Land area from coordinates
Area and perimeter of an irregular plot from vertex coordinates (shoelace formula).
Enter vertices in order (clockwise or counter-clockwise). At least 3.
Enter at least 3 vertices – area and perimeter update instantly.
How to calculate the area of an irregular plot
A plot is rarely a perfect rectangle. When you know the coordinates of its corners (say, from a survey or a cadastral map), you can compute the area with the Gauss (shoelace) formula, named after the cross-multiplication pattern that resembles lacing a shoe:
S = ½ · |Σ (xᵢ · yᵢ₊₁ − xᵢ₊₁ · yᵢ)|
You sum over all vertices going around (the last connects back to the first). The perimeter is simply the sum of the lengths of all sides (distances between neighbouring vertices). The calculator computes both and draws the plot at the same time.
Where to get the coordinates
You can find corner coordinates in a survey plan, a land-registry extract, or by measuring them in a mapping app. It does not matter whether you enter the vertices clockwise or counter-clockwise – the formula takes the absolute value, so the area always comes out positive.
What to watch out for
The vertices must be entered in order along the boundary of the plot – not shuffled, otherwise the boundary would cross itself and the area would be meaningless. For an accurate result, use the same units for all coordinates (ideally meters, so the area comes out in m²).
Tip: to convert to ares and hectares – 1 are = 100 m², 1 hectare = 10,000 m².