Roof Pitch to Degrees: Chart, Formula, and the Multiplier for Ordering Shingles

A roofer says “six-twelve” and a shingle wrapper wants square feet. Neither one gives you degrees, and degrees are not what you need anyway. The number that matters when you order shingles is the area multiplier, because a 2,000 sq ft footprint under a 6/12 roof is 2,236 sq ft of roof. Order against the footprint and you come up 236 sq ft short before you count a single cut or waste piece.

Below: the full 1/12 to 12/12 chart with degrees, percent slope, and the area multiplier side by side, the two formulas behind it, one worked footprint-to-bundles example, and the code minimum for asphalt shingles. Every number in the chart was computed from the same formulas our roof pitch calculator uses.

What “6/12” means

Roof pitch, the way the trade says it, is inches of rise per 12 inches of horizontal run. A 6/12 roof climbs 6 inches for every foot you move in toward the ridge. You might see it written 6/12, 6:12, or 6-in-12. They are the same thing.

Strictly speaking, that ratio is the slope. Wikipedia’s roof pitch article defines pitch as total rise over total span (the full width of the building), and notes that the markings on a framing square are slope, not pitch. Under that definition, a 6/12 roof on a 24 ft wide house rises 6 ft over a 24 ft span, which is a “1/4 pitch”. Almost nobody on a job site talks that way today. If someone says “pitch” and a number over 12, they mean rise over run, and so does this post.

The formulas

degrees      = atan(rise / 12)
percent      = rise / 12 × 100
multiplier   = √(rise² + 12²) / 12
roof area    = footprint area × multiplier

The multiplier is just the Pythagorean theorem. For every 12 inches of run, the roof surface travels along the hypotenuse of a triangle with legs of 12 and the rise. At 6/12 that is √(36 + 144) = √180 = 13.416 inches of roof per 12 inches of floor plan, and 13.416 / 12 = 1.118.

The same multiplier gives you rafter length per foot of run. A steel framing square’s rafter table prints it in inches per foot of run: 13.42 at 6/12.

Roof pitch to degrees chart

All values computed with Math.atan and Math.sqrt in Node, rounded to two decimals for angles and three for the multiplier. The last column applies the multiplier to a 2,000 sq ft footprint.

Pitch	Degrees	Percent slope	Area multiplier	2,000 sq ft footprint becomes
1/12	4.76°	8.3%	1.003	2,007 sq ft
2/12	9.46°	16.7%	1.014	2,028 sq ft
3/12	14.04°	25.0%	1.031	2,062 sq ft
4/12	18.43°	33.3%	1.054	2,108 sq ft
5/12	22.62°	41.7%	1.083	2,167 sq ft
6/12	26.57°	50.0%	1.118	2,236 sq ft
7/12	30.26°	58.3%	1.158	2,315 sq ft
8/12	33.69°	66.7%	1.202	2,404 sq ft
9/12	36.87°	75.0%	1.250	2,500 sq ft
10/12	39.81°	83.3%	1.302	2,603 sq ft
11/12	42.51°	91.7%	1.357	2,713 sq ft
12/12	45.00°	100.0%	1.414	2,828 sq ft

A few things jump out:

Degrees are not linear in pitch. Going from 1/12 to 2/12 adds 4.7 degrees. Going from 11/12 to 12/12 adds 2.5.
The multiplier barely moves on low roofs. Below 4/12 you are within about 3% of the footprint. Above 8/12 it climbs fast. A 12/12 roof has 41% more surface than its footprint.
9/12 is the clean one. It is the 3-4-5 triangle (9, 12, 15), so the multiplier is exactly 1.25 and the angle is 36.87 degrees.
12/12 is 45 degrees and √2. Rise equals run, so the roof surface is the diagonal of a square.

To go the other way, from an angle you measured with a phone level or an angle finder, use rise = 12 × tan(degrees). Thirty degrees comes out to 6.93, so it is a hair under 7/12. The roof pitch calculator accepts degrees, percent, or any rise and run you measured (say, 5 inches over 10) and converts to x/12.

Worked example: footprint to bundles

Say a simple gable house measures 50 ft by 40 ft from above, overhangs included. That is a 2,000 sq ft plan area. The roof is 6/12.

Roof area. 2,000 × 1.118 = 2,236 sq ft.
Squares. Roofing is sold by the square, which is 100 sq ft. 2,236 / 100 = 22.36 squares.
Waste. Add about 10% for a simple gable (starter rows, cut ends at the rakes, ridge). 22.36 × 1.10 = 24.6 squares.
Bundles. Standard 3-tab and most architectural shingles come 3 bundles to the square. 24.6 × 3 = 73.8, so buy 74 bundles.

Skip step 1 and order off the footprint, and you get 20 squares plus 10% = 22 squares = 66 bundles. That is 8 bundles short, which on a Saturday means a second trip to the yard with half the roof stripped.

Two notes on the plan area. First, measure it including overhangs, because the shingles cover the eaves too. Second, the multiplier works for a hip roof as well, as long as every face has the same pitch. The hips change the shape of each face, not the ratio between plan area and surface area. Hip roofs do waste more shingles in cutting, which is why 15% is a common waste figure for them instead of 10%.

Our roofing calculator does this whole chain. Enter the building length, width, and overhang (or a plan area you already know), the pitch, and gable or hip. It returns roof area, squares, bundles with your waste percentage applied, underlayment rolls (synthetic, #15, or #30 felt), ridge cap, starter strip, drip edge pieces, and pounds of nails. Every default, like bundles per square or waste, is editable, and an optional cost per square gives you a material total.

Minimum pitch for asphalt shingles

Low roofs are where the multiplier stops being your main worry. Shingles shed water by gravity and overlap. Too flat and wind-driven rain backs up under the tabs.

The International Residential Code covers this in Section R905.2.2. The text reads: “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 in accordance with Section R905.1.1.”

So in chart terms:

Pitch	Asphalt shingles under the IRC
Below 2/12	Not allowed. Use a low-slope membrane or other covering.
2/12 up to 4/12	Allowed, with two layers of underlayment
4/12 and up	Allowed, standard single-layer underlayment

The code’s “17-percent” is rounded. The chart above shows 2/12 as 16.7%. The two-layer method in the code’s underlayment table starts with a 19-inch strip at the eave, then 36-inch sheets, each lapping the one below by 19 inches (half a sheet plus 1 inch). Your local jurisdiction may amend the IRC, and the shingle manufacturer’s instructions can be stricter than the code, so check both before you roof a 3/12 porch.

Low-slope roofs also need more underlayment than the area alone suggests. If you are between 2/12 and 4/12, plan on a bit more than double the underlayment rolls the calculator gives you, since each 36-inch sheet laps the one below by 19 inches.

The same rise-over-run idea elsewhere

Roof pitch is one instance of a ratio that shows up all over a house.

Gutters. Steeper roofs catch more wind-driven rain, so gutter sizing also uses a pitch factor. It is not the geometric multiplier, though. Our gutter calculator uses the SMACNA table’s stepped factors (1.00 up to 3/12, 1.05 at 4/12 and 5/12, up to 1.30 at 12/12 and steeper) to turn your footprint into a design drainage area.
Ramps. The ADA maximum running slope for a ramp is 1:12. Written as a roof pitch, that is 1/12, the first row of the chart: 4.76 degrees, 8.3%. The ramp slope calculator works out run length, landings, and handrail needs from your rise.
Stairs. A stair is rise over run too, just with a riser and a tread instead of 12 inches. The stair calculator works out riser count and tread depth and checks them against the IRC stair limits.

If you are ordering materials by area for other parts of the job, the same “measure in plan, convert to what the yard sells” logic applies to gravel and soil, which is covered in cubic yards, tons, and density.

Quick reference

Remember three anchors: 4/12 is 18.43 degrees and 1.054, 6/12 is 26.57 degrees and 1.118, 12/12 is 45 degrees and 1.414. For anything else, the roof pitch calculator converts between x/12, degrees, and percent, shows the full multiplier table, sizes common rafters (span, overhang, ridge board), and multiplies a footprint into roof area and squares. When you are ready to buy, the roofing calculator turns that area into a shopping list.