Polygon area calculator from coordinates
List the corners of a field, a lot or any region as latitude, longitude pairs, one per line, in order around the boundary. The calculator measures the area on the curved Earth and gives it in square metres, hectares, acres and square kilometres, together with the perimeter.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Walk around the boundary (on the map or on site) and write down each corner’s latitude and longitude.
- Paste them one per line, in order. Blank lines are ignored, and if the last line repeats the first corner it is dropped.
- Read the area in m², hectares, acres and km², and the perimeter.
How it works
Each edge is a great-circle arc between two corners. Together with the North Pole an edge forms a spherical triangle whose spherical excess is
E = 2·atan2(tan(Δλ/2)·(tan(φ₁/2) + tan(φ₂/2)), 1 + tan(φ₁/2)·tan(φ₂/2)),
where φ is latitude and Δλ the change in longitude. The signed excesses of all edges add up to the excess of the polygon, and area = |ΣE| × R², with R = 6,371,007.2 m, the radius of a sphere with the same surface area as the WGS84 ellipsoid. The perimeter is the sum of the great-circle (haversine) lengths of the edges on the same sphere.
Worked example
A square of 0.01° × 0.01° on the equator:
0, 0
0, 0.01
0.01, 0.01
0.01, 0
One hundredth of a degree on this sphere is 6,371,007.2 × π ÷ 180 ÷ 100 = 1,111.95 m, so the square is about 1,111.95² = 1,236,434 m². The calculator shows 1,236,434 m², 123.6434 ha, 305.529 acres and a perimeter of 4,447.8 m.
The sample in the box is four approximate corners of Central Park in New York; it comes out at 352.4323 ha (870.879 acres) with a perimeter of 9.97 km.
Tips
- More corners on curved edges give a better area: add points along a river bank or a curved road.
- Do not let the edges cross (a figure-eight shape): the parts would partly cancel out.
- Use at least five decimals of a degree (about 1 m); four decimals is only about 11 m.
- Very large polygons should stay smaller than half the globe.
Frequently asked questions
How do I get the coordinates of my plot?
In most map apps a long press or right-click on a spot shows its latitude and longitude; copy one corner at a time and paste each on its own line. A GPS receiver or phone app can also record corners on site. Keep the corners in order around the boundary, clockwise or anticlockwise.
Does the order of the corners matter?
Yes. The corners must follow the boundary. If you jump across the shape, the edges cross each other and the area is wrong. The direction does not matter – clockwise and anticlockwise give the same area.
How accurate is the area?
The math is exact on a sphere of the Earth's surface area. Next to a calculation on the WGS84 ellipsoid, the difference depends on latitude and is small next to typical GPS errors of a few metres per corner. For legal surveys use the official survey: this is an estimate.
Why not just multiply length by width?
For a small rectangle that works, but degrees of longitude shrink toward the poles (by the cosine of latitude), and large regions follow the curve of the Earth. The calculator handles both, so it works for a garden or for a whole county.
Can I paste coordinates with decimal commas?
On this page a point is read as 40.7681, -73.9819 or 40.7681 -73.9819. A semicolon always separates latitude and longitude, so 40,7681; -73,9819 works as well.