Level run reduction and closure

Heights of instrument and elevations from a level book, the arithmetic check, and for a loop or a run between benchmarks, the misclosure, its allowable, and the adjusted elevations.

Experimental: not yet fully verified. How results are checked

Computing your own values needs JavaScript and WebAssembly. The worked example below was computed when this page was built, and the documentation under "How we got this" applies.

13.49ft

ΣBS − ΣFS is 13.49 ft less 13.51 ft, and it checks against the elevations. The run misses closing by -0.02 ft.

Stations
Station	Height of instrument	Elevation	Adjusted elevation
BM 1	104.520 ft	100.000 ft	100.000 ft
TP 1	106.680 ft	100.550 ft	100.557 ft
TP 2	104.260 ft	101.420 ft	101.433 ft
BM 1		99.980 ft	100.000 ft

Sum of foresights
Arithmetic check
Misclosure
Allowable closure
Closure

Provenance

Computed by: survey.reduction.level-run 1.0.0, core 0.1.0
Model: HI = elevation + BS; elevation = HI − FS (or − IS for a side shot); check ΣBS − ΣFS = last − first elevation; misclosure = observed − known closing elevation, distributed in proportion to cumulative distance (or to setups when no distances are given); allowable = C·√K (Ghilani & Wolf 2021, ch. 5)
Accuracy: Exact arithmetic; the allowable closure is the standard you choose, entered as C
Notes: 1 shown with the answer
Cites: Ghilani, C. D., and Wolf, P. R., Pearson, Elementary Surveying: An Introduction to Geomatics

Something look off?

Your values

Showing an example. Change anything.

Starting elevation Of the first benchmark, like 100.00 ft · plain numbers mean ft Level book One row per station, in order, like BM 1 with a 4.52 ft backsight, then TP 1 with a 3.97 ft foresight and a 6.13 ft backsight · one per line: station, backsight, foresight, intermediate sight, distance Closing benchmark elevationoptional Known elevation of the last station, like 247.975 m; a loop back to the start closes on the starting elevation · plain numbers mean ft

More options 1

Allowable constant Coptional Allowable closure is C × √K, K in kilometers, like 12 mm · plain numbers mean ft

Run many at once from a CSV

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How we got thisFormula, worked example, sources, and proof

Model: HI = elevation + BS; elevation = HI − FS (or − IS for a side shot); check ΣBS − ΣFS = last − first elevation; misclosure = observed − known closing elevation, distributed in proportion to cumulative distance (or to setups when no distances are given); allowable = C·√K (Ghilani & Wolf 2021, ch. 5)

Accuracy: Exact arithmetic; the allowable closure is the standard you choose, entered as C

Worked example: A loop from BM 1 through two turning points and back. Source: A level loop in the textbook's note form. It is golden test vector v002, and every build checks the tool still gives its answer within its tolerance.

You enter

Allowable constant C: 0.05 ft
Level book: BM 1, 4.52 ft TP 1, 6.13 ft, 3.97 ft, 300 ft TP 2, 2.84 ft, 5.26 ft, 280 ft BM 1, 4.28 ft, 310 ft
Starting elevation: 100.00 ft

You get

Sum of backsights: 13.49 ft
Sum of foresights: 13.51 ft
Arithmetic check: ΣBS − ΣFS = 13.490 − 13.510 = -0.020 ft, and the last elevation less the first = -0.020 ft: balanced
Misclosure: -0.02 ft
Allowable closure: 0.026 ft
Closure: within the allowable

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 5 (leveling field procedures and computations: level notes, arithmetic check, misclosure, and adjustment).

Terms

BS: backsight: In leveling, the rod reading on a point of known elevation. Added to that elevation it gives the height of the instrument. Source: Elementary Surveying: An Introduction to Geomatics
FS: foresight: In leveling, the rod reading on a point whose elevation is wanted. Subtracted from the height of the instrument it gives that elevation. Source: Elementary Surveying: An Introduction to Geomatics

Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.