##### How to

# How to Calculate Circumference of Circle

## Here we will be looking at how to calculate the perimeter or the circumference of the circle.

A circle is a simple closed shape. The mathematical definition of circle is ‘it is a set of all points in a plane which are at a constant given distance (radius) from a given point (center)’. Explained using conic sections, ‘a circle is a conic section obtained by the intersection of a cone with a plane perpendicular to the cone’s symmetry axis’. Circle is a two- dimensional figure having no edge and no vertex. So as any regular two- dimensional closed figure, it has two main properties i.e. it has a perimeter and an area.

Here we will be looking at how to calculate the perimeter or the circumference of the circle. Let’s first look through the basic terminology.

- Perimeter or circumference is the continuous line forming the boundary of closed geometrical figure
- Area is the quantity that expresses the extent of a two- dimensional figure or shape in the plane.
- The center of circle is a point which is equidistant from the points on the edge of the circle.
- The radius of a circle is the distance from the center point to the point on the circle. Since, circle has radial symmetry, the distance is same of a circle.
- The straight line passing from one side to the other through the center of the circle is called the diameter.
- The number pi or ? is a mathematical constant used to calculate the circumference and the area of the circle. Being an irrational number, ? cannot be expressed as an exact numerical form but it is usually generalized as 3.14 or 22/7 for calculation purposes.

## Before the formula were created, there were other ways to calculate the circumference of the circle.

For instance, a string was used to go along the continuous boundary of the circle and it was straighten to check the perimeter it covers.

## Here, we will talk about three formulas of calculating the circumference of a circle

**When the radius is given-**

The formula used when the radius of a circle is given is:

- C=2?r

Here, C is the circumference and r is the radius given.

**Let’s learn this using an example-**

- Calculate the circumference of circle with radius 14cm

**Solution –** here, the radius given is, r = 14 cm

- C=2?r
- C= 2?14
- C= 2(22/7)(14) or 2(3.14)(14)
- C= 88 cm

Hence, the circumference of the circle is 88 cm.

## When the diameter is given-

The formula used when the diameter of a circle is given is-

- C=?d

Here, C is the circumference of the circle and d is the given diameter of the circle.

**Let’s learn this using simple problem-**

- Calculate the circumference of the circle of diameter 14 cm.

**Solution-** here, diameter given is, d = 14 cm

- C=?d
- C=?14
- C= 22/7(14) or 3.14(14)
- C= 44 cm

Hence, the circumference of the circle is 44 cm.

## When the area of the circle is given-

This formula might look a bit complicated, but it isn’t. The formula used when the area of the circle is given is-

- C= 2 ? ? A

Here, C is the circumference of the circle and A is the given area of the circle.

**Let’s learn this using simple problem-**

- Calculate the circumference of the circle of area 14 cm

**Solution-** here, area given is, A = 14 cm

- C= 2 ? ? A
- C= 2 ? ? (14)
- C= 2 ? (22/7)(14) or C= 2 ? (3.14)(14)
- C= 13.26 cm

Hence, the circumference of the circle is 13.26 cm