Converting a rise/run ratio to degrees
This tool runs in two directions. Pick the one that matches what you already have in hand.
Have a rise and a run? Use "Ratio → Degrees"
Enter the vertical rise and horizontal run — a single riser and tread, a roof's rise and run, or a ramp's rise and length. The units don't need to match; the calculator converts both to a common base before dividing.
Have an angle instead? Use "Degrees → Ratio"
Switch direction, enter the angle in degrees, and set the Reference Run to whatever run length the angle should apply to — 12 for roof-pitch notation, or your actual tread depth for a stair.
Adjust precision and pitch base if needed
Open Advanced to change decimal places, switch the pitch notation base from 12 to 10 for some metric roofing tables, or turn off ratio simplification to see the raw decimal pair.
Read the comparison chip
Set the compliance context to stair comfort or ADA ramp maximum to see whether the resulting angle passes that specific reference range — useful for a fast sanity check before you commit to cutting or grading.
The six conversions behind every result
Nothing on this page is a black box. Here's exactly what runs when you change a number.
Angle from Ratio
The core conversion. Rise and run are converted to a shared unit first, then the arctangent of their ratio gives the angle from horizontal.
Rise from Angle
The reverse direction. Given an angle and a reference run, this returns the rise that would produce that exact angle over that run.
Slope Percent
The same ratio expressed as a percentage — the notation civil engineering, road grades, and ADA ramp specs typically use instead of degrees.
Simplified Ratio
Both values are scaled to whole numbers, then divided by their greatest common divisor — turning 7.5:10 into the cleaner 3:4.
Pitch Notation
Rescales the ratio onto a fixed run — 12 by roofing convention — so it reads as "9 in 12" instead of an arbitrary decimal.
Complementary Angle
The same incline measured from vertical instead of horizontal — the convention some framing and aviation references use.
Walking through a 7.5" rise, 10" run
Same six formulas, filled in step by step, for this calculator's default ratio — a 7.5" riser over a 10" tread, the typical output of the 2R+T comfort rule.
Angle
atan(7.5 ÷ 10) = atan(0.75) = 36.87°. That's the incline measured from horizontal — the number you'd read off a framing square or a digital angle gauge.
Slope percent and radians
Slope: (7.5 ÷ 10) × 100 = 75%. In radians: 36.87 × π ÷ 180 ≈ 0.6435 rad — the form most CAD and CNC software expects for angle inputs.
Simplified ratio and pitch notation
7.5:10 reduces to 3:4 once both sides are divided by their greatest common factor. On a 12-unit pitch base, that same ratio reads as 9 in 12 — the way a roofer would write it on a plan.
Where it lands against the comfort range
36.87° sits inside the 30°–37° stair comfort range this site uses elsewhere — but only just. It's less than a degree from the upper limit, which is exactly why a riser this close to 7.75" IRC max combined with a 10" tread is the most common way a "comfortable" stair ends up feeling steep in practice.
This is why the comfort-range chip is worth checking even when both the riser and tread values individually look fine — it's the interaction between the two, not either number alone, that determines whether the resulting climb actually feels comfortable.
Common rise/run ratios, converted to degrees
A quick lookup across the three domains that use rise/run notation most: ramps, roofs, and stairs.
| Ratio | Slope % | Angle | Typical context |
|---|---|---|---|
| 1:20 | 5.0% | 2.86° | ADA threshold between a "walking surface" and a ramp |
| 1:12 | 8.3% | 4.76° | ADA maximum ramp running slope |
| 4:12 | 33.3% | 18.43° | Common low-slope roof pitch |
| 6:12 | 50.0% | 26.57° | Common moderate roof pitch |
| 7:11 | 63.6% | 32.47° | Traditional "7-11" stair rule of thumb |
| 7.5:10 | 75.0% | 36.87° | Typical comfortable stair (2R+T default, this page's example) |
| 8:9 | 88.9% | 41.63° | Steep, compact stair — approaching spiral-stair territory |
| 12:12 | 100.0% | 45.00° | Equal-pitch roof; the 45° reference angle |
Need the roof-to-stair comparison specifically? Use the Roof Pitch vs Stair Angle Comparison.
Reading the notation: ratio, pitch, slope % and grade
The same incline gets written four different ways depending on who's reading the plan. Knowing which one you're looking at matters as much as the math.
Rise/Run Ratio (carpentry)
The way stair layouts are usually specced — a single riser height over a single tread depth. Because the ratio is scale-invariant, this is identical to total rise over total run for the whole flight; you don't need to re-measure the full staircase to get the angle.
Roof Pitch (roofing)
Roofers always express pitch against a fixed 12-unit run, regardless of the roof's actual size — a "6 in 12" roof rises 6" for every 12" of horizontal run. Convert it to degrees before cutting rafters on a saw with a degree scale instead of a pitch scale.
Slope / Grade Percent (civil & ADA)
Used for ramps, roads, and accessibility code because it scales linearly — a 5% grade is exactly half of a 10% grade, which isn't true of degrees. Easy to confuse with degrees: a 100% slope is 45°, not 90°.
Degrees (universal)
The one notation every trade can read without a conversion table — required for framing squares, digital angle gauges, CAD software, and most CNC stringer-cutting equipment.
All four describe the same physical incline. This calculator converts between them so you don't have to keep a separate table for each trade.
Common mistakes converting rise/run to degrees
Most conversion errors on this specific calculation come from one of these five mix-ups, not from bad arithmetic.
Mixing units before dividing
Entering rise in inches and run in feet without converting first silently produces an angle 12× too steep or too shallow. Use the unit dropdowns — they convert to a shared base automatically.
Inverting rise and run
Swapping which value goes in "rise" and which goes in "run" flips atan(0.75)=36.87° into atan(1.33)=53.13° — a completely different incline from the same two numbers.
Treating slope percent as degrees
A "100% slope" sounds vertical but is only 45°; a "50% slope" is 26.57°, not half of 45. Percent and degrees are related by a tangent, not a straight line — always convert rather than assume.
Reading a pitch note as if it's already an angle
A "6/12" or "6 in 12" roof callout is a ratio, not a degree measurement. It has to run through atan(6÷12) = 26.57° before it means anything on a degree-scale saw or protractor.
Confusing the angle with its complement
Some references measure the incline from vertical instead of horizontal. A 36.87° stair angle from horizontal is a 53.13° angle from vertical — check which convention your source is using before comparing numbers.
When to convert a rise/run ratio to degrees
This specific conversion shows up whenever a plan, spec sheet, or inspection report gives you a ratio and a saw, gauge, or code table needs a degree.
Existing Stair Documentation
Converting a field-measured riser/tread ratio to degrees for a code review or permit note.
Roof Framing
Converting a roof pitch callout like 6/12 to degrees for a rafter saw with a degree, not pitch, scale.
Ramp Slope Checks
Checking a measured ramp rise and length against the ADA's 1:12 maximum before finalizing a design.
CAD & Drafting
Converting a hand-sketched or field-noted ratio into a precise decimal-degree value for CAD input.
Inspection Report Cross-Checks
Converting a slope-percent figure from a home inspection report to degrees for comparison against comfort ranges.
Prefab Stringer Shopping
Checking a prefabricated stringer or ladder's listed angle against your project's actual rise/run before ordering.