---
title: Finding Circumference of a Circle When Given the Area
---
## Background information

##### What is circumference?
  The length of enclosing boundary of a curved geometric figure.
<hr>

##### What is area?
  Area is measure of how much space there is on a flat surface.
  
### Question: Find circumference of circle when area of circle is given?
##### Steps:
+ area of circle = &pi; &times; r<sup>2</sup>, so we shall find radius of circle from with this formulae.
+ circumference of circle = 2 &times; &pi; r, and put radius in this formulae to calculate circumference.

<pre>
Example,
  Question) Find circumference of a circle with area = &pi;<sup>3</sup>?
  Answer: 
        By above steps,
              area = &pi; &times; r<sup>2</sup>
              &pi;<sup>3</sup> = &pi; &times; &pi;<sup>2</sup>
              by comparing, we get,
              radius, r = &pi;
        Now put this value in formulae for circumference,
              cirucumference = 2 &times; &pi; r
                             = 2 &times; &pi; &pi;
                             = 2 &pi;<sup>2</sup>
              Hence, we found the answer.
</pre>

### Area (A) of a Circle

A = π * radius<sup>2</sup>

### Circumference (C) of a Circle

C = 2 * π * radius

## To find the Circumference of a Circle given the area

1. Solve for the radius of the circle

    radius = (A / π)<sup>½</sup>

2. Input the radius into the formula for the circumference and solve. 

    C = 2 * π * (A / π)<sup>½</sup>

#### More Information:

[Area of a Circle](https://guide.freecodecamp.org/mathematics/area-of-a-circle)

### Here are some cool illustrations
#### Circumference
![Circle](https://www.mathplanet.com/Oldsite/media/55567/circle01.png)

#### Area
![Area of circle](http://www.mathwarehouse.com/animated-gifs/images/area-of-circle-through-triangles-area-demo_xl.gif)