Slope & grade calculator.
Percent grade = rise ÷ run × 100. Angle = arctan(rise ÷ run). Example: a rise of 1 ft over a run of 12 ft is 8.33%, 4.76° and 1:12. 1:12 is the steepest ramp slope for new construction in the 2010 ADA Standards (existing sites with limited space may use 1:10 or 1:8 for short rises, §405.2 exception).
Enter rise and run, an angle, a percent grade or a 1:X ratio. Get all four forms, plus roof pitch and an ADA check.
How the math works
grade (%) = rise ÷ run × 100 angle (°) = arctan(rise ÷ run) ratio = 1 : (run ÷ rise) roof pitch = (rise ÷ run × 12) / 12
Percent grade and angle are not the same number. A 100% grade is a 45° angle, because rise equals run. A vertical wall is 90°, but its grade is infinite.
Slope conversion table
| Percent grade | Angle | Ratio (rise : run) | Roof pitch |
|---|---|---|---|
| 1% | 0.57° | 1 : 100 | 0.12 / 12 |
| 2% | 1.15° | 1 : 50 | 0.24 / 12 |
| 2.08% | 1.19° | 1 : 48 | 0.25 / 12 |
| 5% | 2.86° | 1 : 20 | 0.6 / 12 |
| 8.33% | 4.76° | 1 : 12 | 1 / 12 |
| 10% | 5.71° | 1 : 10 | 1.2 / 12 |
| 15% | 8.53° | 1 : 6.7 | 1.8 / 12 |
| 20% | 11.31° | 1 : 5 | 2.4 / 12 |
| 25% | 14.04° | 1 : 4 | 3 / 12 |
| 33.33% | 18.43° | 1 : 3 | 4 / 12 |
| 50% | 26.57° | 1 : 2 | 6 / 12 |
| 100% | 45° | 1 : 1 | 12 / 12 |
Roof pitch to angle
| Pitch (rise / 12 in run) | Angle | Percent grade |
|---|---|---|
| 1/12 | 4.76° | 8.3% |
| 2/12 | 9.46° | 16.7% |
| 3/12 | 14.04° | 25% |
| 4/12 | 18.43° | 33.3% |
| 5/12 | 22.62° | 41.7% |
| 6/12 | 26.57° | 50% |
| 7/12 | 30.26° | 58.3% |
| 8/12 | 33.69° | 66.7% |
| 9/12 | 36.87° | 75% |
| 10/12 | 39.81° | 83.3% |
| 11/12 | 42.51° | 91.7% |
| 12/12 | 45° | 100% |
Accessibility limits (2010 ADA Standards)
- Walking surface running slope: not steeper than 1:20 (5%). Section 403.3.
- Cross slope: not steeper than 1:48 (about 2.08%). Section 403.3.
- Ramp running slope: not steeper than 1:12 (8.33%). Section 405.2.
Common questions
How do I calculate percent grade?
Divide the rise by the run, then multiply by 100. Example: a 5 ft rise over 100 ft of run is a 5% grade.
How do I convert percent grade to degrees?
Angle = arctan(grade ÷ 100). Example: a 10% grade is arctan(0.10) = 5.71°.
Is a 100% grade vertical?
No. A 100% grade means the rise equals the run, which is a 45° angle. A vertical surface has an infinite grade.
What is a 1:12 slope?
1 unit of rise for every 12 units of run. That is 8.33% or 4.76°. It is the steepest ramp slope allowed for new construction by the 2010 ADA Standards (section 405.2); existing sites with limited space may use 1:10 or 1:8 for short rises.
What angle is a 6/12 roof pitch?
A 6/12 pitch rises 6 in for every 12 in of run. That is a 50% grade and an angle of 26.57°.
Should rise and run use the same unit?
Yes. Grade, angle and ratio are ratios, so any unit works if rise and run use the same one.
Sources
- Accessible slopes: 2010 ADA Standards for Accessible Design — sections 403.3 (walking surfaces) and 405.2 (ramps).
- Math: grade, angle and ratio follow from the definition of the tangent of an angle (rise ÷ run).
Disclaimer. Check local building codes for stairs, ramps, roofs and drainage. They can be stricter than the ADA limits shown here.