Pitch Angle Calculator
Roofers quote pitch as rise over a 12-inch run, engineers think in degrees, and material orders need the rafter multiplier. This calculator speaks all three: give it rise and run, an angle, or a pitch ratio, and it returns the angle in degrees, the X/12 ratio, slope percentage, rafter length per foot, and total rafter length for your roof. The rise and run inputs are pre-filled with the classic 6/12 example below.
The roof-type label (Low Slope, Conventional, Steep, Very Steep) is this calculator’s own working band, not a building-code definition. Rafter lengths assume a straight run with no overhang.
Quick Answer
A 6/12 roof pitch is 26.57° with a 50.00% slope. Each foot of horizontal run needs 13.42 inches of rafter, so a 20-foot run takes 22.36 feet of rafter, and the calculator classes it as a Conventional roof. The calculator is pre-filled with this example; click Calculate to reproduce it.
Key takeaways
- Pitch angle = arctan(rise ÷ run). A 6/12 pitch is 26.57°, a 12/12 pitch is exactly 45°, and slope percentage is simply (rise ÷ run) × 100.
- The rafter factor, rafter length ÷ 12, is the number that prices the job: 1.1180 at 6/12 means every foot of run needs 1.118 feet of rafter, and every square foot of plan area needs 1.118 square feet of roofing.
- Enter whichever measurement you have. Rise and run, an angle, or a pitch ratio all reach the same full result set, including the total rafter length for an optional roof length.
- The Low Slope / Conventional / Steep / Very Steep label is this calculator’s own working band. Trade convention generally calls ≤3/12 low slope and ≥7/12 steep, so treat the label as a rough guide, not a code definition.
How to use the pitch angle calculator
Pick the measurement you already have, enter it, and click Calculate. The results stay hidden until you do.
- Rise and Run: enter the vertical rise and horizontal run in the same units (inches is conventional, with run defaulting to 12). This is the mode for tape-and-level measurements.
- Angle (Degrees): enter the pitch angle from a digital level or phone app, between 0 and 90. The calculator works backwards to the rise and the X/12 ratio.
- Pitch Ratio: enter the rise per 12 inches of run, for example 6 for a 6/12 roof. The calculator converts it to degrees, slope and rafter lengths.
- Roof length (optional): enter the horizontal length of the roof in feet and the calculator scales the per-foot rafter length up to a total rafter length. Note it expects the horizontal run here, not the sloped distance; that is what the scaling math assumes.
Three honest quirks to know. A run of 0 is silently treated as the standard 12-inch run, because rise over zero has no angle; enter a real run instead of relying on that. An angle of exactly 90° is accepted but produces a near-infinite rise from the tangent function, which is a math artifact, not a buildable roof. And invalid entries show an inline message naming the problem rather than a popup, with the exact original wording (“Please enter a valid rise value” and the two companions).
The pitch formulas behind the calculator
Every output is right-triangle trigonometry on the rise and run. The angle comes from the inverse tangent, the slope from the ratio itself, and the rafter from Pythagoras, exactly as roofing references such as InterNACHI’s roof pitch guide lay them out. The same triangle shows up off the roof too: when you measure a sight line with a rangefinder or clinometer instead of a tape, the distance-angle calculator splits that slant distance and angle into horizontal range and height.
Slope % = (rise ÷ run) × 100 | Rafter = √(rise² + run²)
From an angle: rise = tan(angle) × 12, then the ratio is rise/12
Total rafter = roof length × rafter ÷ run | Rafter factor = rafter ÷ 12
The X/12 ratio is the trade’s native language because it can be checked with a tape measure: a 6/12 roof climbs 6 inches for every 12 inches of level distance. Degrees suit engineering drawings and digital levels, and slope percentage suits drainage and accessibility work. The calculator keeps all three in view so nothing is lost translating between them. For the sloped area that follows from the rafter factor, the gable roof area calculator carries the material math forward, and the lean-to roof slope calculator handles the single-plane shed-roof case with its own asymmetric framing.
Worked example: 6/12 pitch on a 20-foot run
The calculator opens with rise 6, run 12 and a 20-foot roof length. Clicking Calculate gives a pitch angle of 26.57°, a ratio of 6/12, slope 50.00%, rise 6.00 inches, run 12 inches, rafter 13.42 inches per foot, total rafter 22.36 feet, and roof type Conventional. By hand: arctan(6/12) = arctan(0.5) = 26.565°, and √(36 + 144) = √180 = 13.416 inches of rafter.
The conversion table below is a set of real runs of this calculator in ratio mode, so every row reproduces exactly if you type the pitch in.
| Pitch | Angle | Slope % | Rafter per foot | Calculator’s roof type |
|---|---|---|---|---|
| 3/12 | 14.04° | 25.00% | 12.37 in | Conventional |
| 4/12 | 18.43° | 33.33% | 12.65 in | Conventional |
| 6/12 | 26.57° | 50.00% | 13.42 in | Conventional |
| 8/12 | 33.69° | 66.67% | 14.42 in | Steep |
| 12/12 | 45.00° | 100.00% | 16.97 in | Very Steep |
What the roof-type label means, and what it does not
The calculator labels every result Low Slope (under 10°), Conventional (10° to 30°), Steep (30° to 45°) or Very Steep (45° and up). Those are the tool’s own working bands, chosen for quick orientation. Trade convention is close but not identical, as the comparison shows.
| Pitch range | This calculator says | Common trade convention |
|---|---|---|
| ≤ 2/12 (≤ 9.5°) | Low Slope | Low slope; membrane roofing territory |
| 3/12 to 6/12 (14° to 26.6°) | Conventional | Conventional; 4/12 is the usual shingle minimum |
| 7/12 to 11/12 (30.3° to 42.5°) | Steep | Steep; harnesses and staging enter here |
| 12/12 and up (≥ 45°) | Very Steep | Steep; not walkable |
The one visible difference: the calculator calls a 3/12 roof “Conventional” where many roofers still file it under low slope, and it reserves “Very Steep” for 12/12 and up. Neither label changes any number on the page; use them as orientation and check material and safety requirements against the actual pitch. Fall-protection rules for steep work, including OSHA’s steep-roof provisions in 29 CFR 1926.501, key off the real slope, not the label.
What competing calculators miss
Roof pitch tools are plentiful, and most stop at rise and run:
- Rise/run-only calculators (FIRGELLI, Chippy Tools and the standard roofing-site tools): solid angle, ratio, slope and rafter outputs, but no way to start from a measured angle or a known pitch ratio. If your digital level reads 33.7°, you convert it yourself first.
- Chart-led pages (RoofPitch.net, FreeRoofPitch’s pitch chart): excellent reference tables of every pitch from 0/12 to 24/12, but static. They answer “what is 8/12 in degrees” and not “what is my roof”.
- Material-first calculators (RoofGenius’s multiplier framing): the strongest rival approach, wiring the pitch multiplier and hip/valley factors into ordering math. Their worked examples (4.5/12 from a 24-inch level) are the standard to beat on the content side.
- Lean-to specialists (SageCalculator and similar): three input modes like this page, but built around the asymmetric single-plane case rather than the general pitch problem.
- The gap this page fills: three interchangeable input modes on one tool, so an angle reading converts straight to a 6.93/12 ratio without a detour; the rafter factor printed as a reading under every result for material math; and the roof-type bands disclosed against trade convention instead of presented as code.
Frequently asked questions
Use the inverse tangent: angle = arctan(rise ÷ run), converted to degrees. For a 6/12 pitch, arctan(6/12) = arctan(0.5) = 26.57°.
It means the roof rises 6 inches for every 12 inches of horizontal run. That is a 26.57° angle, a 50.00% slope, and 13.42 inches of rafter per foot of run.
Multiply the tangent of the angle by 12: a 30° reading gives tan(30°) × 12 = 6.93, so the roof is a 6.93/12 pitch. Use the Angle mode and the calculator does it for you.
The rafter factor is the rafter length divided by 12: at 6/12 it is 1.1180. Multiply any horizontal run by it for sloped rafter length, or any plan area by it for sloped roof area, which is what material orders are based on.
A zero run would mean dividing by zero, which has no angle. The calculator falls back to the standard 12-inch roofing run instead of failing. Enter your measured run rather than relying on that fallback.
They are the calculator’s own orientation bands: under 10° is Low Slope, 10° to 30° Conventional, 30° to 45° Steep, and 45° and up Very Steep. Trade convention generally treats ≤3/12 as low slope and ≥7/12 as steep, so use the labels as a guide, not a code definition.
Enter the horizontal run in feet, from wall to ridge. The calculator multiplies it by the rafter-to-run ratio to produce the sloped total rafter length.
Yes. The math is the same right triangle whatever you are building, so rise and run in any consistent unit give the correct angle and slope. The X/12 ratio and roof-type labels are roofing language, but the numbers transfer directly.
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References
- Occupational Safety and Health Administration. Duty to have fall protection, 29 CFR 1926.501. Accessed October 23, 2026.
- International Association of Certified Home Inspectors. Roof Pitch, inspection guide. Accessed October 23, 2026.
- This Old House. How to Calculate Roof Pitch. Accessed October 23, 2026.
- Family Handyman. How to Find Roof Pitch. Accessed October 23, 2026.
- Purplemath. Straight-Line Equations: Slope. Accessed October 23, 2026.