Monte Carlo Pi Simulator
Watch Pi emerge from pure randomness: scatter random points inside a square and use the fraction that land inside a circle to estimate Pi.
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How the Monte Carlo Pi Simulator works
This is a classic Monte Carlo method: a square of side 2 has area 4, and the circle inscribed within it has area π. If you scatter points uniformly at random across the square, the fraction that land inside the circle approximates the ratio of the two areas — π divided by 4 — so multiplying that fraction by 4 gives an estimate of Pi that improves as you add more random points.
Beyond being a neat demonstration, Monte Carlo simulation — using repeated random sampling to estimate results for problems that are hard to solve directly — is a real technique used in finance, physics, and engineering, and this is one of the simplest, most visual examples of the method in action.
How to use it
Frequently asked questions
How accurate is the estimate?
It improves with sample size but never becomes exact; even with 20,000 points, expect the estimate to differ from true Pi by roughly plus or minus 0.02–0.05, since Monte Carlo error shrinks proportionally to the square root of the sample size.
Why do more points make it more accurate?
Monte Carlo error decreases proportionally to 1 divided by the square root of the number of samples, so quadrupling the points roughly halves the typical error.
What's the practical use of this technique?
The same principle — estimating an unknown quantity via repeated random sampling — underlies real-world Monte Carlo simulations in risk modelling, physics, and computational statistics.