Estimating Pi
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The classic classroom Monte Carlo: throw random darts at a square to estimate π
NOTEModel Overview
🎯 ESTIMATING PI
Classic Monte Carlo demonstration:
• Random points in unit square
• Check if inside quarter circle
• Mean × 4 ≈ π
More iterations = better estimate!
VARIABLEX Coordinate
uniform
Random x position (0 to 1)
x
VARIABLEY Coordinate
uniform
Random y position (0 to 1)
y
FORMULADistance²
x^2 + y^2
Squared distance from origin
x
y
dist_sq
FORMULAInside Circle
1 - ceil(max(0, dist_sq - 1))
1 if inside quarter circle (dist² ≤ 1), else 0
dist_sq
inside
FORMULAPi Estimate
inside * 4
Multiply by 4 to estimate π
inside
pi_est
OUTPUTπ Estimate
Mean converges to π ≈ 3.14159
About the creator
The team behind Carlo. We believe everyone deserves tools to reason about risk and uncertainty.
What is Carlo?
Carlo is a visual tool for Monte Carlo simulation. Model uncertainty by dragging probability distributions, connecting them visually, and running thousands of scenarios instantly.