How it’s calculated
Slope is rise divided by run. Expressed as a percentage it is called grade; the angle comes from the arctangent.
Example: a rise of 3 ft over a 12 ft run gives m = 0.25, a 25% grade, an angle of arctan(0.25) ≈ 14.04°, a ratio of 1:4, a 3:12 pitch and a slope length of √153 ≈ 12.37 ft.
| Ratio | Grade | Angle |
|---|---|---|
| 1:12 | 8.33% | 4.76° |
| 1:4 | 25% | 14.04° |
| 1:1 | 100% | 45° |
Frequently asked questions
Is a 100% slope vertical?
No. 100% means the rise equals the run, which is a 45° angle. A vertical wall has an undefined (infinite) slope.
How do I convert slope percent to degrees?
Divide the percent by 100 and take the arctangent. 10% → arctan(0.10) ≈ 5.71°.
What does a 1:12 slope mean?
One unit of rise for every 12 units of run, about 8.33%. It is a common maximum for wheelchair ramps; check your local accessibility code.
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Sources
- Elementary Algebra 2e, 4.4 Understand Slope of a Line — OpenStax
- Precalculus 2e, 5.4 Right Triangle Trigonometry — OpenStax
- Slope — Wolfram MathWorld
Formulas are taken from the free public references above. Results are provided “as is” for informational and educational purposes only. See our disclaimer.
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