Converting between pitch, angle and slope
Pick whichever notation you already have — a framing square reading, a protractor angle, a slope percent off a survey, or a raw rise/run pair — and every other notation updates with it.
Choose your starting notation
Roofers usually think in "X-in-12." Stair layouts and site surveys more often use degrees or a percent slope. Pick the mode that matches what you're holding.
Enter the one number you have
Only one field is needed per mode, except Rise ÷ Run, which takes two — any matching pair of lengths, not just roof dimensions.
Read the full conversion set
The results strip shows the same angle in all four notations at once, plus a simplified rise:run ratio and the nearest standard roof pitch fraction.
Check the classification chips
The green/red chip is a real IRC pass/fail check against the stair comfort range. The grey chips are reference classifications built on thresholds that vary by jurisdiction and manufacturer — verify those locally before relying on them.
The four conversions behind every result
One trig relationship drives all of it — the notations just describe the same right triangle differently.
Angle from Roof Pitch
Roof pitch's run is fixed by convention at 12 inches, so the rise-per-12 number plugs straight into the same arctangent stairs use.
Angle from Rise ÷ Run
The general case — works for a roof, a stair, a ramp or a ladder, since none of them require the run to be 12".
Roof Pitch from Angle
Reverses the first formula — useful when you've measured an angle directly and need to state it the way a framer would.
Slope Percent
Not the same number as the pitch fraction — a 6-in-12 pitch is 50% slope, not "6%." The two only match by coincidence at certain angles.
Comparing a 6-in-12 roof to a 7.5"/10" stair
Same trig, two different jobs on the same project — a porch roof and the stair leading up to it.
Roof angle
A 6-in-12 pitch: θ = atan(6 ÷ 12) = atan(0.5) = 26.57°. Slope percent is (6 ÷ 12) × 100 = 50% — note this is not "6%," a common mix-up between pitch notation and slope percent.
Stair angle
A 7.5" riser over a 10" tread: θ = atan(7.5 ÷ 10) = atan(0.75) = 36.87°. That sits at the steep end of, but still inside, the 30–37° IRC stair comfort range.
Equivalent riser for the roof's angle
If that same 26.57° roof angle were built as a stair with a 10" tread, the riser would be tan(26.57°) × 10 = 5.0" — shallower than any comfortable stair riser, which is exactly why a 6-in-12 roof reads as "gentle" while a 36.87° stair reads as "normal": stairs and roofs occupy very different bands of the same angle scale.
Expressing the stair angle as a roof pitch
Rise-in-12 = tan(36.87°) × 12 ≈ 9.0-in-12. A roof at that pitch would sit right at the edge of the steep-slope classification band — a useful gut-check for how steep a "normal" stair actually is compared to a roof.
This is why converting roof pitch and stair angle through degrees first — rather than trying to compare the raw notations directly — is the only way to get an apples-to-apples comparison.
Common roof pitches vs stair, ramp & ladder angles
The same angle scale, read two ways. Roofers name a point on this scale in-per-12; everyone building access — stairs, ramps, ladders — names it in degrees.
| Roof Pitch | Angle | Slope % | Roof Classification |
|---|---|---|---|
| 1-in-12 | 4.76° | 8.3% | Low-slope [VERIFY: exact low-slope cutoff and required underlayment per local adopted code] |
| 2-in-12 | 9.46° | 16.7% | Low-slope [VERIFY: same threshold as above] |
| 3-in-12 | 14.04° | 25% | Low-slope [VERIFY: same threshold as above] |
| 4-in-12 | 18.43° | 33.3% | Conventional (default low-slope boundary) |
| 5-in-12 | 22.62° | 41.7% | Conventional |
| 6-in-12 | 26.57° | 50% | Conventional |
| 7-in-12 | 30.26° | 58.3% | Conventional |
| 8-in-12 | 33.69° | 66.7% | Conventional |
| 9-in-12 | 36.87° | 75% | Conventional (default steep-slope boundary) |
| 10-in-12 | 39.81° | 83.3% | Steep-slope [VERIFY: exact steep-slope cutoff per manufacturer/local code] |
| 12-in-12 | 45.00° | 100% | Steep-slope [VERIFY: same threshold as above] |
| 16-in-12 | 53.13° | 133.3% | Steep-slope [VERIFY: same threshold as above] |
| Access Type | Typical Angle Range | Notation as Roof Pitch |
|---|---|---|
| ADA-compliant ramp (max) | 4.76° (1:12) | 1-in-12 |
| IRC residential stair (comfort range) | 30°–37° | ~6.9 to ~9.0-in-12 |
| Fixed access ladder (typical) | [VERIFY: typical fixed-ladder angle range, commonly cited near 68–75° but confirm against OSHA/ANSI current standard] | — |
| Vertical ladder | 90° | — |
Angle and slope values are exact trigonometric conversions. Classification labels and the ladder angle range are marked where they depend on a specific code edition, manufacturer spec, or jurisdiction — verify those locally before using them as a pass/fail check.
Why roof pitch and stair angle use different notation
The trig is identical. The reason the two trades never talk in the same units comes down to how each measurement actually gets taken on site.
Roof pitch: a framing-square convention
Fixing the run at 12" lets a roofer read pitch straight off a framing square or speed square without doing trig on site — "6-in-12" is a direct physical measurement, not a computed angle.
Stairs: rise and run vary together
A stair's run per step (the tread) is itself a design decision governed by comfort formulas and code minimums — there's no fixed "12" to anchor a pitch-style notation to, so degrees became the shared language instead.
Slope percent: the surveyor's unit
Civil and landscape work generally uses percent slope because it composes linearly over long, irregular distances — a convenience that doesn't matter over a single roof plane or stair flight, which is why roofing and stair trades didn't adopt it.
Where the mismatch causes real problems
Architectural drawings often spec a porch or entry roof in pitch notation while the stair beneath it is specced in degrees or riser/tread inches — this tool exists specifically to catch the point where those two specs need to visually or structurally line up.
Roofing steepness classification thresholds also drive real construction requirements — underlayment type, fastening pattern, and in some cases fall-protection rules — but those thresholds are set by code editions and manufacturer specs that vary by jurisdiction and product. [VERIFY: current IRC/OSHA thresholds for low-slope underlayment and roof fall-protection requirements applicable to your project.]
Common mistakes converting pitch, angle and slope
Most cross-trade mix-ups on this conversion trace back to one of these five errors.
Treating pitch as a plain fraction
"6-in-12" isn't the fraction 6/12 simplified to 1/2 in the geometric sense — the 12 is a fixed run, not a reducible denominator. Simplifying it loses the notation's whole point.
Assuming a 45° stair is normal
45° reads as unremarkable next to a roof pitch, but on a stair it's well past the 30–37° comfort range and edges toward ladder territory — the same number means very different things in each domain.
Mixing up slope percent and pitch fraction
A 6-in-12 roof is 50% slope, not "6%." Percent slope and pitch notation both derive from rise/run, but they're scaled differently and aren't interchangeable without converting through the ratio first.
Applying a fixed 12" run to a stair calculation
Roof pitch math assumes run = 12" by convention. Plugging a stair's actual tread depth into that assumption instead of using the stair's real run produces a wrong angle.
Rounding pitch to the nearest whole number too early
Rounding 6.4-in-12 down to "6-in-12" can shift which side of a low-slope or steep-slope classification threshold the roof actually falls on — round after checking the classification, not before.
When to compare roof pitch and stair angle
This comparison comes up wherever a roofline and an access route meet on the same drawing.
Porch & Entry Design
Matching a porch roof's visual pitch to the stair angle leading up to it for a coherent design.
Roof Walkability Checks
Deciding whether a roof plane can be walked for maintenance or needs staging and fall protection.
Cross-Trade Drawing Handoffs
Converting between an architect's pitch notation and a framer's or stair builder's degree-based layout.
Attic & Loft Access
Checking whether a fixed ladder or alternating-tread stair angle matches a roof hatch or knee-wall clearance.
Ramp vs Stair Decisions
Confirming a proposed slope actually falls in ADA ramp territory rather than drifting into stair-angle range.
Job-Site Communication
Translating a roofer's "6-in-12" into the degrees a stair builder or inspector expects, without doing trig by hand.