Irregular Polygon Area Calculator

An irregular polygon has sides or angles that are not all equal, so a single rectangle or regular-polygon formula usually does not apply. When the coordinates of its vertices are known, the shoelace formula provides a direct and dependable way to find its area. The method works for triangles, quadrilaterals, and larger simple polygons, whether they are convex or concave. It is widely used in coordinate geometry, computer graphics, mapping, land measurement, architecture, and engineering. The shoelace formula processes each edge in boundary order. For every vertex, it multiplies the current x coordinate by the next y coordinate and subtracts the next x coordinate multiplied by the current y coordinate. The final vertex wraps back to the first, closing the polygon. Adding those cross-products produces a signed doubled area. Taking the absolute value and dividing by two gives the ordinary positive area, so clockwise and counterclockwise input orders return the same magnitude. Vertices must be listed consecutively as you move around the boundary. They should not be sorted independently by x or y, and the path should not jump across the interior. A self-intersecting sequence describes a crossed path, for which the signed regions may cancel and the result may not represent the filled area you intended. You do not need to repeat the first point at the end because the calculator automatically connects the last vertex back to the first. Coordinate units determine area units. If x and y are measured in meters, the answer is in square meters. If they are feet, the answer is in square feet. The calculator does not perform unit conversion because every coordinate should already use the same linear unit and scale. Decimal and negative coordinates are accepted, making the tool suitable for shapes positioned anywhere on a Cartesian plane rather than only in the first quadrant. For field surveying, ensure coordinates use a flat projected system appropriate to the site. Raw latitude and longitude lie on a curved Earth and should not be inserted as if they were ordinary planar distances, especially for large regions. Convert geographic positions to a suitable projected coordinate reference system first. For classroom geometry and small planar designs, simply record each corner in order, enter the pairs, and use the vertex count and computed area to check the shape.