Rafter lengths and pitch, worked out to the inch
Roof Pitch & Rafter Calculator
Give it the span and the pitch and it returns the numbers that set out a roof: common rafter length, ridge height, roof angle, grade and sloped area — plus the hip rafter for a hip roof and the single-slope run for a lean-to. Switch the roof type and the whole calculation, and the section diagram, follow.
The Pitch and Rafter Math
Pitch is written as rise per 12 inches of horizontal run. Everything else falls out of it. The slope factor — how much longer the rafter is than its run — is:
slope factor = √(1 + (rise ÷ 12)²)
Multiply the horizontal run by that factor for the rafter length; multiply the flat footprint by it for the true sloped area. The roof angle is arctan(rise ÷ 12). A gable rafter runs half the span; a lean-to rafter runs the full width in a single slope; a hip roof adds four hip rafters that travel diagonally over the corners — longer per foot of run because they use a 17-inch diagonal base instead of 12. This tool applies the right run for the roof type you pick and adds your overhang before reporting the cut length.
Common Pitches at a Glance
| Pitch | Angle | Grade | Slope factor | Character |
|---|
| 3/12 | 14.0° | 25% | 1.031 | Low-slope limit for most shingles |
| 4/12 | 18.4° | 33% | 1.054 | Common ranch / modern |
| 6/12 | 26.6° | 50% | 1.118 | The residential workhorse |
| 8/12 | 33.7° | 67% | 1.202 | Traditional, sheds snow well |
| 12/12 | 45.0° | 100% | 1.414 | Steep; strong attic volume |
Below 3/12, plan on a membrane roof rather than shingles. Between 6/12 and 9/12 you get reliable water and snow shedding with a surface you can still walk.
Frequently Asked Questions
How do you calculate rafter length from pitch?
Rafter length = run × √(1 + (rise ÷ 12)²). The run is half the span for a gable, the full width for a lean-to. Add the overhang, then deduct half the ridge thickness at the peak.
Hip vs gable vs lean-to?
Gable slopes two ways to a ridge with triangular end walls; hip slopes all four sides with hip rafters and a shorter ridge; lean-to (shed) is a single plane from a high wall to a low wall.
How do you convert pitch to degrees?
Angle = arctan(rise ÷ 12). 4/12 ≈ 18.4°, 6/12 ≈ 26.6°, 12/12 = 45°. The tool shows angle and grade beside the rise-in-12 figure.
How long is a hip rafter?
Its plan run is the common run × √2, so hip length = common run × √(2 + (rise ÷ 12)²), plus overhang. This tool reports it whenever the hip roof type is selected.
What is a good roof pitch?
Most homes run 4/12–9/12. 6/12–8/12 balances shedding, walkability and material. Steeper adds attic volume and a traditional look at higher cost.
This calculator is built and maintained by Nakada Design, the Los Angeles marketing agency for
architects and
interior designers. If you want the clients searching for answers like these to find your firm, see our services or
inquire.
