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.
Live preview
Press ESC to leave fullscreen. Settings are saved in your browser only.
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.