Polygon Area Calculator

How the Polygon Area Calculator works, and what it assumes

With geographic coordinates the area is computed geodesically, by spherical excess: the method of Chamberlain and Duquette, evaluated on a sphere with the WGS 84 authalic radius of 6,371,007.181 m. That radius is chosen deliberately. It is the radius of the sphere whose surface area equals the ellipsoid's, which is what you want for measuring area — the mean radius used for distance would give a slightly different and, for this purpose, wrong answer. The result lands within roughly 0.3 % of a true ellipsoidal area.

With projected coordinates the area is the shoelace formula applied to the numbers exactly as given, in the squared unit you declared. No earth model is involved, so the accuracy is whatever the projection's accuracy is over that extent: an equal-area projection such as EPSG:3035 or EPSG:5070 gives a figure you can rely on, while Web Mercator does not, because its scale error grows as 1/cos(latitude) and its areas are exaggerated by the square of that.

The two are never mixed. Selecting a projected option for coordinates that all sit inside the longitude and latitude range is reported as an error rather than answered, because an area computed from degrees as though they were metres is a plausible-looking number with no physical meaning, and nothing downstream would ever catch it. In both modes the first ring of each polygon is the outer boundary and every later ring is a hole, whose area is subtracted; every part of a MultiPolygon is summed.

Using the Polygon Area Calculator

• Measuring a site boundary, a field or a planning area digitised as a polygon.
• Checking an area column in a dataset that may have been computed in the wrong units.
• Converting between hectares and acres for a parcel whose geometry you already have.
• Confirming that holes in a multipart polygon are being subtracted rather than added.

A worked example

A one-degree square at the equator:

POLYGON ((0 0, 1 0, 1 1, 0 1, 0 0))

measured as geographic degrees gives:

Square metres      12,363,711,861
Square kilometres  12,364
Hectares           1,236,371
Acres              3,055,140

The same polygon measured with the planar option would give 1 — one square degree — which is not an area at all. Move the square to 60 degrees north and the geodesic answer falls to about 6,088 km², roughly half, because a degree of longitude there is half as long as it is at the equator. The shape on the page is identical; the ground it covers is not.

Where this comes up in GIS work

1. Paste a Polygon or MultiPolygon as WKT or GeoJSON, open a file, or select Load example.
2. Say what the coordinates are: geographic degrees on WGS 84, projected metres, or projected feet.
3. Select Calculate area, or press Ctrl + Enter (Cmd + Enter on a Mac).
4. Read the area in each unit and the statement of what was assumed underneath.
5. Select Copy beside a unit to put that value on the clipboard.

When the output looks wrong

These coordinates are outside the longitude and latitude range

They cannot be degrees, so the geodesic calculation would be meaningless. Choose the projected option that matches the unit the data is in, or reproject the geometry to WGS 84 first.

Every coordinate is inside the longitude and latitude range but a planar option is selected

The area is being computed as though degrees were a length, which produces a number with no physical meaning. This is flagged as an error rather than quietly returned, because such a figure looks perfectly plausible until someone acts on it.

A LineString or Point encloses no area

Only Polygon and MultiPolygon geometries have an area. A closed line string is still a line: convert it to a polygon first, which in WKT means wrapping its positions in a second pair of brackets.

The area differs from the figure in a desktop GIS

Expect a small difference. This tool measures on a sphere of the WGS 84 authalic radius, which is within roughly 0.3 % of an ellipsoidal area. Desktop software usually measures on the ellipsoid or in an equal-area projection, and neither is wrong.

Questions about the Polygon Area Calculator