Roof Pitch Calculator

The old manuals meant something different by pitch

This page treats pitch and slope as the same thing, rise per 12 inches of horizontal run, because that is what current practice and the model codes do. It was not always so, and the difference is a factor of two rather than a nuance.

The US Navy's framing manual, Builder 3 & 2, NAVEDTRA 14044, sets out the older system exactly. It defines span as "the horizontal distance between the outside top plates", states that the "unit of span is also fixed, twice the unit of run, or 24 inches", and that "total run is equal to half the span". Then the definition that matters: "Pitch is the ratio of unit of rise to the unit of span." Rise over span, not rise over run.

So the roof this page calls 6/12 an older framing manual calls a quarter pitch, and both are correct about the same roof. The manual even gives the conversion, "unit of span (24 in.) x pitch = unit of rise", and works it: "1/8 pitch is given, so 24 x 1/8 equals 3", which is a 3/12 roof.

One correction this page owes to its own earlier wording. The term NAVEDTRA uses for the rise-over-run ratio is not slope, it is cut: "The term 'pitch' is gradually being replaced by the term 'cut'." Slope appears in the manual only as an informal description, never as a defined ratio. Slope winning out over cut came later. The clean fractions land on 3, 4, 6, 8, 9 and 12 twelfths, which is precisely why those became the standard pitches of the old books.

Working a roof out by hand

Take a building 40 feet by 30 feet with a 6/12 gable roof.

1. Plan area is 40 x 30 = 1,200 sq ft. That is the footprint, not the roof.
2. Slope is 6 / 12 = 0.5.
3. Angle is arctan(0.5) = 26.5651 degrees. The 26.5 you often see is rounded down; it rounds to 26.57.
4. Multiplier is the square root of (1 + 0.5 squared) = square root of 1.25 = 1.118034.
5. Roof surface is 1,200 x 1.118034 = 1,341.6 sq ft, about 11.8 percent more than the footprint.
6. Span is 30 feet, so the run of each side is 15 feet and the total rise at the ridge is 15 x 0.5 = 7.5 feet.

The multiplier is the secant of the pitch angle, which is why it grows slowly at first and then quickly. Two of them are exactly rational, because 5-12-13 and 3-4-5 are Pythagorean triples: a 5/12 roof is exactly 13/12 of its footprint and a 9/12 roof is exactly 5/4 of it. A 9/12 roof is 25 percent more surface with no rounding anywhere, which makes it the tidiest worked example in the whole subject.

Pitch, angle and multiplier for every whole-number pitch

Only 12/12 lands on a round angle. Every other entry in the angle column is irrational, which is why a roof specified in degrees and a roof specified in twelfths are almost never the same roof.

What the code requires at each slope

Minimum slopes from the International Residential Code. The 2024 edition is current and its R905.2.2 is character-for-character the 2021 sentence quoted below, so nothing here changed between them; the section numbers in this list are the ones both editions use. Figures are in units vertical per 12 units horizontal. Your jurisdiction may have adopted a different edition or amended it, so confirm locally.

• Asphalt shingles, 2:12. R905.2.2: "Asphalt shingles shall be used only on roof slopes of 2 units vertical in 12 units horizontal (17-percent slope) or greater. For roof slopes from 2 units vertical in 12 units horizontal (17-percent slope) up to 4 units vertical in 12 units horizontal (33-percent slope), double underlayment application is required."
• Wood shingles and shakes, 3:12 (R905.7.2, R905.8.2).
• Clay and concrete tile, 2.5:12, with double underlayment up to 4:12 (R905.3.2).
• Metal panels: 3:12 lapped without sealant, 0.5:12 with lap sealant, 0.25:12 standing seam (R905.10.2).
• Built-up roofs, 0.25:12, or 0.125:12 for coal tar (R905.9.1).

One of those parentheticals is wrong, and it is worth knowing which. The IRC gives the tile minimum as "21/2 units vertical in 12 units horizontal (25-percent slope)". Two and a half in twelve is 20.833 percent, which rounds to 21, not 25. The same error is in the 2018 edition. The International Building Code has it right, giving the identical slope as a "21-percent slope" at its section 1507.3.2. Every other parenthetical in the series checks out, so the likely cause is 25 being carried across from the 3:12 figures beside it.

Steepness, safety, and a rule that was withdrawn

This page used to say walkable pitch tops out around 6/12 and that above 8/12 most roofers use harnesses. Those are real numbers with a real history, and they are no longer the rule.

OSHA draws exactly one slope line. At 29 CFR 1926.500(b) a steep roof is "a roof having a slope greater than 4 in 12 (vertical to horizontal)" and a low-slope roof is one "having a slope less than or equal to 4 in 12". Above that line, 1926.501(b)(11) requires guardrails with toeboards, safety nets or personal fall arrest for work 6 feet or more above a lower level, and the warning lines and safety monitors allowed at or below 4:12 are not permitted. A 5/12 roof is already steep in the only sense that carries a penalty.

The 6/12 and 8/12 figures come from OSHA Instruction STD 3-0.1A, the 1999 interim guidelines for residential construction, which allowed slide guards "where the roof slope is 8 in 12 or less, and the fall distance, measured from the eave to the ground level, is 25 feet or less", with a separate tier at "Roof Slope: 6 in 12 or less". OSHA Instruction STD 03-11-002, effective 16 June 2011, cancelled it in as many words, and directed that residential builders "must comply with 29 CFR 1926.501(b)(13)". The trade rule of thumb is the memory of a withdrawn directive.

Edge cases the simple formula does not cover

• Valleys run shallower than the roof. Where two equal planes meet at a right angle in plan, the valley line crosses the plan at 45 degrees, so its horizontal run is longer by the square root of two for the same rise. The valley slope is the roof slope divided by 1.414214. NRCA's vice president of technical services puts it in Professional Roofing: "where roofs with a 4:12 slope intersect at a valley, the valley's actual slope is only about 3:12." Exactly, it is 2.83 in 12. A 4/12 roof carrying wood shingles therefore has a valley running below the 3:12 minimum for the material on it.
• Two different pitches do not average. Both planes must reach one ridge, so the ridge sits off centre and each side's run is the span times the other side's slope over the sum of the slopes. A 32 foot span with a 12/12 side and a 4/12 side gives runs of 8 and 24 feet, a common rise of 8 feet, and a blended multiplier of 1.144123. Averaging to 8/12 gives 1.201850 and overstates the roof by about 5 percent.
• Crickets are about width, not pitch. IRC R903.2.2 requires a cricket or saddle "on the ridge side of any chimney or penetration more than 30 inches (762 mm) wide as measured perpendicular to the slope". It covers any penetration, not only chimneys, and the 30 inches is measured perpendicular to the slope rather than horizontally.
• Ice barriers are about climate, not pitch. The IRC ties them to areas "where there has been a history of ice forming along the eaves causing a backup of water as designated in Table R301.2". A steep roof in a cold region needs one and a shallow roof in a warm one does not, so this is not a low-slope requirement however often it is described as one.
• Measure the run level, never along the roof. Rise is vertical and run is horizontal. Measuring the run up the slope gives you the rafter length instead, and the pitch you compute from it will be too shallow every time.

What this page does not know

It does arithmetic on the two numbers you type. It does not know your jurisdiction, which code edition your authority has adopted, what your local amendments change, or what your shingle manufacturer's warranty requires, and manufacturer minimums are sometimes stricter than code. Every code figure here is a starting point for a conversation with your building department, not permission.

Nothing you type leaves this page. The arithmetic runs in your browser. The rise and run are not sent to a server, are not written into the address bar, and are gone when you close the tab. There are no accounts and nothing to sign up for.

Related home calculators

• Roofing calculator for material quantity estimates.
• Rafter calculator for rafter length from the same rise and run.
• Angle converter for converting between degrees, radians, and other angle units.
• Triangle area calculator for the math behind the rise-run-hypotenuse right triangle.
• Pythagorean theorem calculator for finding the rafter length (hypotenuse) from rise and run.
• All home calculators.

Sources

• 2021 International Residential Code, sections R903.2.2, R905.1.2, R905.2.2, R905.3.2, R905.7.2, R905.8.2, R905.9.1 and R905.10.2, read through ICC Digital Codes, for every minimum slope and the cricket and ice-barrier rules.
• 2021 International Building Code, section 1507.3.2, for the 21 percent figure the IRC prints as 25.
• 29 CFR 1926.500(b) and 1926.501(b)(10), (b)(11) and (b)(13), for the steep-roof definition and the fall-protection trigger.
• OSHA Instruction STD 03-11-002, 16 June 2011, for the cancellation of STD 3-0.1A, whose 8-in-12 and 6-in-12 tiers are quoted from OSHA's own letters of interpretation.
• Builder 3 & 2, Volume 2, NAVEDTRA 14044, March 1994, chapter 2, for span, run, pitch and cut. Public domain.
• Mark S. Graham, "Roof slope guidelines", Professional Roofing, NRCA, August 2018, for the valley slope.

Angles, slope percentages and area multipliers in the table above are computed rather than quoted, and each was checked against its exact closed form where one exists.