The Basic Rafter Length Formula
A common rafter runs from the ridge board at the peak to the top plate of the exterior wall. The length depends on the building's half-span (run) and the roof pitch.
Rafter Length = Run ÷ cos(pitch angle)
Run = Building Span ÷ 2
Alternative: Rafter Length = Run × Pitch Multiplier
Pitch Multiplier for 6/12 = 1.118
Example
Building span = 30 feet, pitch = 6/12 (26.57°):
- Run = 30 ÷ 2 = 15 feet
- Rafter length = 15 ÷ cos(26.57°) = 15 × 1.118 = 16.77 feet
Ridge Height
The height of the ridge above the top plate is calculated from the run and pitch:
Ridge Height = Run × tan(pitch angle)
= Run × (rise/12)
Example: 15' run at 6/12 = 15 × 0.5 = 7.5 feet
The Birdsmouth Cut
The birdsmouth is the notch cut into the rafter where it sits on the top plate of the wall. It consists of two cuts:
- Seat cut (level cut): The horizontal portion that sits flat on the top plate. Width equals the top plate width (typically 3.5" for a 2×4 wall).
- Plumb cut: The vertical portion. Depth should not exceed 1/3 of the rafter depth.
Seat Cut Width = Wall Plate Width (3.5" for 2×4)
Plumb Cut Depth = Seat Width × tan(pitch angle)
HAP (Height Above Plate) = Rafter Depth − Plumb Cut Depth
Rule: Plumb cut depth ≤ 1/3 rafter depth
Overhang / Tail Length
The rafter tail extends beyond the wall to create the eave overhang. Calculate the tail length from the desired horizontal overhang:
Tail Length = Horizontal Overhang ÷ cos(pitch angle)
Example: 12" overhang at 6/12 = 12 ÷ cos(26.57°) = 13.4 inches
Total Rafter Board Length
Total = Rafter Length + Tail Length − (½ Ridge Board Thickness)
Ridge board thickness is typically 1.5" (a 2× board)
Rafter Sizing Guide
| Rafter Size | Max Span (20 PSF, 16" OC) | Max Span (40 PSF, 16" OC) |
|---|
| 2×6 SPF #2 | 12' 6" | 10' 2" |
| 2×8 SPF #2 | 16' 6" | 13' 5" |
| 2×10 SPF #2 | 21' 0" | 17' 1" |
| 2×12 SPF #2 | 25' 7" | 20' 10" |
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