Roof Pitch Calculator
Pitch as X in 12, the angle, grade and pitch factor from a rise and run, a pitch or an angle, plus the rafter line length with overhang and the roof area in squares.
The working
X = Rise ÷ Run × 12
= 6 in ÷ 12 in × 12
= 6 in 12
Angle = atan(Rise ÷ Run)
= atan(0.5)
= 26.57°
Grade = X ÷ 12 × 100
= 6 ÷ 12 × 100
= 50%
Pitch factor = √(1 + (X ÷ 12)²)
= √(1 + (6 ÷ 12)²)
= 1.1180
Rafter per foot of run = 12 in × factor
= 12 × 1.1180
= 13.42 in
Roof pitch
in 12
6:12, a rise of 6 in for every 12 in of level run.
- Roof angle
- 26.57°
- Grade
- 50%
- Pitch factor
- 1.118
- Rafter per foot of run
- 13.42in
- Hip or valley per foot of run
- 18in
Roofers talk in X in 12, framers in rise per foot of run, and an angle finder reads in degrees. Enter whichever you have and the calculator gives the others, with the pitch factor that turns a level run into a rafter line length and a footprint into a roof area. Add the building span for the rafter, and the footprint or the measured planes for squares. Waste and bundles per square stay yours to enter.
How this calculator works
Only your inputs and exact unit conversions. Where a figure comes from anywhere else, it is recorded below with its source.
- Formula version
- 1.0.0
- Last reviewed
- 2026-09-29
- External data
- 5 sources
- Category
- Measurement
What this calculates
Pitch is written as the rise in inches for every 12 in of level run: X in 12, X:12 or X/12. From a rise and a run, a pitch or an angle, the calculator returns the other two, the percent grade, the pitch factor and the rafter line length per foot of run. With a building span it adds the rafter line length and the tail for an overhang. With a footprint or measured planes it adds the roof area in square feet and in squares.
The relationships
With r = rise ÷ run: the pitch is X = 12r, the angle is atan(r), the grade is 100r and the pitch factor is √(1 + r²), which is also 1 ÷ cos(angle). All of it is exact; nothing is looked up.
The factor is how much longer a line up the slope is than its level run. Times 12 in, it is the rafter line length for each foot of run, which the US Navy’s Builder manual calls the bridge measure. A hip or valley between two equal pitches meeting at a square corner runs diagonally in plan, √2 ft for each foot of common run, so its length per foot of common run is 12 × √(2 + r²) in.
Span, run and overhang
The rafter inputs follow the US Navy’s Builder training manual (Chapter 2, Roof Framing). It defines span as "the horizontal distance between the outside top plates", total run as half the span, and projection, the overhang, as "the horizontal distance from the building line to the rafter tail". All three are level measurements. A shed roof has one slope across the whole span, so its rafter run is the span.
Owens Corning’s roofing glossary measures span "from eave to eave", which takes in the overhangs, and defines run as half of that. The two definitions differ by the overhangs, so this calculator asks for the span between the wall plates and the overhang separately.
Rafter line length
The Navy manual defines line length as the hypotenuse of the triangle whose base is the total run and whose altitude is the total rise, measured along the rafter from the outside edge of the top plate to the centre line of the ridge. Here that is run × factor. The tail for an overhang is the level projection × factor, the manual’s bridge measure × projection.
A ridge board sits between the rafters, so each rafter stops at its face, half the board’s thickness from the centre line. The manual calls this shortening and deducts half the ridgeboard from each rafter. Here half the thickness you enter comes off the level run, measured square to the plumb cut, before the factor is applied, so the line length shortens by half the thickness × the pitch factor. The manual’s layout step instead marks half the thickness along the line length. The two differ by the pitch factor: at 6:12 with a 1.5 in board, the line length shortens by 0.75 in marked along it, against 0.84 in with the level deduction this calculator uses. That board is an example only: the field starts empty and no thickness is assumed.
Line length is a measuring line, not a board length. Plumb and seat cuts, the birdsmouth, the rafter depth and the length of lumber to buy are not modelled.
Roof area and squares
From a footprint: roof area = footprint × factor. Every roof plane is larger than its outline seen from above by exactly the pitch factor, so for a roof whose planes all share one pitch, hip or gable, the total is exact. Measure the footprint to the edge of the overhangs, and run any part at another pitch on its own.
From measured planes: the length × width of each plane, added up, as GAF’s roofing-square article describes. The pitch does not enter, because those measurements are already along the slope.
Squares = roof area ÷ 100. Owens Corning’s glossary defines a square as "a unit of roof measure covering 100 square feet", and GAF’s article gives the same 10 × 10 ft. Squares are the area, not an order: waste, starters, ridge caps and bundles per square are yours to enter.
What this calculator does not decide
It does not label a pitch low, standard, steep, walkable or snow-shedding, and it does not check a pitch against a roofing product. A sourced pitch for walking on a roof or for shedding snow was not found in the sources reviewed. Where a code limit helps, it is quoted with its section and edition: see the asphalt shingle question below.
A 24 ft gable at 6:12 with a 12 in overhang
No ridge board entered, so the rafter is measured to the ridge centre line. The footprint is measured to the edge of the overhangs: the span plus a 12 in overhang at each eave, by 40 ft along the ridge with no overhang at the gable ends.
- Pitch
- 6 in 12
- Building span
- 24 ft, outside of the wall plates
- Overhang
- 12 in, level, at each eave
- Length along the ridge
- 40 ft, no overhang at the gable ends
- 01r = X ÷ 12= 6 ÷ 12= 0.5
- 02Angle = atan(r)= atan(0.5)= 26.5651°
- 03Grade = r × 100= 0.5 × 100= 50%
- 04Pitch factor = √(1 + r²)= √(1 + 0.5²)= 1.118034
- 05Run = Span ÷ 2= 24 ÷ 2= 12 ft
- 06Total rise = Run × r= 12 × 0.5= 6 ft
- 07Line length = Run × factor= 12 × 1.118034= 13.4164 ft
- 08Tail = Overhang × factor= 1 × 1.118034= 1.1180 ft
- 09Line length with overhang= (12 + 1) × 1.118034= 14.5344 ft (14 ft 6 7/16 in)
- 10Footprint width = Span + 2 × Overhang= 24 + 2 × 1= 26 ft
- 11Footprint = Length × Width= 40 × 26= 1,040 sq ft
- 12Roof area = Footprint × factor= 1,040 × 1.118034= 1,162.76 sq ft
- 13Check: 2 planes × Line length with overhang × Length= 2 × 14.534442 × 40= 1,162.76 sq ft
- 14Squares = Roof area ÷ 100= 1,162.76 ÷ 100= 11.63
14.5344 ft with the overhang; 11.63 squares
Roof pitch chart, 1:12 to 24:12
Every cell is computed from the pitch X: angle = atan(X ÷ 12), grade = X ÷ 12 × 100, pitch factor = √(1 + (X ÷ 12)²), rafter per foot of run = 12 × factor, and hip or valley per foot of common run = 12 × √(2 + (X ÷ 12)²).
| Pitch | Angle (°) | Grade (%) | Pitch factor | Rafter per ft of run (in) | Hip or valley per ft of common run (in) |
|---|---|---|---|---|---|
| 1:12 | 4.76 | 8.33 | 1.0035 | 12.04 | 17.00 |
| 2:12 | 9.46 | 16.67 | 1.0138 | 12.17 | 17.09 |
| 3:12 | 14.04 | 25.00 | 1.0308 | 12.37 | 17.23 |
| 4:12 | 18.43 | 33.33 | 1.0541 | 12.65 | 17.44 |
| 5:12 | 22.62 | 41.67 | 1.0833 | 13.00 | 17.69 |
| 6:12 | 26.57 | 50.00 | 1.1180 | 13.42 | 18.00 |
| 7:12 | 30.26 | 58.33 | 1.1577 | 13.89 | 18.36 |
| 8:12 | 33.69 | 66.67 | 1.2019 | 14.42 | 18.76 |
| 9:12 | 36.87 | 75.00 | 1.2500 | 15.00 | 19.21 |
| 10:12 | 39.81 | 83.33 | 1.3017 | 15.62 | 19.70 |
| 11:12 | 42.51 | 91.67 | 1.3566 | 16.28 | 20.22 |
| 12:12 | 45.00 | 100.00 | 1.4142 | 16.97 | 20.78 |
| 13:12 | 47.29 | 108.33 | 1.4743 | 17.69 | 21.38 |
| 14:12 | 49.40 | 116.67 | 1.5366 | 18.44 | 22.00 |
| 15:12 | 51.34 | 125.00 | 1.6008 | 19.21 | 22.65 |
| 16:12 | 53.13 | 133.33 | 1.6667 | 20.00 | 23.32 |
| 17:12 | 54.78 | 141.67 | 1.7341 | 20.81 | 24.02 |
| 18:12 | 56.31 | 150.00 | 1.8028 | 21.63 | 24.74 |
| 19:12 | 57.72 | 158.33 | 1.8727 | 22.47 | 25.48 |
| 20:12 | 59.04 | 166.67 | 1.9437 | 23.32 | 26.23 |
| 21:12 | 60.26 | 175.00 | 2.0156 | 24.19 | 27.00 |
| 22:12 | 61.39 | 183.33 | 2.0883 | 25.06 | 27.78 |
| 23:12 | 62.45 | 191.67 | 2.1619 | 25.94 | 28.58 |
| 24:12 | 63.43 | 200.00 | 2.2361 | 26.83 | 29.39 |
There is no category, walkability, snow or material column. The sourced slope bands found are the 2024 IRC’s asphalt-shingle limits (R905.2.2) and Owens Corning’s shingle application methods, both quoted in the questions below; a sourced pitch for walking on a roof or for shedding snow was not found in the sources reviewed. The hip or valley column assumes equal pitches meeting at a square corner.
What it assumes
- 01Run, span and overhang are level measurements; rise is plumb.
- 02A gable has two equal slopes, so its rafter run is half the span. A shed rafter runs the whole span.
- 03Footprint modes: every plane of the roof has the pitch entered.
- 04Planes mode: each plane is a rectangle of the size entered, measured along the roof.
- 05A roofing square is 100 sq ft (Owens Corning; GAF).
What it does not do
- Rafter length is the line length along the measuring line (US Navy definition), not a board length. Plumb, seat and tail cuts, the birdsmouth and lumber lengths are not modelled.
- Beyond the per-foot hip or valley figure, hip, valley and jack rafter lengths are not calculated, and that figure assumes equal pitches meeting at a square corner.
- A roof with more than one pitch, dormers or curved surfaces needs each part entered separately.
- Squares are the roof area, not an order quantity. Waste, starter courses and ridge caps are your own allowance.
- No minimum pitch, walkability or snow guidance of its own. A code limit is quoted only where a section can be cited.
Common questions.
- How do you calculate roof pitch?
- Divide the rise by the run and multiply by 12. The answer is the rise in inches for every 12 in of level run, written X:12 or X/12. A roof that rises 4 ft over a 12 ft run is 4 ÷ 12 × 12 = 4:12. Measure the run level, not along the roof: hold a level horizontal with one end on the roof, mark 12 in along it, and the plumb distance from the mark down to the roof is X.
- What is a 4/12, 5/12, 6/12 or 12/12 pitch in degrees?
- 4/12 is 18.43°, 5/12 is 22.62°, 6/12 is 26.57° and 12/12 is exactly 45°. Each is atan(X ÷ 12). The chart above lists 1/12 to 24/12 with the grade and pitch factor.
- How do I convert degrees to pitch?
- Pitch = 12 × tan(angle). 30° is 12 × tan(30°) = 6.93 in 12, a grade of 57.74%. 45° is exactly 12 in 12. Choose "Angle" above and enter the reading from your angle finder.
- What is a roof pitch multiplier?
- The pitch factor, √(1 + (X ÷ 12)²): how much longer a line up the slope is than its level run, and how much larger a roof plane is than its footprint. At 4/12 it is 1.0541, at 6/12 1.1180 and at 12/12 1.4142 (√2). Multiply a footprint by it for the roof area, or a run by it for the rafter line length.
- Why is my roof area bigger than my house footprint?
- Two reasons, and they add up. The overhangs carry the roof past the walls, so the footprint to measure is the outline of the roof seen from above, to the edge of the overhangs, not the floor area. Then the slope makes every plane larger than its outline by the pitch factor. For a roof whose planes all share one pitch, hip or gable, footprint × factor is exact. GAF’s roofing-square article gives the same warning against working from the home’s square footage.
- How many squares is my roof?
- Divide the roof area in square feet by 100. Owens Corning’s roofing glossary defines a square as a unit of roof measure covering 100 sq ft, and GAF gives the same 10 × 10 ft. A 1,500 sq ft footprint at 6/12 is 1,500 × 1.118034 = 1,677.05 sq ft of roof, or 16.77 squares. That is the area, not what to order.
- How long should my rafters be?
- Line length = run × pitch factor. The US Navy’s Builder manual takes the span between the outside top plates, the run as half of it, and the line length from the outside edge of the plate to the ridge centre line. A ridge board takes half its thickness off each rafter’s level run, so the line length shortens by half the thickness × the pitch factor; the manual’s layout step marks the half thickness along the line length instead, and the method above compares the two. An overhang adds a tail of level projection × factor. A 24 ft span at 6/12 with a 12 in overhang gives a 12 ft run, a 13.4164 ft line length and a 1.1180 ft tail: 14.5344 ft in all (14 ft 6 7/16 in). That is the measuring line, not the board to buy: cuts and lumber lengths are not included.
- Can asphalt shingles go on a 3/12 roof?
- The 2024 International Residential Code, Section R905.2.2, allows asphalt shingles only on slopes of 2 units vertical in 12 horizontal or more, and from 2:12 up to 4:12 it requires double underlayment in accordance with Section R905.1.1. A 3/12 roof falls in that band. Section R905.1 also requires roof coverings to be applied according to the manufacturer’s installation instructions. Which edition is in force, with any local amendment, depends on your jurisdiction. The code writes 2:12 as a 17-percent slope; 2 ÷ 12 is 16.67%.
- What does "1/4 pitch" mean?
- It is the older way of writing pitch: rise divided by span rather than by run. The US Navy’s Builder manual defines pitch as the ratio of the unit of rise to the unit of span (24 in), and converts it as unit of span × pitch = unit of rise. So 1/4 pitch is 24 × 1/4 = 6 in of rise per foot, or 6:12; 1/3 pitch is 8:12; 1/2 pitch is 12:12. The manual notes that this "pitch" is gradually being replaced by "cut", the rise over a 12 in run that this calculator uses.
- What counts as a low-slope or steep roof?
- It depends on who draws the line, and this calculator labels no pitch. Owens Corning’s roofing glossary names three methods of installing asphalt shingles by slope: Low Slope Application from 2 in to less than 4 in per foot, Standard Slope Application from 4 in to 21 in per foot, and Steep Slope Application above 21 in per foot. Those are one manufacturer’s application methods, not a building-code category. A sourced pitch for walking on a roof or for shedding snow was not found in the sources reviewed.
- How much waste should I add, and how many bundles make a square?
- The calculator sets neither. GAF writes that the number of bundles per square is listed in the specifications of each shingle and varies with the design; its own examples are three for Timberline HDZ and five for Grand Sequoia. Owens Corning’s glossary says there are typically 3, 4 or 5 bundles per square. Enter the figure from your product’s spec sheet, and your own allowance for waste, starters and ridge caps; the arithmetic is shown.
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