freeCodeCamp/guide/english/mathematics/finding-circumference-of-a-circle-when-given-the-area/index.md

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.

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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 = π × r², so we shall find radius of circle from with this formulae.
• circumference of circle = 2 × π r, and put radius in this formulae to calculate circumference.

Example,
  Question) Find circumference of a circle with area = π3?
  Answer: 
        By above steps,
              area = π × r2
              π3 = π × π2
              by comparing, we get,
              radius, r = π
        Now put this value in formulae for circumference,
              cirucumference = 2 × π r
                             = 2 × π π
                             = 2 π2
              Hence, we found the answer.

Area (A) of a Circle

A = π * radius²

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)^½

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

   C = 2 * π * (A / π)^½

More Information:

Area of a Circle

Here are some cool illustrations

Circumference

Area