Angular closure of a loop traverse
How far a loop traverse's measured angles miss their geometric sum, (n − 2) × 180° for interior angles, against an allowable K√n, with the angles balanced.
Experimental: not yet fully verified. How results are checked
The angles miss their required sum by 25″. The allowable is 22.4″, so the closure is beyond the allowable.
| Adjusted angle |
|---|
| 108°00'00.0" |
| 101°59'50.0" |
| 115°00'05.0" |
| 94°59'55.0" |
| 120°00'10.0" |
- Sum of the angles
- Required sum
- Allowable misclosure
- Closure
- Correction per angle
Provenance
- Computed by
- survey.cogo.angular-closure 1.0.0, core 0.1.0
- Model
- Required sum (n − 2)·180° for interior angles and (n + 2)·180° for exterior; misclosure = Σ measured − required; allowable = K·√n; each angle corrected by −misclosure/n (Ghilani & Wolf 2021, ch. 10)
- Accuracy
- Exact; the allowable depends on the standard, entered as K
- Notes
- 1 shown with the answer
- Cites
- Ghilani, C. D., and Wolf, P. R., Pearson, Elementary Surveying: An Introduction to Geomatics
Something look off?
How we got thisFormula, worked example, sources, and proof
Model: Required sum (n − 2)·180° for interior angles and (n + 2)·180° for exterior; misclosure = Σ measured − required; allowable = K·√n; each angle corrected by −misclosure/n (Ghilani & Wolf 2021, ch. 10)
Accuracy: Exact; the allowable depends on the standard, entered as K
Worked example: Five interior angles summing to 540°00'25". Source: add-survey-suite angular-misclosure scenario: +25". It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.
You enter
- Allowable K
- 10
- Measured angles
- 108°00'05" 101°59'55" 115°00'10" 95°00'00" 120°00'15"
You get
- Angular misclosure
- 25″
- Sum of the angles
- 540°00'25.0"
- Required sum
- 540°00'00.0"
- Allowable misclosure
- 22.4″
- Closure
- beyond the allowable
- Correction per angle
- -5″
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
- 2026-09-23, fixed: Survey tools cite Ghilani and Wolf's Elementary Surveying, 16th edition (2021), but their method notes said "Ghilani & Wolf 2018". The notes now give 2021, the edition cited. No results change. Changelog
Checked against: 6 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. Chapter 10 (traverse computations: angular misclosure and balancing angles).
Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.
Learn the concept: Traverse closure and precision explained