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
Checked against published worked examples from: FM 5-233 Construction Surveying (by name).
Details, formula, and sources
Formula or tableShoelace / 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).
Source and editionThe 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.
Free accessFM 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.
What governsEstimate. AHJ and licensed professional govern.
API field namespoints, area_ft2, perimeter_ft
- Coordinate order North/East (surveying convention), labeled inlineFM 5-233