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
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?
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
- Elementary Surveying: An Introduction to Geomatics, Ghilani, C. D., and Wolf, P. R., Pearson, 16th edition. Grades and slopes in route surveying and construction layout.
Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.