Plot Area by Coordinates Calculator (Shoelace)
Exact area of a 5-corner plot from X-Y coordinates — total-station math.
The shoelace (surveyor's) formula is exact for any non-crossing polygon — duplicate the last point to handle four corners. This is precisely what total stations and CAD compute.
Formula
Plot Area by Coordinates Calculator (Shoelace) is a free shoelace formula for surveyors, civil engineers and property buyers — instant, accurate and 100% client-side, with the governing formula and reference shown next to the result so the number can be defended, not just quoted.
About Plot Area by Coordinates Calculator (Shoelace)
Exact area of a 5-corner plot from X-Y coordinates — total-station math. The calculation implements A = ½|Σ(xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)| (Gauss's shoelace formula; surveying computation). The shoelace (surveyor's) formula is exact for any non-crossing polygon — duplicate the last point to handle four corners. This is precisely what total stations and CAD compute.
How to use Plot Area by Coordinates Calculator (Shoelace)
- 1Enter X₁ in m.
- 2Enter Y₁ in m.
- 3Enter X₂ in m.
- 4Enter Y₂ in m.
- 5Read Area instantly — no submit button needed.
- 6Need US units? Flip the SI/Imperial toggle and every field converts.
Why use Plot Area by Coordinates Calculator (Shoelace)?
- ✓Implements the standard formula — A = ½|Σ(xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)|
- ✓Reference cited on-page: Gauss's shoelace formula; surveying computation
- ✓One-click SI ⇄ Imperial toggle — values convert in place, physics stays in SI
- ✓Runs entirely in your browser — nothing uploaded, free forever
Frequently asked questions
What formula does the Plot Area by Coordinates Calculator (Shoelace) use?+
It computes A = ½|Σ(xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)|, per Gauss's shoelace formula; surveying computation. The formula is displayed under the result.
What should I keep in mind when using this calculator?+
The shoelace (surveyor's) formula is exact for any non-crossing polygon — duplicate the last point to handle four corners. This is precisely what total stations and CAD compute.
Are regional land units exact?+
Conversion factors follow state revenue-department values noted on the tool. Units like bigha and katha vary by region, so always confirm the local factor named in your land records.
Is the Plot Area by Coordinates Calculator (Shoelace) free to use?+
Yes — completely free, no sign-up, no limits. It runs client-side in your browser, so inputs stay private and results are instant even on slow connections.
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