# 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

The source code related this visualization can be found in this Python Notebook. For more information, please follow me on Twitter.

If you liked what you just saw, it would be really helpful to subscribe to the mailing list below. You will not get spammed that's a promise! You will get updates for the newest blog posts and visualizations from time to time.

Updated: