Why do I need slope to build a roof or a ramp?
Slope is rise divided by run, one number that decides whether a roof sheds rain and whether a ramp is safe. Roofers say it as inches of rise per foot, like 6 in 12. Ramp codes say it as a ratio: at most 1 inch of rise for every 12 inches of run, about 4.8 degrees, for wheelchair access.
- Grade
- 33.3%
- Angle
- 18.4°
- Roof pitch (inches per foot)
- 4
- Length along the slope
- 3.16 m
Challenge: Build a ramp exactly at the 1:12 limit.
Play
Change the rise and the run. The dashed line is the steepest allowed ramp.
Challenge: Build a ramp exactly at the 1:12 limit. The box under the picture turns green when you get it.
Stuck? Pick one of the examples from the “Try an example” menu, or press “New example.”
Understand
Slope is how much you go up for each step across:
It's the same slope as in . Multiply by 100 for a percent grade, by 12 for roof pitch, or take for the angle. The dashed line is the 1:12 accessible-ramp limit: anything steeper is above it.
Use
Every input has a unit menu, so you can type values in the units you already have. Results follow your units.
Show the work
- Slope
m = \frac{\text{rise}}{\text{run}} = \frac{1}{3} = 0.3333 - As a percent grade
0.3333 \times 100 = 33.33\% - As an angle
\theta = \tan^{-1} 0.3333 = 18.43^\circ - Roof pitch
0.3333 \times 12 = 4\text{ in 12}
Export
Enter the rise and run in meters or feet. The length along the slope (by Pythagoras) tells you how long the ramp surface or rafter must be.
- Long ramps need level landings, typically every 30 inches of rise.
- Low-slope roofs (under about 2 in 12) need special roofing materials.
For learning and estimation. Verify with applicable codes, standards, and a qualified professional before using in design, construction, or safety-critical work.
Cheat card
| Symbol | Meaning | Unit |
|---|---|---|
| slope | ||
| angle from horizontal | ° |
- Accessible ramps: 1:12 or gentler (8.33% or less).
- A 4-in-12 roof is about 18°; 12-in-12 is 45°.
- Keep rise and run in the same units.
Where it’s used
- Civil & Construction
Engineers set road grades, drainage slopes, and ramp slopes with rise over run. - Trades
Roofers and carpenters cut rafters from the pitch. - Home Projects
It sizes a deck ramp, a shed roof, or the fall of a patio for drainage.
Related exhibits
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One shadow and the sun’s angle give you the height, no climbing needed.
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Length × width × depth, plus a little extra. Get it right and you won’t run short mid-pour.
Questions people ask
What does a 6/12 roof pitch mean?
The roof rises 6 inches for every 12 inches of horizontal run. That's a slope of 0.5, about 26.6°.
What slope is required for a wheelchair ramp?
In the US, the ADA allows at most 1 inch of rise per 12 inches of run (1:12, about 4.8°).
Is slope the same as angle?
No. Slope is rise over run; the angle is the inverse tangent of the slope. A slope of 1 is 45°.