Area from coordinates calculator
Calculate area in square metres and hectares from survey coordinates, with perimeter, per-leg bearings and distances, and crossing warnings.
This tool runs in your browser and nothing you enter is uploaded. Check results independently before relying on them for survey work.
How it works
Area is half the absolute shoelace sum Σ(EᵢNᵢ₊₁ − Eᵢ₊₁Nᵢ). Coordinates are shifted to the first point before summing to reduce cancellation with large grid coordinates. Perimeter is the sum of all leg lengths, including the closing leg. Crossings and overlapping legs trigger a warning; their algebraic area is not a usable parcel area.
Worked example
A square with corners (1000,1000), (1100,1000), (1100,1100), (1000,1100) has area 10000.000 m² (1.0000 ha) and perimeter 400.000 m. Reversing the point order gives the same area.
Sources and further reading
Area from coordinates uses the shoelace formula, also called the surveyor’s area formula. Braden (1986), “The Surveyor’s Area Formula”, The College Mathematics Journal 17(4), 326–337, explains why it works.
Frequently asked questions
Must I repeat the first point at the end?
No. The figure is closed automatically. One repeated final copy of the first point is also accepted.
Does clockwise order change the area?
No. The absolute area is reported for either orientation. Points must follow the boundary, rather than being sorted by name or coordinate.
What does a crossing warning mean?
Non-adjacent legs cross or touch, or legs overlap. Review the point order. The displayed shoelace result is only an algebraic area and should not be used as a parcel area.
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