Circle - Area f(Circumference)

The Area of a Circle from the Circumference calculator computes the area of a circle (A)  based on the circle's circumference (c).

INSTRUCTIONS: Choose units and enter the following:

• (c)  Circumference or perimeter of the circle

Area from Circumference (A): The calculator returns the area in square meters.  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

A circle is the set of all points equal in distance from a center point.  This formula uses a form of the equation for the area of a circle to compute the circumference.  

`A = pi * r^2` .  Therefore we know that `r =  sqrt(A/pi)`.  We also know that circumference of a circle is a function of the radius (`c = 2 pi r`), therefore:

     `A =  pi * (c/(2pi))^2`

Uses

If you want to know the area enclosed in a circular fence, this formula will let you walk and measure the circumference and determine the area.