Rafter length calculator for gable and shed roofs: line length, tail, plumb and seat cuts, birdsmouth and height above plate. A 6/12 roof on a 24 ft span with a 1-1/2" ridge needs 13' 4-3/16" of rafter line, pitched at 26.57°; a 3-1/2" seat cuts a 1-3/4" heel and leaves 6-3/8" HAP on a 2x8.
24.00 ft wall to wall
≥ 1-1/2″ bearing
30.0 ft of ridge
Gable · 6/12 · 24' 0" span
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| 4.76° | 12-1/16"− · 12.042" | 1.0035 | 1 tongue · 12 body | 85.24° | 5/16" | 7" | ||
| 9.46° | 12-3/16"− · 12.166" | 1.0138 | 2 tongue · 12 body | 80.54° | 9/16" | 6-3/4" | ||
| 14.04° | 12-3/8" · 12.369" | 1.0308 | 3 tongue · 12 body | 75.96° | 7/8" | 6-5/8" | ||
| 18.43° | 12-5/8"+ · 12.649" | 1.0541 | 4 tongue · 12 body | 71.57° | 1-3/16" | 6-1/2" | ||
| 22.62° | 13" · 13.000" | 1.0833 | 5 tongue · 12 body | 67.38° | 1-7/16" | 6-3/8" | ||
| 26.57° | 13-7/16"− · 13.416" | 1.1180 | 6 tongue · 12 body | 63.43° | 1-3/4" | 6-3/8" | ||
| 30.26° | 13-7/8"+ · 13.892" | 1.1577 | 7 tongue · 12 body | 59.74° | 2-1/16" | 6-3/8" | ||
| 33.69° | 14-7/16" · 14.422" | 1.2019 | 8 tongue · 12 body | 56.31° | 2-5/16" | 6-3/8" | ||
| 36.87° | 15" · 15.000" | 1.2500 | 9 tongue · 12 body | 53.13° | 2-5/8" | 6-7/16" | ||
| 39.81° | 15-5/8" · 15.620" | 1.3017 | 10 tongue · 12 body | 50.19° | 2-15/16" | 6-1/2" | ||
| 42.51° | 16-1/4"+ · 16.279" | 1.3566 | 11 tongue · 12 body | 47.49° | 3-3/16" | 6-5/8" | ||
| 45.00° | 17"− · 16.971" | 1.4142 | 12 tongue · 12 body | 45.00° | 3-1/2" | 6-3/4" | ||
| 49.40° | 18-7/16" · 18.439" | 1.5366 | 14 tongue · 12 body | 40.60° | 4-1/16" | 7-1/16" | ||
| 53.13° | 20" · 20.000" | 1.6667 | 16 tongue · 12 body | 36.87° | 4-11/16" | 7-7/16" |
Rafter length per foot of run = √(144 + pitch²). Heel = seat × pitch ÷ 12. HAP = height above plate for a 2x8 with a 3-1/2" seat.
05 / Field guide
Common rafters all come off one pattern, so the job is to get that pattern right: the line length from ridge to wall, the plumb cut at the top, the birdsmouth that seats on the plate and the tail. A 6/12 roof on a 24 ft building with a 1-1/2" ridge works out to 13' 4-3/16" of rafter line at 26.57°, and the whole rafter including a 12" overhang comes out of a 16 ft board.
Pitch is rise per 12" of run. The rafter is the hypotenuse, so every foot of run needs √(144 + pitch²) inches of rafter: 13.42" at 6/12, 15.62" at 10/12. On a gable the run is half the building span, less half the ridge board thickness measured level.
line length = run × √(1 + (pitch ÷ 12)²) run (gable) = span ÷ 2 − ridge ÷ 2 tail = overhang × the same factor
Hold the framing square with 12 on the body and the pitch on the tongue, both on the rafter’s top edge: the tongue gives the plumb cut and the body the level (seat) cut. On a speed square, pivot on the pitch number on the COMMON scale.
The birdsmouth is a seat cut that bears on the wall plate and a heel cut that drops plumb from it. Bear at least 1-1/2" on the plate. Keep the notch shallow: measured square to the rafter edge it should not exceed one quarter of the rafter depth, so at least three quarters of the depth stays intact above it (IRC R802.7.1 limits end notches in sawn rafters to 1/4 of the depth).
The height above plate (HAP) is the plumb distance from the top of the plate to the top edge of the rafter at the heel line. It is the same on every rafter, and it sets the ridge height: on the example roof the HAP is 6-3/8".
heel = seat × pitch ÷ 12 notch = seat × sin θ ≤ depth ÷ 4 HAP = depth ÷ cos θ − heel
It lays out rafters; it does not size them. Rafter size and spacing for your snow load, dead load and span come from the IRC rafter span tables (R802.4) or an engineer. Ceiling joists or rafter ties are also needed to stop the walls spreading on most gable roofs.
Questions
Multiply the run by √(1 + (pitch ÷ 12)²). For a gable, the run is half the building span minus half the ridge thickness. Add the overhang times the same factor for the tail.
26.57°. A 4/12 is 18.43°, an 8/12 33.69°, a 10/12 39.81° and a 12/12 45°.
Keep the notch, measured square to the rafter edge, to no more than one quarter of the rafter depth so at least three quarters stays intact, and bear at least 1-1/2" on the plate.
The plumb distance from the top of the wall plate to the top edge of the rafter where it crosses the outside of the wall. Keeping it the same on every rafter keeps the roof plane flat and sets the ridge height.
Put the pivot on the rafter’s top edge and rotate the square until the pitch number on the COMMON scale lines up with the same edge; mark along the pivot side.
At 4/12, 12.65"; at 6/12, 13.42"; at 8/12, 14.42"; at 12/12, 16.97". The roof pitch chart lists every pitch from 1/12 to 16/12.
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