Gable roof, 6/12 pitch, building is 24 feet wide outside to outside, ridge is a 2x (1-1/2 in.

Rafter Length Calculation:

1. Run: 24' ÷ 2 = 12' (144")
2. Rise: 6" per 12" run = 72"
3. Rafter Length: √(144² + 72²) = √(20,736 + 5,184) = √25,920 = 161.25" (≈161¼")

Framing Square Setup:

• Body (tongue): 12"
• Blade (heel): 6"
• Mark along the blade edge for the 6/12 pitch.

Birdsmouth to Ridge Cut:

• Heel Cut: Mark 161¼" from the plumb cut at the ridge, using the square's 6/12 pitch to mark the birdsmouth seat and heel cut.
• Ridge Plumb Cut: At 161¼", mark the plumb cut (perpendicular to the 6/12 pitch line).

Note: This is the theoretical length. Always verify with a test fit and adjust for ridge board thickness (1.5") if needed. For rafter seat cuts, ensure compliance with local building codes (IBC Section 2304.12 for rafter spans). If unsure, consult a structural engineer.

Rafter Length: 12' 5-1/2"

The Math

1. Total Run: Building width ÷ 2 = 24' ÷ 2 = 12' 0".
2. Ridge Deduction: 1-1/2" (ridge thickness) ÷ 2 = 3/4".
3. Effective Run: 12' 0" – 3/4" = 11' 11-1/4".
4. Unit Length (6/12): √(12² + 6²) = 13.4164" per foot of run.
5. Total Length: 11.9375 ft × 13.4164 = 160.16" ≈ 13' 4-3/16".

Wait—standard framing square tables give the line length (ridge center to plate outside). You need the plumb cut at ridge face to heel of birdsmouth.

Correct Field Length (Ridge Face to Heel):

• Theoretical line length (center ridge to outside plate): 13' 4-3/16".
• Minus 1/2 ridge thickness (3/4") = 13' 3-7/16".
• But the birdsmouth heel sits on the plate. The "heel to ridge plumb" distance is the hypotenuse of the effective run triangle.
• Effective Run = 11' 11-1/4".
• Length = 11.9375 × 13.4164 = 160.16" = 13' 4-3/16".

Let's simplify: Most framers step it off.

• Run = 11' 11-1/4".
• Step off 11 full feet (12" run / 6" rise).
• Remaining run: 11-1/4".
• Step off 11-1/4" run (rise = 5-5/8").

With a Framing Square (Step-Off Method):

1. Climb stair gauges at 12" (tongue) and 6" (blade).
2. Start at ridge plumb cut line (top edge).
3. Step off 11 full times (12" run each). Mark plumb lines.
4. Final step: Slide square to 11-1/4" on tongue (run), 5-5/8" on blade (rise). Scribe plumb cut at ridge face.
5. Birdsmouth: From the last plumb line (heel), measure level 11-1/4" back toward tail? No. The heel cut is the intersection of the seat cut and the plumb line at the plate. Measure **run distance (11'