Pi (π)

Pi (π) is a mathematical constant defined as the ratio of a circle's circumference to its diameter — approximately 3.14159. It appears throughout mathematics and physics, and shows up any time something is round: engineering, signal processing, statistics, you name it.

Pi is irrational — its decimal expansion never ends and never repeats — so it can only ever be approximated. Below is one way to estimate it yourself, plus as many digits as you'd like to browse.

π = Circumference ÷ Diameter

Some of the ways mathematicians have calculated Pi:

1. Measuring real circles directly (circumference ÷ diameter)
2. Approximating a circle with regular polygons of increasing sides
3. Summing infinite series that converge to π
4. The Monte Carlo method — see below

Scatter random points inside a square that circumscribes a circle of radius 1. The fraction of points that land inside the circle, times 4, estimates π — because the circle's area (πr²) is π/4 of the square's. Move your mouse over the diagram to re-roll the points and watch the running estimate improve.