Irregular Polygon Calculator
Enter the vertices of your polygon in order (clockwise or counterclockwise) and we’ll compute the area using the shoelace formula, the perimeter, the centroid (geometric center), and the orientation.
Tip: click “Prefill sample” to see how the table works.
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Keep this checked for normal polygons. Uncheck if your points already include the first point again at the end.
Formulas used (shoelace / Gauss area)
Area (signed): for vertices \((x_1,y_1), (x_2,y_2), ..., (x_n,y_n)\)
\[ A = \frac{1}{2} \left( \sum_{i=1}^{n} x_i y_{i+1} - x_{i+1} y_i \right) \] where \((x_{n+1}, y_{n+1}) = (x_1, y_1)\).
Perimeter: \(\text{Perimeter} = \sum_{i=1}^{n} \sqrt{(x_{i+1}-x_i)^2 + (y_{i+1}-y_i)^2}\)
Centroid: \[ C_x = \frac{1}{6A} \sum_{i=1}^{n} (x_i + x_{i+1}) (x_i y_{i+1} - x_{i+1} y_i) \] \[ C_y = \frac{1}{6A} \sum_{i=1}^{n} (y_i + y_{i+1}) (x_i y_{i+1} - x_{i+1} y_i) \]
Notes & best practices
- Order matters: follow the polygon edges.
- No crossings: this is for simple polygons (no self-intersections).
- Same units: if coordinates are in meters, area is in m²; if in feet, area is in ft².
- Orientation: positive area usually means counterclockwise order.
FAQs
Can I calculate a land plot area from coordinates?
Yes, if your coordinates are in a planar system (e.g. local survey x/y). For GPS lat/long you should first project or approximate.
How many vertices can I enter?
This page supports up to 20 vertices in the browser for quick calculations.
Why is my area negative?
That means your vertices are in clockwise order. We display absolute area and tell you the orientation.