Polygon Area Calculator from Coordinates

Calculating land area from GPS coordinates requires more than simple geometry. Because the Earth is not flat, using a flat Euclidean formula on lat/lon degrees produces errors that grow with polygon size. A 1-hectare field near the equator and a 1-hectare field at 60°N latitude span very different longitudinal distances even though their areas are identical.

This calculator uses the spherical excess formula — the same algorithm used by Turf.js and OpenLayers — which accounts for the curvature of the Earth. It treats the Earth as a sphere with the WGS84 semi-major axis (6,378,137 m) and sums the spherical angle contributions of each edge. The result is accurate to within 0.3% for polygons up to continental scale.

To use it: collect the latitude and longitude of each boundary corner of your land parcel in order (clockwise or counter-clockwise — the formula returns the absolute value). Enter them as decimal degrees, or paste them directly from Google Earth, QGIS, or a GPS unit.

The spherical excess formula computes the area of a polygon projected onto a sphere. For each vertex i in the polygon, the contribution is:

After summing all vertices (with the index wrapping around), the area in square metres is:

The absolute value ensures a positive result regardless of whether vertices are listed clockwise or counter-clockwise. This is the same formula used by Turf.js, a widely-used open-source GIS library, making results comparable across platforms.

For very large polygons spanning more than a few degrees of latitude, a more accurate approach would use the WGS84 ellipsoid rather than a sphere, but for parcels up to 10,000 km² the spherical approximation introduces an error of less than 0.1%.

The accuracy of this calculator depends entirely on the accuracy of your input coordinates, not the formula. The spherical excess algorithm is mathematically exact for a spherical Earth — the only approximation is that the Earth is not a perfect sphere (it is an oblate spheroid with a 0.3% polar flattening).

A standard consumer-grade GPS (phone or handheld unit) has a typical accuracy of 3–5 metres. For a 1-hectare field with a 400-metre perimeter, a 5-metre coordinate error translates to roughly a 1–2% area error. Survey-grade GNSS receivers with RTK correction achieve centimetre accuracy, reducing the area error to less than 0.01%.

Practical recommendations:

• Walk the boundary with a GPS unit or phone, recording waypoints at each corner.
• For large, irregular parcels, add extra waypoints along curved sections.
• Average multiple GPS readings at the same corner to reduce noise.
• Compare your result with the land registry or cadastral area as a sanity check.

Land area calculation from coordinates is one of the most common tasks across multiple disciplines. Farmers use it to calculate seed rates, fertiliser quantities, and subsidy applications — the EU Common Agricultural Policy (CAP) payment is calculated per hectare, making accurate boundary measurement a financial requirement. A 2% error on a 200-hectare farm can mean thousands of euros in incorrect payments.

Land surveyors use polygon area to verify cadastral records, compute easement areas, and generate subdivision plans. Urban planners calculate plot ratios, floor area ratios (FAR), and green space percentages from polygon extents. Environmental scientists use it to measure deforestation extents, wetland coverage, and habitat patch sizes from satellite imagery.

Google Earth Pro has a built-in polygon area tool, but it requires the desktop application and saves data to KML files. This calculator lets you paste raw coordinates from any source — GPS exports, QGIS, ArcGIS attribute tables, or plain text — and instantly get all standard area units without any GIS software.