Maps and geodesy
Polygon area on the ellipsoid from coordinates
Paste latitude/longitude points, GeoJSON or WKT and get the area and perimeter of the polygon on the WGS84 ellipsoid, in km², hectares, acres and square miles.
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Showing the worked example. Results update as you type.
Result
- Edges are geodesics (shortest paths on the ellipsoid) joining the points in the order given, closing back to the first point. The smaller of the two regions the boundary divides the Earth into is reported, whichever direction the points run.
Method and limits
The polygon’s edges are geodesics joining the points in order and back to the first. Its area on the WGS84 ellipsoid is computed with Karney’s method, which sums, edge by edge, the exact area between the geodesic and the equator using a series accurate to a fraction of a square millimetre per edge, and handles polygons that cross the antimeridian or enclose a pole. The perimeter is the sum of the geodesic edge lengths.
For comparison the same polygon is measured on a sphere with the WGS84 ellipsoid’s surface area (authalic radius 6,371.007 km); the difference shows the error of a spherical approximation.
Worked example (GeographicLib documentation): the 18-point outline of Antarctica shown above has a perimeter of 16,831,067.893 m and an area of 13,662,703,680,020.1 m², about 13.66 million km².
Limits
Edges are geodesics: a boundary drawn on a web map as straight lines in Web Mercator follows different paths, which matters for long edges. Self-intersecting outlines give a net signed area that is not meaningful. Height and terrain are ignored, as in land registers.
References
Related tools
- Coordinate converter: decimal degrees, DMS, UTM and MGRSConvert WGS84 coordinates between decimal degrees, degrees-minutes-seconds, degrees and decimal minutes, UTM and MGRS, with grid convergence and scale factor.
- Distance and bearing between two coordinatesGeodesic distance, initial and final bearing and midpoint between two latitude/longitude points on the WGS84 ellipsoid, with the haversine great-circle result for comparison.
- Destination point from bearing and distanceFind where you arrive after travelling a distance on an initial bearing from a start point, on the WGS84 ellipsoid, with the final bearing and the spherical answer for comparison.