Area by Coordinates
Enclosed area, perimeter, and winding of a closed traverse by the shoelace method.
Example
You enter
- Points n 0, e 0; n 0, e 100; n 100, e 100; n 100, e 0
You get
- Area 10000
- Perimeter 400
Details, formula, and sources
Shoelace / coordinate method: A = 1/2 * |sum (E_i * N_{i+1} - E_{i+1} * N_i)| over the closed ring; acres = ft^2 / 43560; m^2 = ft^2 * 0.0929. Coordinates are North/East (surveying order).
The coordinate (shoelace) method for the area of a closed traverse per FM 5-233 Construction Surveying and the standard surveying texts, by name; public-domain US Government work and first-principles coordinate geometry.
FM 5-233 is public-domain US Government work, free at US Army publication archives. The recorded plat and the surveyor of record govern the legal area.
Estimate. AHJ and licensed professional govern.
Field names used by the API: points, area_ft2, perimeter_ft
- Coordinate order North/East (surveying convention), labeled inlineFM 5-233