pi estimation

Inside Circle

Outside Circle

Speed: 1

Statistics

π Approximation: 0.00000000

Actual π: 3.14159265

Total Points: 0

Inside Circle: 0

Accuracy: 0.00%

Error: 0.00000000

How It Works

The Monte Carlo method uses random sampling to solve mathematical problems. Here, we generate random points in a square and count how many fall inside the inscribed circle

π ≈ 4 * (points inside circle / total points)

As we add more points, our approximation converges to the true value of π. The relationship between the areas of the circle (πr²) and square (4r²) gives us the factor of 4 in our formula

Convergence: The error decreases proportionally to 1/√N, where N is the number of points sampled.