find its circumference.

Q4. When the radius of a circle is 14 cm find its circumference.

FAQs on Circumference of Circle

What is Circumference of Circle? 

The perimeter of a circle is a curve that runs along the edge of the circle. In other words, the boundary of the circle is its circumference.

What is Value of Pi?

For general purpose calculations, we use the approximate value of π, which is 22/7 or 3.14, but as π is an irrational number, it has infinitely many digits in its expansion. The value of for the first 10 digits in the expansion after the decimal, is 3.1415926535. . .  

What is Difference between Perimeter and Circumference?

Difference between perimeter and circumference is that perimeter is a general word for all polygons and curves, while circumference is only used for the circle.

How to Calculate Diameter from Circumference?

Formula for circumference is C= diameter × π

What is Formula of Perimeter of Circle, if its Area is Given?

If the area of a circle is given, then the formula to calculate the perimeter or circumference of a circle is given by: C = 2√(πA) units.

What is Circumference of a Semicircle Formula? 

Formula for the circumference of a semicircle is C = (πr + 2r)

What is Circumference of Quadrant of a Circle? 

Quadrant of a circle is the sector of the circle whose sectorial angle is 90°. The perimeter of the quadrant of a circle is one-fourth of the circumference and 2 times the radius of a circle. 

What are Circumference Formulas?

Circumference Formula of a Circle are,

  • Circumference = 2π × Radius
  • Circumference = π × Diameter

How to Find the Circumference of Circle?

To find the circumference of a circle, we can use the formula,

Circumference = 2πr

How do you find Circumference of Circle with a Thread?

To find the circumference of a circle, you can use a simple method with a thread,

  • Step 1: Wrap a thread around the circle, marking the initial and final points.
  • Step 2: Measure the length of the thread with a ruler; this approximates the circumference.


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