Vertical curve length for sight distance

The shortest crest or sag vertical curve that gives a sight distance, from the standard formulas with your eye, object, or headlight heights, stating which case applies; design values come from your design manual.

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.

368.34ft

The curve must be at least 368.34 ft long (S > L: the sight line extends past the curve).

Case
K for that length

Provenance

Computed by: survey.curves.sight-distance 1.0.0, core 0.1.0
Model: Crest: L = AS²/(200(√h1 + √h2)²) when S < L, else L = 2S − 200(√h1 + √h2)²/A. Sag (headlight): L = AS²/(200(H + S tan β)) when S < L, else L = 2S − 200(H + S tan β)/A (Ghilani & Wolf 2021, ch. 25). Design values are inputs: no design table is reproduced
Accuracy: Exact for the formulas; the design values, and whether they apply to your road, come from your design manual
Notes: 1 shown with the answer
Cites: Ghilani, C. D., and Wolf, P. R., Pearson, Elementary Surveying: An Introduction to Geomatics

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Your values

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Curve crest or sag Sight distance S From your design manual's table, like 400 ft · plain numbers mean ft Grade change A The algebraic difference of the grades in percent, like 5 Eye height h1optional Crest: the driver's eye height your manual uses, like 3.5 ft · plain numbers mean ft Object height h2optional Crest: the object height your manual uses, like 2.0 ft · plain numbers mean ft

More options 4

Headlight height Hoptional Sag: the headlight height your manual uses, like 2 ft · plain numbers mean ft Headlight divergence βoptional Sag: the upward spread of the beam your manual uses, like 1° · plain numbers mean degrees Design Koptional Optional: the K from your design manual's table, to compare, like 44 Design K sourceoptional Title, edition, and table number, like AASHTO Green Book, 7th ed., Table 3-34

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

Model: Crest: L = AS²/(200(√h1 + √h2)²) when S < L, else L = 2S − 200(√h1 + √h2)²/A. Sag (headlight): L = AS²/(200(H + S tan β)) when S < L, else L = 2S − 200(H + S tan β)/A (Ghilani & Wolf 2021, ch. 25). Design values are inputs: no design table is reproduced

Accuracy: Exact for the formulas; the design values, and whether they apply to your road, come from your design manual

Worked example: A crest curve for 400 ft of sight with A = 5%. Source: add-survey-suite crest SSD scenario: about 368.3 ft, S > L. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

You enter

Curve: crest
Eye height h1: 3.5 ft
Grade change A: 5
Object height h2: 2.0 ft
Sight distance S: 400 ft

You get

Minimum curve length: 368.34 ft
Case: S > L: the sight line extends past the curve
K for that length: 73.7

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: 7 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 25 (vertical curves: sight distance on crest and sag curves).

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: Vertical curves explained

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