Polygon area from coordinates.

Area of a polygon on the earth's surface

Treating latitude and longitude as flat x and y coordinates gives the wrong area, because a degree of longitude covers less ground away from the equator. This tool joins the points with great-circle edges and finds the area of the spherical polygon: by Girard's theorem the area is the spherical excess times R². It sums, edge by edge, the signed area between each great-circle edge and the equator, and takes the magnitude. NASA's JPL paper on polygons on a sphere covers the same problem of computing area directly on the sphere instead of through a map projection.

Worked example. The four corners (43, -80), (43, -79), (44, -79), (44, -80) enclose 8,969 km² (896,857 ha) with a perimeter of 384 km. Flat arithmetic would multiply 1° of latitude by 1° of longitude at one latitude and miss the narrowing of the box towards the north.

Edges are great-circle arcs, not straight lines on a map. For small sites the difference from map-straight edges is tiny, but for large areas it matters. Do not use this for legal property areas, which come from a survey. Enter the points in order around the edge, and do not make edges cross each other; a self-crossing outline gives a meaningless area.