Monte Carlo π Estimation Screensaver
The Monte Carlo π Estimation screensaver scatters real random points into a square, using the fraction landing inside its circle to converge on a genuine running estimate of π. It is free, runs in your browser, and ESC exits.
How the Monte Carlo π Estimation screensaver works
The saver drops a real random point into a square every frame, checking whether it also falls inside the circle inscribed within that square.
The real running ratio of points-inside-circle to total-points-thrown is multiplied by four, which converges toward the true value of π.
A live readout tracks this real estimate and its error against the true value of π as more random points accumulate.
Once a large sample size is reached, it holds briefly to show the final estimate, then a fresh run starts scattering points from zero.
A worked example
After just a few hundred real random points, the estimate is often noticeably off; by tens of thousands of points, it genuinely settles in close to 3.14159, exactly as the real law of large numbers predicts.
Settings & tips
- Accent recolours points that land inside the circle.
- The random points and running estimate are real, not scripted.
- A fresh run starts automatically once the sample size target is reached.
Frequently asked questions
- Is this really estimating π?
- Yes — a real Monte Carlo method; the ratio of points inside the circle to the total genuinely converges toward π.
- Why does the estimate wobble early on?
- With few real random samples, chance causes real variance; the estimate only settles down as the sample size grows large.
- Is a key needed?
- No — it is a pure local computation.
- Is it free?
- Yes — free, no download, in your browser.