How it works
A common rafter runs from the ridge down to the wall plate at the roof pitch. The pitch is stated as inches of rise per 12 inches of run. The rafter is the hypotenuse of a right triangle, so its length is the run times √(1 + (rise ÷ 12)²). For a 6/12 roof that is 1.118 feet of rafter for every foot of run.
The birdsmouth is the notch that lets the rafter sit flat on the wall plate. The seat cut is level and the heel (plumb) cut is vertical. Cutting too deep weakens the rafter where it carries the most load, so the code limits an end notch to one-fourth of the rafter depth.
Worked example
A 24 ft wide building with a 6/12 roof, 12 inch overhang, 1.5 inch ridge board, and 2x8 rafters bearing 3.5 inches on the plate:
- Slope factor = √(1 + (6 ÷ 12)²) = 1.118
- Rafter length = (24 ft ÷ 2) × 1.118 = 13.42 ft
- Cut length = 13.42 + 1 ft overhang × 1.118 − 0.063 ft ridge deduction × 1.118 = 14.46 ft
- Notch depth = 3.5 in seat × sin(26.6°) = 1.57 in; limit = 7.25 ÷ 4 = 1.81 in
| Input | Value |
|---|---|
| Roof pitch: rise per 12 in of run | 6 in |
| Building span (outside of wall to outside of wall) | 24 ft |
| Overhang (horizontal distance beyond the wall) | 12 in |
| Ridge board thickness | 1.5 in |
| Rafter actual depth (2x8 = 7.25 in, 2x10 = 9.25 in, 2x12 = 11.25 in) | 7.25 in |
| Birdsmouth seat length (bearing on the wall plate) | 3.5 in |
| Result | Value |
|---|---|
| Roof angle | 26.6 ° |
| Rafter length along the slope, wall line to ridge centerline | 13.42 ft |
| Rafter length to cut, including overhang and ridge deduction | 14.46 ft |
| Ridge height above the top of the wall plate | 6 ft |
| Plumb (heel) cut height for the seat length | 1.75 in |
| Notch depth measured square to the rafter edge | 1.57 in |
| Maximum notch depth allowed (1/4 of the rafter depth) | 1.81 in |
| Longest seat cut that stays within that limit | 4.05 in |
Assumptions and limits
- Common rafters with a level seat cut at a level wall plate, and a plumb cut at the ridge.
- Length is measured along the top edge from the ridge centerline to the outside face of the wall, then extended for the overhang. Rafter tails may be cut plumb or square, which changes the exact tail length slightly.
- The one-quarter-depth end notch limit follows the International Residential Code. Your adopted code edition and local amendments control, and the limit does not apply where an engineered design says otherwise.
- This does not size the rafter. It only handles geometry and the notch check.
Common questions
How do I figure rafter length for a 6/12 pitch?
Multiply the run (half the span) by 1.118. A 24 ft span has a 12 ft run, so the rafter measures 13.42 ft along the slope before the overhang and the ridge deduction.
How deep can I cut a birdsmouth?
The IRC limits notches at the ends of a rafter to one-fourth of the member depth, so 1.81 in on a 2x8 and 2.81 in on a 2x12. Measure the depth square to the rafter edge.
Do I include the ridge board in the rafter length?
Yes. Measure the theoretical length to the ridge centerline, then subtract half the ridge board thickness along the slope so the rafter fits against its face.
What if my roof is a hip roof?
The common rafters use this calculator. The hip and valley rafters and the jacks are in the hip and valley rafter calculator.
Sources
- Right-triangle geometry for common rafter length (unit length per foot of run: 6/12 = 13.42 in, 8/12 = 14.42 in, 12/12 = 16.97 in, as printed in standard rafter tables).
- International Residential Code R802.7.1: notches at the ends of rafters may not exceed one-fourth the depth of the member. Verify against the code edition your jurisdiction has adopted.
- Read them: IRC R802.7.1 sawn lumber notching (UpCodes)
Updated 2026-09-30