Getting the direction of conversion right
This converter runs both ways. Which direction you need depends on which number you already have and which one your spec sheet, code section, or contractor is asking for.
Know your starting number
If you already ran the Rise and Run Calculator or a stair-angle tool, you have degrees — use Angle → Slope %. If a civil drawing, ramp spec, or grading plan gave you a percent, use Slope % → Angle.
Enter the number as given
Don't pre-convert anything. Enter the raw degree or percent value exactly as it appears on your source — the calculator handles the trig.
Read the result you actually need
The results strip gives you all four common notations at once — percent, degrees, ratio, and roof pitch — so you don't have to re-run the calculator when the next person asks for a different one.
Check the comparison chips
The chips underneath show where your number sits relative to stair comfort range, the steepest angle IRC's riser/tread limits allow, and the ADA ramp maximum — useful context even if none of those apply directly to your project.
The four formulas behind every result
Nothing on this page is a black box. Here's exactly what runs when you change a number, in either direction.
Slope Percent from Angle
The tangent of the angle, as a percentage. This is rise over run, not rise over the sloped hypotenuse — the single most common source of error on this conversion.
Angle from Slope Percent
The inverse tangent of the decimal slope. Used when you're starting from a percent figure — a ramp spec or a civil grading plan — and need the angle.
Roof Pitch Notation
US roofing convention states rise per 12 inches of run instead of a percent. Same underlying ratio, different denominator convention.
Rise : Run Ratio
Normalized so run is exactly 1 — the calculator flips this to "1 : X" for angles under 45°, which is how most rise:run ratios are conventionally written for stairs and ramps.
Walking through a 35° stair angle, and back again
Same formulas, filled in step by step — first converting a stair angle to slope percent, then reversing an ADA ramp spec back to degrees.
Angle to slope percent
A 35° stair angle: tan(35°) = 0.7002, so Slope% = 0.7002 × 100 = 70.0%. That's a steep number compared to a ramp — stairs are supposed to be far steeper than anything wheelchair-accessible, so this is expected, not a red flag.
Same angle, as a ratio and roof pitch
Rise:Run = tan(35°) : 1 = 0.7002 : 1, which the calculator inverts to 1 : 1.43 for readability. As roof pitch: 0.7002 × 12 = 8.40/12 — a steep residential roof pitch, coincidentally in the same range as a comfortable stair.
Where rounding bites you
If you round the angle to a whole degree before converting — 36° instead of 35.6° — you get tan(36°) = 0.7265 → 72.7%, versus tan(35.6°) = 0.7159 → 71.6%. That's over a full percentage point of drift from rounding a single degree early. Always convert from the most precise angle you have, then round the output — not the other way around.
Reversing an ADA ramp spec
An accessibility drawing lists a ramp at 8.33% maximum slope. Switch to Slope % → Angle and enter 8.33: θ = atan(0.0833) = 4.76°. That's the number to compare against a site survey's measured angle, or to hand to a surveyor who works in degrees rather than percent.
Notice how far apart 35° (stair) and 4.76° (ADA ramp max) are — roughly 7.4×. That gap is exactly why a wheelchair ramp can't simply be "a shallower stair": at a stair-like angle it would fail accessibility code by a wide margin, and at ramp-legal angles it would need roughly seven times the horizontal run to climb the same rise.
Angle, slope %, ratio & roof pitch side by side
Common angles from a shallow ramp-like slope to a steep stair, pre-converted to all four notations.
| Angle | Slope % | Rise : Run | Roof Pitch (X/12) |
|---|---|---|---|
| 5° | 8.7% | 1 : 11.43 | 1.05/12 |
| 10° | 17.6% | 1 : 5.67 | 2.12/12 |
| 15° | 26.8% | 1 : 3.73 | 3.22/12 |
| 20° | 36.4% | 1 : 2.75 | 4.37/12 |
| 25° | 46.6% | 1 : 2.14 | 5.60/12 |
| 30° | 57.7% | 1 : 1.73 | 6.93/12 |
| 35° | 70.0% | 1 : 1.43 | 8.40/12 |
| 37.75° | 77.4% | 1 : 1.29 | 9.29/12 |
| 40° | 83.9% | 1 : 1.19 | 10.07/12 |
| 45° | 100.0% | 1 : 1.00 | 12.00/12 |
| 50° | 119.2% | 1 : 0.84 | 14.30/12 |
37.75° is included because it's the steepest angle IRC's residential riser/tread maximums allow — see Code & Practical Limits below. All values computed directly from θ, not looked up from a separate table.
Where common slope limits actually sit
Percent, ratio and degrees get compared across very different rulebooks. Here's where the numbers that matter fall on the same scale.
| Limit | Ratio | Slope % | Angle |
|---|---|---|---|
| ADA ramp, maximum | 1 : 12 | 8.33% | 4.76° |
| ADA ramp, recommended for long runs | 1 : 16 – 1 : 20 | 5.0–6.25% | 2.9–3.6° |
| Stair comfort range (IRC-based) | 1 : 1.73 – 1 : 1.33 | 57.7–75.4% | 30–37° |
| Stair steepest allowed (IRC riser/tread max) | 1 : 1.29 | 77.4% | 37.75° |
| Fixed ladder (steep-slope classification) [VERIFY] | — | [VERIFY: confirm OSHA/ANSI slope threshold separating a "ladder" from a "stair"] | 75–90° |
| Roof, walkable low slope | 2/12 – 4/12 | 16.7–33.3% | 9.5–18.4° |
| Roof, steep slope | 8/12+ | 66.7%+ | 33.7°+ |
The IRC-derived stair figures are computed from the 7.75" max riser / 10" min tread limits used across this site's stair calculators — not separate figures. Always confirm ladder and ramp limits against your local adopted code before building.
Roof pitch, grade & ladder notation
The same tan(θ) relationship gets written four different ways depending on which trade is reading it — mixing them up is where most miscommunication happens.
Roof pitch isn't stair angle
A roofer's "8/12 pitch" and a stair's 33.7° angle describe the same steepness, but nobody in roofing thinks in degrees and nobody in stair-building thinks in twelfths. Convert before you compare a roof spec to a stair spec, or you'll misjudge the steepness by feel.
Grade (‰) is a civil-engineering habit
Per mille — parts per thousand — shows up on European civil drawings and rail/road grading plans instead of percent. It's the same ratio, just multiplied by 10 instead of 100, so a 5% grade is 50‰.
"Slope" vs "grade" vs "pitch"
All three describe rise over run — the words differ by trade, not by math. Roofers say pitch, civil engineers say grade, and stair/ramp work generally says slope. This converter treats them as interchangeable because the underlying formula is identical.
Ladders live at the steep end
Past roughly 75°, a "stair" typically becomes a ship's ladder or fixed ladder under most building and safety codes, with different tread/rung spacing rules entirely. This page's comfort and IRC chips stop being meaningful well before that range — treat anything above ~50° as outside this tool's stair-code context.
These are planning-stage reference conversions, not a substitute for the specific ladder, roofing, or accessibility code that governs your project.
Common mistakes converting angle and slope
Almost every wrong number that comes out of this kind of conversion traces back to one of these five mix-ups.
Using rise ÷ hypotenuse instead of rise ÷ run
Slope percent is defined against the horizontal run, not the sloped stringer or ramp surface length. Dividing by the hypotenuse instead of the run understates the percentage every time.
Assuming a 45° slope is "45%"
It isn't — tan(45°) = 1, so a 45° slope is 100%. Percent and degrees only happen to be numerically close at very shallow angles, which is exactly where the confusion starts.
Reading roof pitch as a direct angle
An "8/12" roof isn't 8°, and it isn't a rise:run of 8:1 either — it's rise 8" per 12" of run, which works out to about 33.7°. Always run it through the conversion before comparing to a stair or ramp angle.
Rounding the angle before converting
As the worked example above shows, rounding to a whole degree before applying tan() can shift the resulting slope percent by a full point or more. Convert from the precise angle first, then round the output.
Applying stair comfort range to a ramp, or vice versa
Stair comfort (30–37°) and ADA ramp maximum (4.76°) are different code universes with different intents — one is about a rhythmic climbing gait, the other is about wheelchair traction and rollback. Neither range applies to the other.
When to use an angle-to-slope converter
This conversion shows up whenever two people describing the same incline are using two different notations.
Comparing a Stair to a Ramp Alternative
Checking how much shallower — and longer — a compliant ramp would need to be versus an existing stair angle.
Talking to a Civil Engineer or Surveyor
Converting a stair or site angle into the percent grade a survey or grading plan expects.
Cross-Checking a Roof Pitch Spec
Translating a roofer's X/12 pitch notation into degrees to compare against an attic stair or access ladder angle.
Reading an Accessibility Drawing
Converting an ADA ramp's percent-slope callout into degrees to verify against a field-measured angle.
Landscaping & Driveway Grade
Turning a slope percent into "inches of rise per 10 feet" — the way most landscapers and excavators actually think about grade.
Comparing Spec Sheets from Different Trades
Normalizing a mix of degree, percent, and ratio figures from different subcontractors onto one scale before a design review.