Paste the boundary coordinates of a parcel — one vertex per line, in decimal degrees or DMS — and this land area calculator returns the ground area in square metres, hectares, acres, square feet and square miles, together with the perimeter, the centroid and the number of vertices. It works for any number of corners from three upwards.
Accepted formats: 39.906111, 116.3974 ·
39.906111 116.3974 ·
N 39 54 22, E 116 23 50. Separate the latitude from the longitude with a comma
(or a single space for plain decimal pairs). Blank lines and lines starting with
# are ignored. Do not repeat the first vertex at the end.
Every vertex that was read, so you can spot a typo before trusting the area.
| # | Latitude | Longitude | Leg length (m) |
|---|
The area of a polygon is computed with the shoelace formula, which sums the cross products of consecutive vertices. That formula only works on a flat plane, so the coordinates are first projected onto a local horizontal plane centred on the parcel's own centroid. Northings on that plane come from the true meridian arc of the WGS84 ellipsoid and eastings from the local radius of the parallel, which means the plane carries ground distances rather than grid distances distorted by a map projection.
Because the projection is built around the centroid, the result meets the ground area for parcels of ordinary size without any correction: tests against a known one-acre square agree to within a fraction of a square metre. Accuracy decreases as a parcel grows, because the local plane is a tangent approximation. As a rule of thumb the method is reliable to better than 0.01 % for extents up to about 20 km across; beyond that, use a projected coordinate reference system with a declared scale factor and compute the area in that system instead.
The perimeter is not taken from the plane at all — each leg is measured as a geodesic distance on the ellipsoid, so the perimeter figure is independent of the area approximation.
An acre is not a shape, it is a fixed area: 43,560 square feet, or 4,046.8564224 square metres. To calculate acres from coordinates, work out the ground area of the boundary first and then divide by that constant — the acreage is simply the square-metre result divided by 4,046.86. This converter performs the division for you and reports the acre figure next to the metric result, so no separate step is needed.
Two cautions are worth remembering. An acre is a unit of area, so an "acre" quoted as a side length or a frontage is a mistake; and acreage computed from latitude and longitude is ground acreage, which is what a deed or a valuation normally means. If the coordinates came from a projected map with a scale factor away from 1, the raw grid area will differ slightly from the ground area — for a parcel of ordinary size that difference is far below survey tolerance, but for a large holding it is worth computing in the projected system instead.
The same 43,560 square foot constant explains why a square parcel of exactly one acre measures about 208.71 ft on each side: multiply the side by itself and you are back to 43,560 sq ft.
Area from coordinates is the standard calculation for parcels, plots, easements and any boundary that has been surveyed or digitised:
List the boundary vertices in order, one pair of latitude and longitude per line, and read the area from the results. The vertices are projected onto a local plane centred on the parcel, the shoelace formula gives the area in square metres, and the result is also reported in hectares, acres, square feet and square miles.
Enter the boundary coordinates as usual and read the "Area (acres)" row. Internally the converter computes the ground area in square metres from the shoelace formula and divides by 4,046.8564224, the number of square metres in one acre, so you never have to do the conversion by hand. One acre is also 43,560 square feet, which is why a square parcel of one acre is about 208.71 ft on each side.
Square metres, hectares, acres, square feet and square miles, all at once. One hectare is 10,000 square metres, one acre is 4,046.8564224 square metres, and one square mile is 2.589988 square kilometres.
They must follow the boundary in sequence, either clockwise or anticlockwise, but the direction does not matter: the result is identical either way. What does matter is that the order is the order of the boundary. If the vertices are listed in a random order you will get a self-crossing shape and an area that is too large. The tool shows every vertex it read in the check table so you can spot a mistake.
For parcels up to a few kilometres across the result agrees with the ground area to better than 0.01 percent, because the coordinates are projected onto a local plane built around the parcel centroid rather than onto a map projection with a varying scale factor. For very large areas — tens of kilometres across — the local plane approximation loses accuracy and a projected coordinate system should be used instead. The tool warns you when the extent grows that large.
No. The closing leg back to the first vertex is added automatically. If you do repeat the first vertex, the duplicate point adds a zero-length edge and can distort the result, so remove it.
Yes, the calculation is purely geometric and works anywhere on the WGS84 ellipsoid. The values you enter should be in WGS84 coordinates, which is what GPS and most modern mapping produces. If your coordinates come from an older local datum the area will still be close, but for a legal or contractual figure convert to a common datum first.
Calculations run locally in your browser. Verify critical values against your project's coordinate reference system and specification before use in the field. About · Privacy & cookies · Terms of use · Developers