Area by coordinates (acreage)

Model: Coordinate (shoelace) method on plane coordinates

Show your work

1. Twice the area

   2A = Σ (xᵢ − x₀)(yᵢ₊₁ − y₀) − (xᵢ₊₁ − x₀)(yᵢ − y₀)

   the shoelace sum over 4 corners, about the first = 10,000 ft²

2. Area

   $$A=\left|2A\right|/2$$

   10,000 ft² / 2 = 5,000 ft²

3. In acres

   acres = A converted from the coordinate unit

   5,000 ft² = 0.1148 ac

The same steps an agent gets from the MCP server with explain: true.

Accuracy: Exact for plane coordinates; for latitude and longitude use a geodesic area tool

When to use this: Use this when you have plane survey coordinates for a parcel or a figure and need the area it encloses: the coordinate, or shoelace, method with the perimeter beside it, in square units, acres, and hectares. It is the standard way to take an area from a closed traverse or a plotted deed.

Limitations: The coordinates must be plane — State Plane, UTM, or a local grid — because the method is plane geometry; latitude and longitude need a geodesic area tool instead. A grid area is not a ground area until the combined factor is applied, and the figure has to close: points listed out of order enclose a different shape.

Worked example: A 100 × 50 ft rectangle. Source: add-survey-suite scenario: 5,000 ft², 0.1148 ac. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

Review: Not yet independently reviewed by a licensed surveyor.

Last verified: 2026-09-23, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.

Status: version 1.0.0, core 0.1.0. See this tool in the verification report.

Changes

• 2026-09-19, result change: The horizontal curve, vertical curve, and area by coordinates are now stable, so their results no longer carry the EXPERIMENTAL_TOOL warning; the legacy-unit warning on area moved to the first position. They match FM 5-233 (Army Construction Surveying), the Indiana Design Manual vertical-curve example, and Wikipedia's shoelace example. No numbers changed. Changelog

Checked against: 20 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

• Elementary Surveying: An Introduction to Geomatics, Ghilani, C. D., and Wolf, P. R., Pearson, 16th edition. Chapters 10 (traverse computations), 12 (area), 24 (horizontal curves), 25 (vertical curves), 26 (volumes).