Polygon Area from Coordinates Calculator
To measure the area enclosed by a set of map points, you need a formula that respects the curvature of the Earth, not a flat shoelace sum. This calculator takes a list of latitude and longitude vertices in decimal degrees, one per line, and applies the spherical polygon area formula on a sphere of mean radius 6,371,008.8 meters. It closes the ring automatically and returns the enclosed area in square meters, square kilometers, acres and hectares. Useful for land parcels, paddocks, lakes, and project footprints.
Spherical polygon area formula
For each edge i to i+1 (longitudes in radians):
sum += (lon[i+1] - lon[i]) * (2 + sin(lat[i]) + sin(lat[i+1]))
Area = abs(sum * R^2 / 2), R = 6,371,008.8 m
1 acre = 4,046.8564224 m^2; 1 hectare = 10,000 m^2
This is the standard spherical excess area used in GIS libraries. The ring is closed by wrapping the last vertex back to the first.
Polygon area context
- List vertices in order around the boundary; the ring is closed automatically.
- Winding direction does not matter; the absolute area is reported.
- Coordinates are decimal degrees, north and east positive.
- Areas use exact unit factors: 1 acre is 4,046.8564224 square meters.
- Very large or survey-grade polygons need an ellipsoidal geodesic area method.
Polygon area: frequently asked questions
How is the area of a polygon found from latitude and longitude?
This calculator uses the spherical polygon area formula. For each edge it accumulates the product of the longitude difference and the sine of the average latitude, multiplies by the square of the Earth radius, and halves the absolute value. The result is the geodesic surface area enclosed by the vertices.
What format should the coordinate list use?
Enter one vertex per line as latitude then longitude, separated by a comma or space, in decimal degrees. List the vertices in order around the boundary. You do not need to repeat the first vertex at the end; the calculator closes the ring automatically.
Does the winding direction matter?
No. The calculator takes the absolute value of the signed area, so clockwise and counterclockwise orderings give the same positive area. The vertices must, however, be listed in sequence around the perimeter rather than in random order.
What Earth radius is used?
The mean spherical Earth radius of 6,371,008.8 meters (the IUGG mean radius) is used. The area is reported in square meters, square kilometers, acres and hectares using exact unit conversions.
How accurate is the spherical area?
For small to medium polygons the spherical formula is accurate to a fraction of a percent. Very large polygons spanning many degrees, or high-precision survey work, are better served by an ellipsoidal geodesic area algorithm.
Official sources
- U.S. Geological Survey: U.S. Geological Survey.
- NIST: Fundamental physical constants and units.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.