Roof Pitch Chart — Degrees, Multiplier & Rafter Length

What roof pitch means

Roof pitch is the steepness of a roof expressed as a rise over a fixed run of 12 inches: a roof that climbs 4 inches for every 12 inches of horizontal travel is a 4:12 pitch. The convention is handy because the run is always 12, so the pitch number is also the rise in inches per foot — a 6:12 roof rises exactly 6 inches for every foot you move sideways under it. Everyone from the framer with a speed square to the estimator reading a plan uses that same 12-inch base.

Pitch is not the same as the angle, and it is not the same as the percentage slope, even though all three describe one incline. The angle in degrees is the arctangent of the pitch over 12; the percentage is the pitch over 12 times 100. A 6:12 roof is 26.57 degrees and a 50 percent slope at the same time. Plans from outside the US often give degrees only, so the chart below carries all three columns to remove the ambiguity.

The roof pitch chart — pitch, angle, multiplier and hip factor

The slope multiplier (also called the slope factor or the common-rafter factor) is the column people actually came for: it converts a flat plan area into the real sloped surface. The hip & valley factor is the longer version used for the diagonal rafters at a hip or valley. Both are computed here from the pitch using the formulas on this page, not copied from a flyer.

Read the table at the two ends to see why pitch matters so much. A low 2:12 roof has a multiplier of 1.0138 — the sloped surface is only 1.4 percent bigger than the footprint, so a 1,000 ft² plan is a 1,014 ft² roof. A steep 12:12 roof has a multiplier of 1.4142, so the same 1,000 ft² plan is a 1,414 ft² roof. Between the two lies a 40 percent swing in the material order for the identical footprint.

The multiplier — how a flat area becomes a sloped roof

The multiplier comes straight from the right triangle the roof forms. Over a 12-inch horizontal run the roof rises by the pitch, so the slope length of that little triangle is the hypotenuse:

Check a 6:12. Pitch/12 = 0.5, so the multiplier is √(1 + 0.25) = √1.25 = 1.1180 — the figure in the chart. The rafter triangle for a 20 ft run then has a length of 20 × 1.1180 = 22.36 ft and a rise of 20 × 0.5 = 10 ft, and those three numbers close as a right triangle: 20² + 10² = 500 = 22.36². The multiplier is just the Pythagorean theorem applied once.

Worked example — pricing a roof from its footprint

A simple gable roof covers a 30 ft × 40 ft house at a 6:12 pitch, and you need the roof area for a shingle order.

• Plan area. 30 × 40 = 1,200 ft². This is the flat area under the roof, which is what a real-estate footprint gives you.
• Multiplier. At 6:12 the chart gives 1.1180.
• Roof area. 1,200 × 1.1180 = 1,342 ft² of actual sloped surface. Shingles are sold by the square (100 ft²), so that is about 13.4 squares — order 14 to cover laps, hips, valley and waste.
• Rafter check. Half the 30 ft span is a 15 ft run. Rafter length = 15 × 1.1180 = 16.77 ft, and the rise at the ridge = 15 × 0.5 = 7.5 ft. Add for overhang and the ridge board before cutting.

Every figure in that estimate keys off the single multiplier from the chart, and the converter above reproduces all of them from your own dimensions.

Hip and valley rafters

A hip rafter runs diagonally from a corner of the building to the ridge, and a valley rafter does the same in the re-entrant corner where two roof planes meet. Both travel farther than the common rafters beside them, because they cross the plan at an angle instead of straight up the slope. For the usual case — a hip running at 45° in plan at the same pitch as the commons — the factor is:

Hip & valley factor = √(2 + (pitch/12)²). At 6:12 that is √2.25 = 1.5000, so a hip whose plan run is 20 ft is 20 × 1.5 = 30 ft long. The table above lists the factor for every pitch. Where the two roof planes have different pitches, or the hip is not at 45° in plan, the simple factor no longer applies and the rafter is laid out per the individual pitches.

Minimum pitch by roofing material

Roofing materials are rated by the lowest pitch they are allowed on, because low-slope roofs drain slowly and are more exposed to wind-driven rain and ice dams. The clearest rule is in the code: IRC R905.2.2 permits asphalt shingles only on slopes of 2:12 or greater, and from 2:12 up to 4:12 it requires double underlayment — two layers — beneath them. Below 2:12 asphalt shingles are not permitted at all, and the roof becomes a low-slope membrane job: rolled roofing, EPDM, TPO or modified bitumen.

Other materials have their own floors, generally set by the manufacturer rather than the code: standing-seam metal can go down to about ¼:12 with the right panel profile and seams, tile and slate usually ask for 2½:12 or 3:12 and up, and wood shakes sit in the middle. Whoever makes the product sets the minimum in the installation instructions, and that instruction is what an inspector enforces, so read the actual spec sheet before you commit a low-slope roof to a material.

Common mistakes with roof pitch

• Using the footprint as the roof area. A flat length × width is the plan area, not the sloped surface. Skip the multiplier and you under-order every steep roof — by 41 percent at 12:12.
• Mixing pitch and angle. A "6 pitch" is not 6 degrees and not a 6 percent slope. It is 6 in 12, which is 26.57 degrees and 50 percent. Say "6:12" and there is no argument.
• Using the common-rafter factor for a hip. The hip and valley factor is larger (√(2 + slope²), not √(1 + slope²)). Applying the common factor to a hip rafter cuts it short.
• Forgetting that pitch is measured on the run, not the slope. The 12 in "x:12" is horizontal. Measuring 12 inches along the rafter instead of along the level gives a pitch that is too low on any steep roof.
• Assuming the lowest pitch a material "can" go is the lowest it may go. The code or the manufacturer sets a hard minimum, and 2:12 to 4:12 has an extra requirement — double underlayment — that a plain install misses.
• Reading a plan that quotes degrees as if it were pitch. A "30°" roof is roughly a 7:12, not a 30:12. Convert before you order anything.

Roof pitch FAQ

Where these numbers came from

Every angle, multiplier and hip factor on this page is computed from the pitch itself using angle = arctan(pitch/12) and multiplier = √(1 + (pitch/12)²), then cross-checked on 2026-10-03 against the Everlast Roofing Slope Factor Chart, which lists the same multipliers from 1:12 to 12:12 (3:12 = 1.0308, 4:12 = 1.0541, 6:12 = 1.1180, 8:12 = 1.2019, 12:12 = 1.4142) and whose own valley and hip column reproduces √(2 + (pitch/12)²) exactly. The angles agree with the published pitch-to-degree charts (3:12 = 14.04°, 4:12 = 18.43°). The shingle minimum and the double-underlayment range are quoted from IRC R905.2.2.

This is a working reference, not engineering or a roofing specification. Pitch geometry is exact, but every material has its own minimum slope in its installation instructions, and structural questions — rafter size, snow load, wind uplift — are separate calculations. Confirm the material limits and the structural design against the code your authority having jurisdiction enforces.

Related pages

• Deck joist span table — IRC 2021 R507.6 — the span side of structural framing, for the deck under the roof line
• Deck beam & joist span calculator — turns the span tables into one layout
• Rebar size chart — ASTM A615 — bar diameter, area and weight, the other table people look up by number
• Wire ampacity chart — NEC Table 310.16 — the electrical counterpart
• Reference tables — every code table, with its source and verification date