Polygon Area Calculator (Shoelace Formula from Coordinates)
List the corner coordinates in order around the shape (clockwise or anticlockwise).
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Polygon Area Calculator (Shoelace Formula from Coordinates) by TheCalcTools
How the Polygon Area Calculator (Shoelace Formula from Coordinates) works
The shoelace formula multiplies coordinates crosswise around the polygon: area = ½ |Σ (xᵢyᵢ₊₁ − xᵢ₊₁yᵢ)|, wrapping from the last corner back to the first.
List corners in order around the boundary; the result is wrong if the edges cross each other. Surveyors use it to find land areas from boundary coordinates.
The formula
Worked example
Using the default values shown in the calculator:
| x coordinates, in order | 0, 6, 6, 2, 0 |
|---|---|
| y coordinates, same order | 0, 0, 4, 7, 4 |
- The pentagon (0,0), (6,0), (6,4), (2,7), (0,4) has area 33.0000.
Result:
| Area | 33.0000 |
|---|---|
| Number of corners | 5 |
| In acres (if units are feet) | 0.0008 |
| In hectares (if units are metres) | 0.0033 |
Frequently asked questions
Does it matter which corner I start with?
No, and the direction does not matter either, as long as the corners go around in order.
Sources and further reading
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