Stair Slope Calculator

Slope as a percentage: (rise ÷ run) × 100. A 7.5 in riser over a 10 in tread gives (7.5 / 10) × 100 = 75%.

Slope as a ratio: simplify rise:run. 7.5:10 reduces to 3:4.

Slope in degrees: arctan(rise ÷ run) = arctan(0.75) ≈ 36.9°.

Slope as a pitch (rise per 12, borrowed from roofing convention): (rise ÷ run) × 12 = (7.5 / 10) × 12 = 9, written as a "9-in-12" pitch.

For stairs, slope is mostly a design and comfort check — it tells you at a glance whether a flight is going to feel gentle or steep before you commit to a riser/tread combination.

For ramps, slope is the primary spec. ADA guidance is commonly cited as a maximum 1:12 ratio for accessible ramps (about 8.3%), though exact requirements depend on the specific code and jurisdiction involved, so always confirm with the authority having jurisdiction for a real project.

Slope also matters for exterior stairs and walkways, where a steeper-than-expected pitch can create drainage or ice problems even if the riser/tread numbers technically meet code.

The same rise-over-run ratio expressed four ways, across a range from ramp-like to steep stair.

A shallow slope (low percentage) covers more floor with less height gained per step — comfortable for older users or heavy foot traffic, but it demands more run, which is often the constraint that rules it out indoors.

A steep slope packs more rise into less run, saving floor space but reducing margin for error underfoot and usually pushing riser height toward the upper end of code limits.

If you only have one format, here's how to get the others without starting over.

1. From percent to degrees: angle = arctan(percent ÷ 100).
2. From degrees to percent: percent = tan(angle) × 100.
3. From ratio to percent: divide the two numbers and multiply by 100 (3:4 → 0.75 → 75%).
4. From percent to pitch: pitch = percent ÷ 100 × 12.

Treating pitch (rise per 12) as if it were the same as percent slope is a frequent mix-up — a 9-in-12 pitch is 75%, not 9%. Always check which unit a spec sheet or code table is actually using.

Another mistake is applying ramp slope limits to stairs or vice versa; the two have different comfort and safety logic even though the math behind slope is identical.

If you want degrees specifically, with saw-setting guidance for cutting a stringer, the stair angle calculator covers that in more depth. For full riser/tread layout, use the stair rise and run calculator.