Construction calculator

Free Roof Pitch calculator

Convert a roof pitch between every form it comes in. Enter the pitch as rise-per-12 or as a degree angle, and this calculator returns the x/12 ratio, the angle in degrees, the percent grade and the pitch multiplier — then uses your horizontal run to give the rafter line length, updated live, as you type.

InputsLive
Enter pitch as
Run units
Rise (per 12 in run)
/12
Horizontal run
ft
How the result is calculated
Roof pitch is the same slope written four ways. The calculator fixes the run at 12 and converts:angle = atan(rise ÷ 12), multiplier = √(1 + (rise ÷ 12)²)
  • angle — the arctangent of rise over 12, in degrees
  • percent — rise ÷ 12 × 100
  • multiplier — √(1 + (rise/12)²), also 1 ÷ cos(angle)
  • rafter — your horizontal run × the multiplier
The rafter run is your building dimension in feet, not the fixed 12 used for the pitch.
Check our examples
6/12 pitch, 15 ft run → gable roof4/12 pitch, 12 ft run → low slope30° angle, 16 ft run → designer's angle
Result
Roof pitch
26.57 degrees
A 6/12 pitch is a 50% grade and a ×1.118 multiplier. Over a 15 ft run the rafter is 16.77 ft.
Pitch (x/12)6/12
Percent grade50%
Pitch multiplier×1.118
Rafter line length16.77 ft
All four forms of this pitch
FormValue
Rise over run6/12
Angle (degrees)26.57°
Percent grade50%
Pitch multiplier×1.118

The rafter is the line length to the ridge centreline — add the eave overhang and deduct half the ridge-board thickness for the board you cut. Run is the horizontal distance to the ridge, usually half the span.

Rafter length is the line length, before overhang and ridge deductions. How accurate is this?

Results are estimates. Consult a professional.

How it's calculated

How the roof pitch calculator works

Roof pitch is the steepness of a roof, and it is the same number written four ways. US builders write it as rise in 12 — the inches a roof climbs for every 12 inches it runs across. A designer wants that as a degree angle. An engineer wants a percent grade. A framer wants the pitch multiplier that turns a flat run into the sloped length of the rafter. This calculator takes any pitch you have and returns all four, then uses your building's horizontal run to give the rafter length.

Enter the pitch as rise-per-12 or as a degree angle. The run for the conversions is always 12 by convention, so the math is fixed trigonometry. The run for the rafter is your real building dimension in feet, which is a separate input. Keeping those two runs apart is the one thing most people get wrong.

angle (deg) = atan(rise ÷ 12) × 180 ÷ π
percent grade = (rise ÷ 12) × 100
pitch multiplier = √(1 + (rise ÷ 12)²)
rafter length = horizontal run × pitch multiplier
Pitch-to-angle is the arctangent of rise over run; the pitch (slope) multiplier is the secant of that angle (1/cos) — standard right-triangle trigonometry. US roofing convention fixes the run at 12 inches, as in the ICC International Residential Code, which defines roof slope as "units vertical in 12 units horizontal" (IRC R905.2.2).

Why one pitch needs four numbers

Each trade reads slope in its own unit. The roofer orders shingles and quotes labour by the x/12 pitch. The architect draws the angle in degrees in a CAD model. The civil drawing calls out a percent grade. The framer cutting rafters needs the multiplier to know how long to cut. They all describe the same roof. The calculator does the conversion so a number from one trade is usable by the next.

The four forms

Roof pitch in x/12, degrees, percent, and multiplier

A pitch carries four equivalent values. Understand what each one measures and you can move between them without a chart.

Rise over run (x/12)

The ratio of vertical rise to a fixed 12-inch horizontal run. A 6/12 pitch rises 6 inches across 12 inches of run. This is the standard US way to call out a pitch, and it is the input a roofer expects.

Angle in degrees

The angle the roof makes with the horizontal. It is the arctangent of rise over run, so a 6/12 pitch is 26.57°. Degrees are what designers and CAD tools use, and what you set on a saw or a digital level.

Percent grade

Rise divided by run, times 100. A 6/12 pitch is a 50% grade because 6 is half of 12. Percent grade is common on engineering and site drawings, the same way road and ramp slopes are written.

Pitch multiplier

The factor that converts a flat horizontal distance into the sloped distance along the roof. It is √(1 + (rise/12)²), which is also 1/cos of the angle. For a 6/12 pitch it is 1.118, meaning the roof surface is 11.8% longer than its footprint. This is the number that turns run into rafter length and footprint into roof area.

Conversion chart

Roof pitch to degrees, percent, and multiplier chart

This table converts the common pitches between all four forms. The angle is the arctangent of rise over 12; the multiplier is √(1 + (rise/12)²). Use it as a quick reference, or enter any pitch in the calculator for an exact figure.

Pitch (x/12)Angle (degrees)Percent gradePitch multiplier
1/124.76°8.3%1.0035
2/129.46°16.7%1.0138
3/1214.04°25.0%1.0308
4/1218.43°33.3%1.0541
5/1222.62°41.7%1.0833
6/1226.57°50.0%1.1180
7/1230.26°58.3%1.1577
8/1233.69°66.7%1.2019
9/1236.87°75.0%1.2500
10/1239.81°83.3%1.3017
12/1245.00°100.0%1.4142

Angles rounded to two decimals. A 12/12 pitch is exactly 45°, a 100% grade, and a ×√2 (1.4142) multiplier — the point where rise equals run.

Example

A worked example: 6/12 pitch over a 15-foot run

Example: a common 6/12 gable roof, 15 ft from wall to ridge

Maria is framing a gable roof at the standard 6/12 pitch. The building is 30 ft wide, so the horizontal run from the outside wall to the ridge is half of that — 15 ft. She needs the angle for her saw, the percent grade for the plans, and the rafter line length to cut her lumber.

Step 1 — Convert the pitch to a degree angle

The angle is atan(6 ÷ 12) = atan(0.5) = 26.57°. That is the angle Maria sets on the saw and the bevel gauge.

Step 2 — Convert the pitch to a percent grade

Percent grade is (6 ÷ 12) × 100 = 50%. The roof rises half a foot for every foot it runs across.

Step 3 — Find the pitch multiplier

The multiplier is √(1 + 0.5²) = √1.25 = 1.118. The roof surface is 11.8% longer than the flat distance it covers.

Step 4 — Get the rafter line length

Multiply the 15 ft horizontal run by the multiplier: 15 × 1.118 = 16.77 ft. That is the line length of the rafter from the outside wall to the ridge, before any overhang or ridge-board deduction.

6/12 = 26.57° = 50% grade = ×1.118 → 16.77 ft rafter
One pitch, four numbers, plus the rafter. The 16.77 ft is the line length — the straight run along the slope. Add your eave overhang to that, then deduct half the ridge-board thickness, to get the board you actually cut.
Rafter length

How to find rafter length from run and pitch

Rafter length is where the two runs matter. The pitch conversions use a fixed run of 12. The rafter uses your real horizontal run — the distance from the outside wall to the ridge, in feet, which is normally half the building's span. The rafter is the hypotenuse of a right triangle whose base is that run and whose height is the rise over it.

horizontal run = span ÷ 2
rafter length = run × pitch multiplier
rafter length = √(run² + rise_over_the_run²)

Line length vs. the board you cut

The 16.77 ft from the worked example is the line length — the geometric run along the slope from the wall to the ridge centreline. The board you cut is different in two ways. Add the eave overhang (the tail past the wall) to make it longer. Deduct half the thickness of the ridge board, because the rafter stops at the ridge face, not its centre. Most framers cut to the line length plus overhang, then trim at the ridge.

Run is half the span
For a simple gable, the run is half the building width. A 30 ft-wide building has a 15 ft run on each side. Feed the run — not the full span — into the rafter calculation, or you will double your lumber.
Common pitches

Common roof pitches and what counts as walkable

Most US homes fall between 4/12 and 9/12. Below that range a roof reads as low-slope; above it, as steep. The pitch decides what you can install and how safely you can work on it.

Pitch rangeAngleCategoryWhat it means
Flat to 2/120° – 9.5°Low-slope / flatNeeds membrane roofing; shingles are not rated below 2/12
3/12 – 4/1214° – 18.4°Low conventionalShingles allowed with double underlayment from 2/12 to 4/12
5/12 – 9/1222.6° – 36.9°ConventionalThe common residential range; standard shingle installation
10/12 and up39.8°+SteepNeeds roof jacks and fall protection; not safely walkable

Walkable is roughly up to 6/12 (26.57°) for most people; past 8/12 (33.69°) you need staging and harnesses. The 2/12 shingle minimum and the 2/12–4/12 double-underlayment rule follow ICC IRC R905.2.2.

A 30-degree roof is close to a 7/12 pitch (6.93/12 exactly). A 45-degree roof is exactly 12/12, where the rise equals the run. Those two are the conversions people search for most.

Stock allowances

Rafter stock allowances: overhang, ridge, and birdsmouth

The calculator returns the line length. To buy and cut real rafters, you adjust that figure three ways. None of these is a percentage waste margin — each is a measured length you add or subtract.

  • Eave overhang (the tail) — the part of the rafter that runs past the wall to form the eave. Add it to the line length; a 12–24 in overhang is common, measured along the slope.
  • Ridge-board deduction — the rafter meets the ridge board at its face, not its centreline, so deduct half the ridge-board thickness from the line length.
  • Birdsmouth — the notch cut where the rafter sits on the top of the wall. It locates the seat cut; it does not change the line length but it sets where the tail begins.
Buy to the next standard length
Lumber comes in 2 ft increments (12, 14, 16 ft). A 16.77 ft line length plus a 1 ft overhang is about 17.8 ft, so you buy 18 ft (or 20 ft) stock and cut to fit. Buying to the next standard length is the only "waste" a pitch calculation carries.
Definitions

Roof pitch definitions

The vertical distance a roof climbs over a given run. In the x/12 pitch notation it is the "x" — the inches of climb per 12 inches of horizontal run.
The horizontal distance the roof covers. The pitch run is fixed at 12 inches by convention; the rafter run is the real building dimension in feet, usually half the span.
The full width of the building from outside wall to outside wall. For a symmetrical gable, the run to the ridge is half the span.
The slope factor √(1 + (rise/12)²), equal to 1/cos of the pitch angle. It converts a horizontal run into the sloped rafter length and a flat footprint into roof area.
The straight-line distance along the slope from the outside wall to the ridge centreline. It is the geometric length, before adding the eave overhang or deducting half the ridge board.
The triangular notch cut into a rafter so it seats flat on the top plate of the wall. It locates the rafter on the wall and sets where the overhang tail begins.
FAQ

Roof pitch questions, answered

A 30-degree roof is about a 7/12 pitch. Exactly, 30° is a rise of 12 × tan(30°) = 6.93 per 12 of run, which rounds to 7/12. The percent grade is roughly 57.7%.
It is the factor √(1 + (rise/12)²) that converts a flat horizontal distance into the sloped distance along the roof. For a 6/12 pitch it is 1.118, so the rafter and the roof surface are 11.8% longer than the footprint they cover.
Exactly 45 degrees. At 12/12 the rise equals the run, so the angle is atan(12/12) = atan(1) = 45°, and the percent grade is 100%. It is the steepest of the "even" pitches.
Up to about 6/12 (26.57°) is walkable for most people with care. From 7/12 to 8/12 it gets risky without roof jacks; past 8/12 (33.69°) you need staging and a harness. Wet or mossy roofs are far less walkable than the angle alone suggests.
Yes. Asphalt shingles are allowed down to 2/12 under the IRC, but from 2/12 to 4/12 the code requires double underlayment. A 3/12 roof is fine for shingles with that double-underlayment detail; below 2/12 you need membrane roofing instead.
A roof that rises 4 inches for every 12 inches of run. That is an 18.43-degree angle, a 33.3% grade, and a 1.0541 multiplier. It is the lower end of the common conventional range and the usual threshold for standard shingle installation.
Accuracy

How accurate is this roof pitch calculator?

The conversions are exact trigonometry. The angle is the arctangent of rise over 12, the percent grade is rise over run times 100, and the multiplier is √(1 + (rise/12)²) — there is no estimation in any of them. Enter a pitch and the four forms are right to the decimal.

The rafter length is exact for the run you enter, but the run and the finished board are on you. Make sure the run is the horizontal distance to the ridge — half the span on a symmetrical gable — not the full building width. The result is the line length; add your eave overhang and deduct half the ridge-board thickness to get the board you cut. For the surface area and material side of a roof, pair this with the roofing calculator and the concrete calculator for footings and piers.

Trigonometric conversions are exact and standard (arctangent for the angle, secant for the multiplier). Slope categories, the 2:12 shingle minimum, and the 2:12–4:12 double-underlayment rule follow the ICC International Residential Code (IRC R905.2.2). Common-pitch and walkability ranges follow published roofing references (Omni Calculator, MyCarpentry).
Questions

Frequently asked questions about the free Roof Pitch calculator

A roof Pitch calculator is a free online tool that helps you convert roof pitch between x/12, degrees, percent grade and the pitch multiplier, and find rafter length from the run. Roof pitch is one slope written four ways. The calculator fixes the run at 12 to convert between forms, then uses your building's horizontal run for the rafter length. It runs entirely in your browser with instant results and no sign-up.
About a 7/12 pitch. Exactly, 30° is a rise of 12 × tan(30°) = 6.93 per 12 of run, which rounds to 7/12 — roughly a 57.7% grade.
The factor √(1 + (rise/12)²) that converts a flat horizontal distance into the sloped distance along the roof. For a 6/12 pitch it is 1.118, so the rafter is 11.8% longer than the run it covers.
Exactly 45 degrees. At 12/12 the rise equals the run, so atan(12/12) = atan(1) = 45°, which is also a 100% grade.
Up to about 6/12 (26.57°) is walkable for most people with care. From 7/12 to 8/12 it gets risky without roof jacks; past 8/12 you need staging and a harness.
Yes. Asphalt shingles are allowed down to 2/12 under the IRC, but from 2/12 to 4/12 the code requires double underlayment. Below 2/12 you need membrane roofing instead.
About

About this roof pitch calculator

This roof pitch calculator runs entirely in your browser — nothing you type is sent anywhere or stored. It converts a pitch between rise-over-run (x/12), degrees, percent grade and the pitch multiplier using exact trigonometry, and derives the rafter line length from your horizontal run, recomputing the moment you change an input.

It is one of the construction calculators on calculator-s.cloud — pair it with the roofing calculator for area and shingles. Browse every tool in the full calculator directory.

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