geoprimsField-grade geospatial math

Side slope and grade (H:V)

A construction side slope or grade with its ratio labeled H:V and V:H, refusing an unlabeled 3:1, with rise, run, or slope length from any two; for a plain unit conversion of a slope, use the slope converter.

Experimental: not yet fully verified. How results are checked

33.333

That grade is 33.333%, a slope of 18.4349°, or 3H:1V.

Slope angle
Per mille
Ratio H:V
Ratio V:H
Provenance
Computed by
survey.earthwork.grade 1.0.0, core 0.1.0
Model
Grade g = rise / run; percent = 100·g, per mille = 1,000·g, angle = atan g, ratio H:V = (1/g):1 and V:H = g:1; slope length = √(rise² + run²)
Accuracy
Exact
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.
More options 1
Run many at once from a CSV

Loading…

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

Model: Grade g = rise / run; percent = 100·g, per mille = 1,000·g, angle = atan g, ratio H:V = (1/g):1 and V:H = g:1; slope length = √(rise² + run²)

Accuracy: Exact

Worked example: A 3H:1V side slope. Source: add-survey-suite scenario: 3H:1V is about 18.43° and 33.3%. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

You enter

Grade
3H:1V

You get

Percent grade
33.333
Slope angle
18.4349°
Per mille
333.33
Ratio H:V
3H:1V
Ratio V:H
0.333V:1H

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.

Checked against: 10 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

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