Enter the vertical rise and the horizontal run in any units. The calculator gives the slope as a percent grade, an angle in degrees, a rise-to-run ratio, inches per foot and the length along the slope.
Slope formulas
Percent grade = rise ÷ run × 100 Angle (degrees) = arctan(rise ÷ run) Ratio = 1 : (run ÷ rise) Slope length = √(rise² + run²)
Worked example: 2 ft of fall over 10 ft
- Grade: 2 ÷ 10 × 100 = 20%.
- Angle: arctan(0.2) = 11.31°.
- Ratio: 1 : 5.
- Length along the slope: √(4 + 100) = 10.2 ft.
Percent grade to degrees
| Grade | Degrees | Ratio | Inches per foot |
|---|---|---|---|
| 1% | 0.57° | 1 : 100 | 0.12 |
| 2% | 1.15° | 1 : 50 | 0.24 |
| 5% | 2.86° | 1 : 20 | 0.6 |
| 8.33% | 4.76° | 1 : 12 | 1 |
| 10% | 5.71° | 1 : 10 | 1.2 |
| 25% | 14.04° | 1 : 4 | 3 |
| 50% | 26.57° | 1 : 2 | 6 |
| 100% | 45° | 1 : 1 | 12 |
Percent and degrees are not the same: a 100% grade is 45°, because the rise equals the run. Small slopes are almost proportional, about 0.57° per percent.
Where slope matters
- Drainage: ground and pipes need enough fall to move water away from a building.
- Ramps: the ADA limits the running slope of a ramp to 1:12 (8.33%); see the ramp calculator.
- Roofs: roof pitch is usually written as inches of rise per 12 in of run; use the roof pitch calculator.
Questions
What is a 2% slope?
2 ft of fall per 100 ft, or about 1/4 in per foot (0.24 in).
How do I convert percent slope to degrees?
Take the arctangent of the percent divided by 100. 10% is 5.71°.
Is a 1:12 slope the same as 8.33%?
Yes. 1 ÷ 12 × 100 = 8.33%.
Sources
- Chapter 4: Ramps and Curb Ramps, U.S. Access Board.
Used for: Maximum ramp running slope of 1:12. - NIST Guide to the SI, Appendix B.8: Factors for units listed alphabetically, National Institute of Standards and Technology.
Used for: Unit definitions.