# Calculation of the Circle’s Area Explained Visually

Have you asked why we calculate the area of a circle with radius $$R$$ as $$\pi R^{2}$$? There is a good reason behind it. We can tackle this problem from an integration point of view.

So, first things first. We split our circle in $$N \in \mathbb{N}$$ rings and calculate the total area as a sum of the rings' areas. For a large $$N$$, these rings will start resembling like rectangles with sides $$dr$$ and $$2\pi r$$. Now, we can translate the problem to integrating the function $$2\pi rdr$$ on the interval $$[0, R]$$. This principle is illustrated in the animation below by using Matplotlib's Animation API:

Animation: Numerically calculate the area of a circle