Roof Pitch Calculator – Measure, Convert and Cut Rafters
A roof pitch calculator answers two questions: how steep is my roof, and what does that mean in practice? This tool takes whatever measurement you can get (a known pitch, a level and tape in the attic, the rise and span of a gable end, a rafter length or a photo) and turns it into every form roofers and framers use, plus the rafter lengths and saw angles you need to cut one.
What "X in 12" means
In North America, pitch is written as inches of rise per 12 inches of horizontal run. A 6/12 roof climbs 6 in for every foot it runs inward, which is atan(6/12) = 26.57° or a 50% grade. Internally the calculator stores a single ratio, p = rise ÷ run, and derives everything else from it: degrees (atan p), percent (100 × p) and the ratio 1 : 1/p.
Pitch, slope and fractional pitch
Strictly, "6 in 12" is the slope. The older carpentry meaning of pitch is rise divided by the full span of a gable, so a 6/12 roof is a 1/4 pitch and a 12/12 roof is a 1/2 pitch. Most people now use the words interchangeably, so the results show both.
Three ways to measure, and how accurate each is
- Level and tape in the attic: hold a level horizontal against a rafter and measure plumb up to it. With a 12 in level, a 1/8 in reading error shifts the result by about 0.125 in 12, so a 24 in level halves the error. This is the most accurate method.
- Gable end from the ground: measure the building width and the height from the top of the wall to the ridge. For a gable, the run is half the span.
- From a photo: a square-on shot of the gable end, with guide lines dragged onto the roof edge. Quick and safe, but only good to a degree or two.
Slope factor: why a roof is bigger than its footprint
The slope factor k = √(1 + p²) converts plan measurements to sloped ones. A rafter is run × k long, and a roof plane of one pitch covers plan area × k. At 6/12, k = 1.118, so a 2,000 ft² footprint (including overhangs) carries about 2,236 ft² of roofing.
Common pitches and what they suit
Below 2/12 a roof is effectively flat and needs a membrane such as EPDM or TPO. Asphalt shingles are allowed from 2/12, but up to 4/12 they need a double layer of underlayment, and many exposed-fastener metal panels want at least 3/12. 4/12 to 8/12 is the conventional range for houses: walkable and suitable for almost any material. Above 8/12 roofs get harder to work on, and above 12/12 (45°) they are effectively walls.
Hips, valleys and "X in 17"
Where two planes of equal pitch meet at a 90° corner, the hip or valley runs diagonally. For every 12 in of common run it travels 12 × √2 ≈ 16.97 in, so framers describe its slope as X in 17. Its true pitch is p / √2 and its length is run × √(2 + p²), the hip/valley factor.
Cutting rafters with a speed square
The plumb cut at the ridge and tail is set at the roof angle from square, and the seat cut of the bird's mouth is its complement. With a speed square, pivot on the pencil point and rotate until the Common scale number matching your rise (for example 6) lines up with the rafter edge. Hip and valley rafters use the Hip-Val scale at the same number. The calculator also works out the bird's mouth heel, notch depth and height above plate, so every rafter lands at the same height.
Steep-roof safety
The pitch bands in this tool are trade conventions, not safety law. US federal construction rules (OSHA, 29 CFR 1926.500) define a steep roof as one with a slope greater than 4 in 12, and require fall protection accordingly. Check local regulations and building codes before working on or framing any roof.