Slope Ratio to Percent and Degrees
Slopes on civil plans are written three ways: as a ratio of horizontal to vertical (3:1), as a percent grade (33.3%), or in degrees. This table converts common slope ratios. Note that 3:1 on a grading plan means 3 horizontal to 1 vertical, which is a gentle slope; 100% is a 45 degree slope, not vertical.
| Slope ratioH:V | Grade% | Angle from horizontaldegrees | Rise per foot of runin/ft |
|---|---|---|---|
| 1/4:1 | 400.0 | 76.0 | 48.0 |
| 1/2:1 | 200.0 | 63.4 | 24.0 |
| 3/4:1 | 133.3 | 53.1 | 16.0 |
| 1:1 | 100.0 | 45.0 | 12.0 |
| 1-1/2:1 | 66.7 | 33.7 | 8.0 |
| 2:1 | 50.0 | 26.6 | 6.0 |
| 2-1/2:1 | 40.0 | 21.8 | 4.8 |
| 3:1 | 33.3 | 18.4 | 4.0 |
| 4:1 | 25.0 | 14.0 | 3.0 |
| 5:1 | 20.0 | 11.3 | 2.4 |
| 6:1 | 16.7 | 9.5 | 2.0 |
| 8:1 | 12.5 | 7.1 | 1.5 |
| 10:1 | 10.0 | 5.7 | 1.2 |
| 12:1 | 8.3 | 4.8 | 1.0 |
| 20:1 | 5.0 | 2.9 | 0.6 |
| 50:1 | 2.0 | 1.1 | 0.24 |
| 100:1 | 1.0 | 0.6 | 0.12 |
Notes
- Percent grade = vertical / horizontal x 100. Degrees = arctan(vertical / horizontal).
- Common limits: many codes cap cut and fill slopes at 2:1 without a geotechnical report (IBC Appendix J uses 2:1); lawns that are mowed are often kept at 3:1 or flatter; ADA accessible routes are limited to a running slope of 1 in 20 (20:1 H:V, 5%) unless built as a ramp, and ramps to 1 in 12 (12:1 H:V, 8.33%).
- Values are computed with the formulas above and rounded to one decimal.
Frequently asked questions
What is a 2:1 slope?
Two feet horizontal for every one foot vertical. That is a 50% grade, about 26.6 degrees.
Is a 100% slope vertical?
No. 100% means one foot of rise per foot of run, which is 45 degrees. A vertical face has infinite percent grade.
What slope is allowed for a wheelchair ramp?
Under the 2010 ADA Standards the maximum running slope of a ramp is 1:12 (8.33%), with a maximum rise of 30 inches per run.
Sources
- Trigonometric conversion (computed)
- ADA Standards for Accessible Design (2010), Sections 403.3 and 405.2
- IBC Appendix J, Grading
More reference tables
Civil Engineering Unit ConversionsLumber Nominal vs Actual SizesMinimum Concrete Cover for Rebar (ACI 318)OSHA Trench Soil Types and Maximum Allowable SlopesPVC SDR 35 Sewer Pipe Sizes (ASTM D3034)Presumptive Soil Bearing Values (IBC Table 1806.2)Runoff Coefficients (C) for the Rational MethodUS Rebar Sizes, Areas and WeightsUnit Weights of Common Construction Materials
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