Monte Carlo area

Edit the polygons or enter coordinates under Coordinates, then estimate. One x,y pair per line; separate polygons by a blank line. Comma, semicolon or whitespace separators are accepted. Consecutive duplicate points and a repeated closing point are normalized. Coordinates must be finite and within ±1,000,000; at most 32 polygons,256 points per polygon and 1024 total. New polygon starts a chain; click its first point to close. Drawing coordinates use a fixed 760× 380 logical view, not physical screen pixels.

Uniform pseudorandom points are sampled in the tight bounding rectangle. The estimate is rectangle area × hit fraction. A point in any polygon counts once, so overlaps are not added twice. Holes and self-crossing polygons are unsupported. The displayed drawing shows at most 4000 of the sampled points; all requested samples are used.

The 95% Wilson interval models the hit count as binomial under independent uniform sampling. It remains nonzero at all or no hits and is not a guarantee or a probability that this specific interval contains the area. A deterministic Seed reproduces a run;1000–250000 samples and Seed 0–4294967295. Larger samples usually reduce uncertainty but do not ensure smaller error in every run. Coordinates use arbitrary units, with area in units squared. Input or geometry changes cancel the old estimate; Cancel leaves no stale result. Shapes are not retained after navigation or reload.

NIST — Wilson