Paste the list of vertex coordinates — from a survey, a cadastral record, Excel or a traverse sheet. The calculator computes the area with the shoelace formula and a check formula, the perimeter and side lengths, plots the parcel and warns about crossing boundaries.
Area from coordinates
When the rectangular coordinates of all vertices are known, the area is computed analytically, as accurately as the coordinates themselves.
The shoelace (Gauss) formula
2S = Σ Xᵢ·(Yᵢ₊₁ − Yᵢ₋₁) and the check 2S = Σ Yᵢ·(Xᵢ₋₁ − Xᵢ₊₁), indices taken cyclically. Both sums must agree.
Sign and point order
With survey axes (X north, Y east) clockwise order gives 2S > 0. The area is the absolute value, but the vertices must follow the boundary: a wrong order makes a self-intersecting outline, which the calculator reports.
Example
For six vertices н1…н6 of the example, 2S = 7930.93 m², S = 3965.47 m² = 0.3965 ha, perimeter 237.72 m.
Units
- 1 are = 100 m²;
- 1 hectare = 10 000 m²;
- 1 acre ≈ 4046.86 m².
FAQ
How do I compute a parcel area from coordinates?
Paste the boundary point coordinates (name, X, Y) in boundary order. The area is computed with the shoelace formula and checked with the second formula.
Why is the sum negative?
The sign of 2S depends only on the direction of travel; counter-clockwise order gives a negative sum. The area is its absolute value.
Does the order of points matter?
Yes, points must follow the boundary. A wrong order makes the sides cross and the area wrong; the calculator flags crossings.
How do I convert square metres to hectares?
Divide by 10 000. For example, 3965 m² = 0.3965 ha.
Can I do this in Excel?
Yes: compute Xᵢ·(Yᵢ₊₁ − Yᵢ₋₁) for each row, sum, take half of the absolute value. Subtract a constant from large grid coordinates first to keep precision.