Polygon Land Area Calculator
The polygon land area calculator uses the Shoelace formula (also known as the Gauss area formula or surveyor's formula) to compute the area of any polygon defined by a list of coordinate pairs. Enter your X,Y vertices one per line in the format "X,Y" and the calculator returns the enclosed area in square units. This is the standard method used in land surveying to calculate parcel areas from traverse coordinates. Use projected coordinates (UTM, state plane, or local grid) in meters or feet for real-world area results.
Shoelace formula
Area = (1/2) * |sum(x(i)*y(i+1) - x(i+1)*y(i))|
where the last vertex connects back to the first vertex.
The formula is exact for any simple (non-self-intersecting) polygon and requires no assumptions about shape. It is used directly in surveying software and GIS systems to compute parcel areas from traverse data.
Converting area to acres or hectares
- If coordinates are in meters: divide by 4,046.86 for acres, or by 10,000 for hectares.
- If coordinates are in feet: divide by 43,560 for acres.
- Vertices must be entered in order (either clockwise or counterclockwise) around the polygon perimeter.
- For geographic parcels, use UTM or state plane coordinates instead of lat/lon to get correct area results.
Polygon land area calculator: frequently asked questions
What is the Shoelace formula?
The Shoelace formula (also called the Gauss area formula or surveyor's formula) computes the area of a polygon from its vertex coordinates. It sums products of consecutive x and y coordinates in a specific cross-multiplication pattern, giving the signed area. Taking the absolute value yields the actual area.
What coordinate units should I use?
The result is in the square of whatever unit your coordinates are in. If you enter coordinates in feet, the area is in square feet. If in meters, the area is in square meters. For geographic lat/lon coordinates, you need to convert to a local projected coordinate system (such as UTM) first for meaningful area results.
How many vertices can I enter?
Enter as many coordinate pairs as your polygon has vertices. The polygon can be any simple (non-self-intersecting) shape: triangles, rectangles, irregular parcels, and complex outlines all work. Enter vertices in order (clockwise or counterclockwise).
Does the polygon need to be closed?
No. The calculator automatically connects the last vertex back to the first, so you do not need to repeat the starting coordinate at the end of your list.
Can I calculate acreage from UTM coordinates?
Yes. Enter UTM easting/northing pairs in meters. The Shoelace formula returns area in square meters. Divide by 4,046.86 to convert to acres, or divide by 10,000 to get hectares.
Official sources
- USGS: USGS mapping and surveying references.
- NOAA National Geodetic Survey: NGS coordinate systems and geodesy.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.