Traverse closure and adjustment

Model: Latitudes and departures; compass rule corrections ∝ course length; transit rule ∝ |latitude| and |departure|; Crandall rule holds every bearing and corrects distances only, by weighted least squares with weights ∝ 1/length

Show your work

1. Sum of latitudes

   ΣL = Σ distance × cos(bearing)

   4 courses = 0.1198 ft

2. Sum of departures

   ΣD = Σ distance × sin(bearing)

   4 courses = 0.02 ft

3. Error of closure

   $$e=\sqrt{({\mathrm{\Sigma L}}^2+{\mathrm{\Sigma D}}^2)}$$

   √(0.1198² + 0.02²) = 0.1215 ft

4. Precision

   precision = perimeter / error of closure

   1,399.97 ft / 0.1215 ft = 1:11,525

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

Accuracy: Exact arithmetic; the adjusted traverse closes to within 1e-9 of the unit

When to use this: Use this to close a loop traverse: it gives the latitudes and departures, the linear misclosure and its direction, the precision ratio, and the adjusted courses by the compass, transit, or Crandall rule, so you can see how good the fieldwork was before the coordinates are used.

Limitations: Adjustment distributes error by a rule rather than finding a blunder: a large misclosure usually means a mistake in a bearing or a distance, and the rule will spread it across every course. The three rules assume different error behavior, and the one to use is the one your specification names. Distances are treated as plane and level.

Worked example: A four-course loop. Source: add-survey-suite scenario: ΣLat 0.1198, ΣDep 0.0200, misclosure 0.1215, precision about 1:11,525.

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

• 2026-09-22, changed: Traverse closure now offers the Crandall rule: it holds every measured bearing and puts the whole correction into the distances. Existing compass and transit results are unchanged. Changelog
• 2026-09-19, result change: Traverse closure and the combined grid-to-ground factor are now stable, so their results no longer carry the EXPERIMENTAL_TOOL warning; the perfect-closure and elevation-as-ellipsoid-height warnings moved to the first position. Both match published worked examples (University of Memphis traverse notes and NOAA Manual NOS NGS 5) to every printed digit. No numbers changed. Changelog

Checked against: 26 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).