Monte Carlo Pi Simulator

Estimate pi by random sampling inside a circle

Points

Monte Carlo Pi Formula

Area ratio	circle area / square area = pi / 4
Estimate	pi approx 4 x inside / total

How to Read the Simulation

Blue points land inside the circle.
Red points land outside the circle but inside the square.
The ratio of blue points to all points estimates pi / 4.
Increasing sample size usually reduces error, but randomness remains.

Example: if 785 out of 1000 points land inside the circle, pi is estimated as 4 x 785 / 1000 = 3.14.

Frequently Asked Questions

How does Monte Carlo estimate pi?▼

Random points are placed in a square containing a quarter circle. The fraction inside the circle is used to estimate pi.

Why does more sampling improve the estimate?▼

Larger random samples usually reduce random error and make the estimate more stable.

What is the formula for pi estimate?▼

The estimate is pi approximately equal to 4 times inside points divided by total points.

Is Monte Carlo exact?▼

No. It is a random approximation method, so estimates vary from run to run.

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