Area from Coordinates Calculator

The shoelace formula (also called Gauss's area formula) computes a polygon's area from nothing but its vertex coordinates, by summing cross-products around the boundary and taking half the absolute value — no trigonometry and no need to decompose the shape into triangles by hand. Number of Vertices is a select limited to 4, 5, or 6 points; it is not an open-ended "add as many corners as you like" tool, so a genuinely irregular parcel with more than six corners needs to be split into sub-polygons first. Every coordinate pair beyond the fourth is conditionally shown — X5/Y5 only appear once Number of Vertices is set to 5, and X6/Y6 only once it's set to 6 — but they are still real inputs that feed directly into the same shoelace sum, not separate calculations.

Centroid X and Centroid Y use a different, area- weighted formula (not a simple average of the vertex coordinates), so the reported centroid can sit closer to whichever side of the polygon encloses more area. Compactness Ratio compares the shape to a circle of the same perimeter (a value of 1 would be a perfect circle); the default 500-by-400 rectangle comes out around 0.78, and long, thin, or highly irregular parcels will read noticeably lower. This calculator assumes coordinates are already in one consistent, planar system — it does not project, convert datums, or check for self-intersecting boundaries.