Roof Pitch Calculator
Turn a rise-over-12 roof pitch into its angle, pitch multiplier, and rafter length for any run.
Rafter length here is the theoretical run-to-ridge line length only, it doesn't add the overhang or account for the ridge board and birdsmouth cuts a framer subtracts on site.
| Pitch | Angle | Multiplier |
|---|---|---|
| 3/12 | 14° | 1.031 |
| 4/12 | 18.4° | 1.054 |
| 5/12 | 22.6° | 1.083 |
| 6/12 | 26.6° | 1.118 |
| 7/12 | 30.3° | 1.158 |
| 8/12 | 33.7° | 1.202 |
| 9/12 | 36.9° | 1.25 |
| 10/12 | 39.8° | 1.302 |
| 11/12 | 42.5° | 1.357 |
| 12/12 | 45° | 1.414 |
How it works
Roof pitch on a residential drawing is almost always given as a rise over a run of 12 inches, written like 6/12 or shown as a little triangle symbol on the elevation with the rise number stacked over a 12. That single number determines three things you actually need on site or when estimating material: the angle of the roof in degrees, a multiplier you use to convert a flat horizontal run into the longer sloped rafter length, and the rafter length itself for whatever run you're working with.
Worked example: a 6/12 pitch, a common, moderate slope, works out to a 26.6 degree angle. Its multiplier is 1.118, meaning every foot of horizontal run needs 1.118 feet of rafter to span it. Over a 12 foot run (half the width of a 24 foot wide building, measuring from the wall plate to the ridge), that's 12 × 1.118 = 13.42 feet of rafter. A steeper 12/12 pitch, a true 45 degree roof, needs a multiplier of 1.414, nearly 30 percent more rafter material for the same run than the 6/12 does.
Keep in mind the length this tool gives you is the theoretical line from the top plate to the ridge centerline, the geometry only. A framer building the actual roof adds the tail overhang past the wall, and cuts a birdsmouth notch and a plumb cut at the ridge that shorten the usable board slightly, so real lumber ordering always adds a margin on top of this number.
FAQ
Why is roof pitch always measured over 12 instead of some other number?
It's a carpentry convention going back generations, framing squares are laid out with a 12 inch body, so a rise-over-12 pitch could be marked and cut directly with that tool without any extra math. It stuck as the standard way to express and read pitch even now that most cutting is done with a saw and a calculator instead of a framing square alone.
What's considered a "steep" roof pitch?
Anything from about 4/12 to 9/12 is typical for most houses and reads as a normal, moderate slope. Pitches above 9/12 or 10/12 start to look steep and are more common on traditional or cottage-style designs, and very low pitches under 3/12 usually need special low-slope roofing membranes rather than standard shingles, since shallow slopes don't shed water as fast.
Does a steeper pitch cost more to build?
Generally yes. A steeper pitch needs more rafter length and more roofing material to cover the same footprint, as the multiplier table above shows, and steep roofs are slower and more hazardous to work on, which shows up in labor cost too. The trade-off is more attic headroom and, in snow country, better shedding of snow load.
Where do I find the roof pitch on a set of plans if it isn't labeled directly?
Look at the building elevations first, the little rise-over-12 triangle symbol is almost always drawn right on the roof line there. If it's missing, a section drawing through the roof will show the actual slope angle or the rise and run dimensions you can compute it from.
For more on where roof pitch shows up in a set of plans, see Understanding Building Elevations and How to Read a Section Drawing.