How to Calculate Rafter Length (Formula, Slope Factor & Cuts)
Part of Decks, Fences & Roofing
Quick answer
A common rafter is the hypotenuse of the roof triangle, so its length is √(run² + rise²). The run is half the span minus half the ridge thickness; the rise is run × pitch ÷ 12. Multiply by the slope factor √(pitch² + 144) ÷ 12 as a shortcut, then add the overhang along the slope. A 24 ft span at 6-in-12 gives about a 13.4 ft line length.
Every common rafter forms a right triangle with the roof's run and rise, so its length is pure Pythagoras. You only need two numbers to start: the building span and the roof pitch.
The steps
- Run = Span ÷ 2 − (ridge thickness ÷ 2). For a 24 ft span with a 1½ in ridge, the run is about 11.94 ft.
- Rise = Run × pitch ÷ 12. At 6-in-12 that run rises about 5.97 ft.
- Line length = √(Run² + Rise²) — the rafter from the wall to the ridge, here about 13.35 ft.
- Overhang = level overhang × slope factor. A 12 in (1 ft) eave at 6-in-12 is 1.12 ft along the slope.
- Total rafter = line length + overhang ≈ 14.46 ft. Buy the next stock length up (16 ft) and cut to fit.
Slope factor by pitch
The slope factor — √(pitch² + 144) ÷ 12 — is the carpenter's shortcut: rafter length per unit of run. Multiply your run by it for the line length. The last column shows the line length for a 12 ft run (a 24 ft span).
| Pitch | Slope factor | Line length, 12 ft run |
|---|---|---|
| 3-in-12 | 1.031 | 12.37 ft |
| 4-in-12 | 1.054 | 12.65 ft |
| 5-in-12 | 1.083 | 13.00 ft |
| 6-in-12 | 1.118 | 13.42 ft |
| 7-in-12 | 1.158 | 13.89 ft |
| 8-in-12 | 1.202 | 14.42 ft |
| 9-in-12 | 1.250 | 15.00 ft |
| 10-in-12 | 1.302 | 15.62 ft |
| 12-in-12 | 1.414 | 16.97 ft |
The cuts
- Plumb cut: the vertical cut at the ridge (and the matching tail cut). It equals the roof angle, arctan(pitch ÷ 12) — 26.6° at 6-in-12.
- Seat cut: the level cut of the birdsmouth that rests on the wall plate. It's the complement of the plumb cut, so the two add to 90°.
- Birdsmouth depth: code (IRC R802.7) caps the seat cut at one-third of the rafter depth — about 1.83 in on a 2×6, 2.42 in on a 2×8.
Hip and valley rafters run diagonally, so their run is about 1.414× (√2) a common rafter's run — they're noticeably longer. Jack rafters step down in length between a hip or valley and the common rafters. This calculator sizes the common rafters; add the diagonal members separately.
FAQs
What is the formula for rafter length?
Rafter length = √(run² + rise²), where run = span ÷ 2 − half the ridge thickness and rise = run × pitch ÷ 12. Add the overhang (level overhang × slope factor) for the full board length.
How much longer should I cut a rafter for the overhang?
Multiply the level overhang by the slope factor, because the tail runs down the slope. A 12 in overhang at 6-in-12 adds about 13.4 in (1.12 ft) to the rafter, not 12 in.
What size lumber do I buy for a rafter?
Round the total rafter length up to the next stock board length (8, 10, 12, 14, 16, 18, 20 ft) and cut to size. A 14.46 ft rafter is cut from a 16 ft board. Rafter depth (2×6 to 2×12) is set by span, spacing and load — check a span table.
How do I find the run if I only know the span?
The run is half the span, minus half the ridge-board thickness. For a 24 ft span with a 1½ in (2×) ridge, the run is 12 − 0.0625 = 11.94 ft. With no ridge deduction it's an even 12 ft.