Land Area from Coordinates Calculator
When you know the latitude and longitude of the corners of a parcel of land, you can estimate its area without walking the boundary. This tool projects the corner coordinates onto a local flat plane using an equirectangular projection centred on the plot, then applies the shoelace formula, which finds the area of any simple polygon from its vertex coordinates. Enter up to five corners in order around the boundary, in decimal degrees; leave unused corner pairs at zero only if you genuinely have fewer points (set both lat and lon of an unused corner equal to the previous corner, or use exactly the corners you have). The result is given in square metres, hectares, and acres.
Coordinate area formula
x = (lon - lon0) * 111,320 * cos(lat0) (metres east)
y = (lat - lat0) * 110,540 (metres north)
area = 0.5 * | sum over edges of (x_i * y_(i+1) - x_(i+1) * y_i) |
1 hectare = 10,000 m2; 1 acre = 4,046.8564224 m2
Each corner is converted from degrees to local metres east and north of a reference point using the length of a degree of latitude (about 110,540 metres) and of longitude (about 111,320 metres scaled by the cosine of the latitude, since meridians converge). The shoelace formula then sums the cross products of consecutive vertices and halves the absolute total to give the area. This planar approximation is accurate for small parcels where the Earth's curvature is negligible.
Worked example
A rectangular plot has corners at (40.0000, -105.0000), (40.0000, -104.9990), (40.0010, -104.9990), and (40.0010, -105.0000). The 0.0010 degree of longitude is about 0.0010 * 111,320 * cos(40 degrees) = 85.27 metres east, and 0.0010 degree of latitude is about 110.54 metres north. The shoelace area is about 85.27 * 110.54 = 9,426.69 square metres, which is 0.94 hectares or 2.33 acres.
Frequently asked questions
What is the shoelace formula?
The shoelace formula, or surveyor's formula, computes the area of any simple polygon from the coordinates of its vertices. It sums the cross products of each pair of consecutive vertices, takes half the absolute value, and gives the enclosed area. It works for any number of corners as long as they are listed in order around the boundary and the edges do not cross.
How accurate is the coordinate-based area?
For small parcels, up to a few square kilometres, the equirectangular projection introduces negligible error and the result is close to a proper geodesic area. Over large or high-latitude areas the flattening of the projection causes growing error, so a full geodesic calculation or a survey-grade method should be used instead.
In what order should I enter the corners?
List the corners sequentially around the boundary, either all clockwise or all counter-clockwise. The shoelace formula uses the absolute value, so either direction gives a positive area. Do not jump across the parcel between corners, because crossed edges produce a self-intersecting polygon and an incorrect area.
Can I use fewer than four corners?
The polygon needs at least three distinct corners to enclose an area. If your parcel is a triangle, enter three real corners and set the fourth equal to the third (a repeated point adds no area). For more complex shapes than this four-corner tool supports, a dedicated GIS package or a licensed survey is the right approach.
Official sources
- NOAA National Geodetic Survey: geodetic area computations.
- U.S. Geological Survey: coordinate systems and mapping.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.