It’s Pi Day once again (14th March 2023), and this year, I thought I’d go back to basics and calculate pi using the humble circle. This circle will be more humbling than humble, however, as it will be entirely imaginary and rely on the user’s judgement.

The Theory

One fundamental fact about pi is that it relates the radius of a circle to its area (area = pi * r2). We can create a circle of known radius and approximate its area by counting how many randomly generated points are within it. From this, we can calculate pi with the re-arranged formula pi = area / sqrt(r).

The Twist

Computers are really good at checking whether points fall within a circle. It’s a simple calculation based on Pythagoras. But how good are humans? What about when they can’t see the circle? Let’s find out.

Imagine a circle filling the square below. Click on each of the points that you think are within that circle, turning them green. Then click Submit and repeat. The stats below will show the current approximation of pi, based on your points classifications. To see how well you’ve done, click View all to show all of your classified points and the actual circle.



Total points: -
Number "inside": -
Pi: -