Roof Pitch Calculator
Pitch, angle, grade and slope factor from a rise and run or from an angle, and the rafter lengths for the run of your roof.
Rafter
Roof pitch
6/12
26.57° · 50 % grade · rafter 13' 5"
- Pitchinches of rise per foot of run
- 6/12
- Angle
- 26.57°
- Grade
- 50 %
- Slope factorrafter length per unit of level run
- 1.118
- Hip / valley factor
- 1.5
- Rafter per foot of run
- 13-7/16"
- Rise
- 6' 0"
- Common rafterwall line to ridge centre line
- 13' 5"
- With overhang
- 14' 6-7/16"
- Hip / valley
- 18' 0"
- Jack differenceeach jack is this much shorter
- 17-7/8"
- Jack raftersper side of each hip
- 8
- Longest jack
- 11' 11-1/8"
Roof triangle
Kalku is coming to iPhone and Android
Kalku has Pitch, Rise, Run, Rafter and Hip keys on its feet-inch keypad, so a roof is a few taps on site, plus calcs for rafter cuts, birdsmouths, hip and valley rafters, roof area, shingles and ventilation. Rafters are drawn in 3D, it works with no signal, and every job can be saved and shared as a PDF.
How pitch, angle and slope factor relate
Roof pitch is written as the rise for 12 units of level run: a 6/12 roof climbs 6 inches every foot. It is a ratio, so the units do not matter; 0.5 m over 1 m is 6/12 too. The calculator works out the pitch as rise ÷ run × 12, the angle as arctan(pitch ÷ 12) and the grade as rise ÷ run as a percentage. From an angle, the pitch is 12 × tan(angle).
The number that does the work on site is the slope factor, √(144 + pitch²) ÷ 12. Multiply any level distance by it and you have the length along the slope: a run into a rafter, an overhang into the length of tail it needs, a jack spacing into the jack difference. A hip or valley crosses the plan diagonally, so it has its own factor, √(288 + pitch²) ÷ 12, per foot of common run.
Worked example: a 6/12 roof on a 24 ft span
These are the numbers the calculator opens with: a rise of 6 in 12, a run of 12 ft (half the span), a 12 inch overhang and jacks at 16 inches.
- Pitch 6/12, angle arctan(0.5) = 26.57°, grade 50%.
- Slope factor √(144 + 36) ÷ 12 = 1.118; hip factor √(288 + 36) ÷ 12 = 1.5.
- Rise: 12 ft × 6/12 = 6' 0".
- Common rafter: 12 ft × 1.118 = 13' 5", or 14' 6-7/16" with the overhang (12" × 1.118 added).
- Hip or valley rafter: √(2 × 144² + 72²) = 216" = 18' 0".
- Jacks at 16": each 16 × 1.118 = 17-7/8" shorter than the last, 8 per side, the longest 11' 11-1/8".
Common roof pitches
| Pitch | Angle | Grade | Slope factor | Rafter per foot of run |
|---|---|---|---|---|
| 1/12 | 4.76° | 8.33 % | 1.0035 | 12-1/16" |
| 2/12 | 9.46° | 16.67 % | 1.0138 | 12-3/16" |
| 3/12 | 14.04° | 25 % | 1.0308 | 12-3/8" |
| 4/12 | 18.43° | 33.33 % | 1.0541 | 12-5/8" |
| 5/12 | 22.62° | 41.67 % | 1.0833 | 13" |
| 6/12 | 26.57° | 50 % | 1.118 | 13-7/16" |
| 7/12 | 30.26° | 58.33 % | 1.1577 | 13-7/8" |
| 8/12 | 33.69° | 66.67 % | 1.2019 | 14-7/16" |
| 9/12 | 36.87° | 75 % | 1.25 | 15" |
| 10/12 | 39.81° | 83.33 % | 1.3017 | 15-5/8" |
| 12/12 | 45° | 100 % | 1.4142 | 17" |
Questions
What is a 6/12 roof pitch in degrees?
26.57°. A 6/12 roof rises 6 inches for every 12 inches of level run, so the angle is arctan(6 ÷ 12). Its grade is 50% and its slope factor 1.118: each foot of run takes 13-7/16 inches of rafter. The table on this page has the common pitches.
How do I measure the pitch of an existing roof?
Hold a level against the underside of a rafter, or on the roof surface, with one end touching. Measure 12 inches along the level and then straight down (or up) to the rafter: that distance in inches is the rise, and the pitch is that number over 12. In the calculator, type the rise and 12 as the run. Any run works, as long as both are in the same unit.
Why does the calculator say the rafter length is theoretical?
The common rafter is measured from the wall line to the centre line of the ridge. At the top, deduct half the ridge board's thickness, measured along the slope (half the thickness × the slope factor). The overhang is added along the slope from the level distance you give, and the birdsmouth and tail cuts are laid out on the rafter itself.
What are jack rafters and the jack difference?
On a hip roof, jack rafters run from the wall plate up to the hip, each one shorter than the last. The jack difference is how much shorter: the jack spacing times the slope factor, 17-7/8 inches at 16 inches on centre on a 6/12 roof. The calculator gives the count per side and the longest jack; deduct for the hip's thickness the same way as at a ridge.
What is the lowest pitch for asphalt shingles?
The International Residential Code allows asphalt shingles down to 2/12, with a double layer of underlayment between 2/12 and 4/12. Below that a roof needs a low-slope covering. The shingle maker's instructions and your local code have the final word.
