Circle Area

Formula

r: The length of the radius of a circle

A: Area of the interior of the circle

Area of a Circle

π = 3.141 592 653 589 793 238 462 643 383 279 ...

For calculations, pi (π) is usually approximated by using a limited number of digits after the decimal point. To two decimal places, pi is approximately 3.14.


Explanation

To determine the formula for the area of the interior a circle, break up the circle into sectors and rearrange the sectors into a shape approximating a parallelogram.


As the number of sectors increases, the resulting "parallelogram" shape approaches that of a rectangle.


The area of the interior of a rectangle is the product of the length of the rectangle(l) and the width of the rectangle(w) [A = lw].

When the number of sectors is large:


Area of a Circle Formula