Slope and grade converter
Converts a slope between rise/run ratio, percent grade, per mille, and degrees.
A grade of 8.33% is a slope of 4.76°.
- Rise/run
- Percent grade
- Per mille
Provenance
- Computed by
- units.slope.convert 1.0.0, core 0.1.0
- Model
- ratio = tan(angle); percent = 100 × ratio
- Accuracy
- Exact for ratio, percent, and per mille; degrees to double precision (libm tan/atan)
- Notes
- None
- Cites
- National Institute of Standards and Technology, Guide for the Use of the International System of Units (SI), NIST Special Publication 811
Something look off?
How we got thisFormula, worked example, sources, and proof
Model: ratio = tan(angle); percent = 100 × ratio
Accuracy: Exact for ratio, percent, and per mille; degrees to double precision (libm tan/atan)
When to use this: Use this whenever a slope is written one way and needed another: a ramp or road at a percent grade against a limit in degrees, a railway gradient in per mille, a rise-over-run on a drawing, a roof pitch. Give it any one of the four and all four come back.
Limitations: A percent grade is not an angle, and the two are only close on shallow slopes -- a 100% grade is 45°, not 90°. Vertical has no grade at all, so ±90° is refused rather than returned as an infinity. This is the slope of a straight line, not a route: a road that climbs and descends has no single grade, and an average of two grades is not the grade of the whole. And the angle conversions go through tan and atan, so they carry a few units in the last place that the exact ratio conversions do not.
Worked example: A 1:12 wheelchair ramp (about 8.33%) in degrees. Source: Definition of grade: angle = atan(0.0833) = 4.76°; a 1:12 ramp is 8.33%.
You enter
- Given as
- percent
- Slope
- 8.33
You get
- Angle
- 4.76°
- Rise/run
- 0.0833
- Percent grade
- 8.33%
- Per mille
- 83.3‰
Review: Not yet independently reviewed by a metrologist.
Last verified: 2026-09-18, 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: 25 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.
Sources
- Guide for the Use of the International System of Units (SI), NIST Special Publication 811, National Institute of Standards and Technology, 2008 edition. Appendix B.8, Factors for units listed alphabetically.