Area and perimeter of a polygon from coordinates (UTM or lat/long)
Paste the polygon vertices in traverse order and get the area (m², hectares, acres, square feet), the perimeter and the azimuth and length of every side, with a drawing of the parcel. No need to repeat the first point at the end.
Accepts E N or name E N (separated by spaces, tabs or semicolons). Pasting from Excel or CAD works.
Latitude and longitude in decimal degrees or degrees/minutes/seconds (without a letter, positive = North/East). The area is computed on the UTM grid of the zone at the center of the polygon (or of the zone you choose).
Result
Paste at least 3 vertices above.
How the area is calculated
We use the coordinate (shoelace) formula, also known as Gauss’s area formula: 2·Area = Σ (Ei·Ni+1 − Ei+1·Ni). It is exact for any simple polygon (no sides crossing each other), convex or not.
The UTM area is the area on the projection (grid) plane. Because UTM distorts distances (scale factor k) and the ground lies above the ellipsoid, the true area on the ground is slightly different. When you enter the average elevation, we also show the ground area on a local plane: Aground ≈ AUTM ÷ k² × ((R + h) ÷ R)². It is the same grid-to-ground idea as the combined scale factor surveyors use to turn grid distances into ground distances.
- 1 hectare = 10,000 m² ≈ 2.4711 acres · 1 km² = 100 ha
- 1 acre (international) = 43,560 ft² = 4,046.86 m² (0.4047 ha) · 1 square mile = 640 acres ≈ 259 ha
FAQ
Why does this area differ from the one in my GIS or on the official record?
Each area refers to a different surface. The UTM (grid) area is on the projection plane; GIS software often reports the geodesic area on the ellipsoid; a ground survey measures at ground level. With the average elevation entered, the “ground area” here comes very close to a ground survey, but it is not identical, because a rigorous computation uses the elevation of each vertex. The grid area can differ from the others by a few tenths of a percent. For legal documents, the figure on the official survey or record always prevails.
Do I need to repeat the first vertex at the end?
No. If you do, the calculator notices and ignores the repeated point. The polygon is always closed from the last vertex back to the first.
Does the order of the vertices matter?
Yes: the vertices must follow the boundary in order (clockwise or counterclockwise, either works). Out of order, the sides cross each other and the area comes out wrong. The calculator warns you when it finds crossing sides.
How big is an acre?
The international acre is exactly 4,046.8564224 m² (43,560 square feet, about 0.4047 ha); one hectare is about 2.4711 acres. The US survey acre, based on the US survey foot (deprecated since the end of 2022), is about 4 parts per million larger. Many countries also have traditional local units, so in documents always state the unit — or use hectares or square meters.
Can I calculate the area of a parcel that straddles two UTM zones?
Yes: choose a single zone for all the vertices (extended zone). In latitude/longitude mode with the automatic zone, the calculator already uses the zone at the center of the polygon for all of them.