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sci.pi-estimation-Monte-Carlo Calculator
Estimates π using Monte Carlo integration by counting random points (x,y) in the unit square that fall inside the quarter-circle x²+y² < 1: π ≈ 4×hits/N. Monte Carlo converges as N^(−0.5) — 10⁸ samples give ≈ 4 decimal places; it is best used to estimate multi-dimensional integrals, not π.
Inputs
N Samples
Count of items or occurrences.
Results
π estimate (Monte Carlo)
The value at the specified point or condition.
exact π
Reference formula or conversion factor shown for context.
absolute error
The difference between the computed result and the exact or true value — a measure of approximation accuracy.
relative error
The difference between the computed result and the exact or true value — a measure of approximation accuracy.
expected error ≈ 1/√n
The difference between the computed result and the exact or true value — a measure of approximation accuracy.