A birdsmouth is the notch cut into a rafter so it sits flat on the wall’s top plate. The horizontal “seat” bears on the plate and the vertical “heel” (plumb) cut butts against its outside edge. A common rule is that the heel cut should not remove more than one-third of the rafter depth, so the rafter keeps enough wood above the notch to carry the overhang.
How to use the Birdsmouth Cut Calculator
- Building width (outside of plates)
- Top plate width (seat cut)
- Roof pitch (rise per 12)
- Overhang (horizontal)
- Rafter size (actual depth)
- Ridge board thickness
Results update as you type, and every field accepts the units shown in its menu.
How it works
Enter the building width, the top plate width, the roof pitch, the horizontal overhang, the rafter depth and the ridge board thickness. The calculator gives every dimension you need to mark the rafter and a warning value for notch depth.
Inputs explained
| Field | What to enter |
|---|---|
| Building width (outside of plates) | Units: ft, m, in, yd, cm |
| Top plate width (seat cut) | Choose one: 2×4 wall is 3½ in, 2×6 wall is 5½ in, 89 mm, 140 mm |
| Roof pitch (rise per 12) | In /12 |
| Overhang (horizontal) | Units: in, cm, mm, ft, m |
| Rafter size (actual depth) | Choose one: 2×6 is 5½ in, 2×8 is 7¼ in, 2×10 is 9¼ in, 2×12 is 11¼ in |
| Ridge board thickness | Units: in, cm, mm, ft, m |
What each result means
- Roof angle = deg(atan([Roof pitch (rise per 12)]÷12))
- Rafter run = [Building width (outside of plates)]÷2 – [Ridge board thickness]÷2
- Rafter length incl. overhang = ([Rafter run] + [Overhang (horizontal)])÷cos(rad([Roof angle]))
- Rafter length (ft-in) = [Rafter length incl. overhang]÷0.0254
- Heel (plumb) cut = [Top plate width (seat cut)]×[Roof pitch (rise per 12)]÷12
- Plumb depth of rafter = [Rafter size (actual depth)]÷cos(rad([Roof angle]))
- Height above plate = [Plumb depth of rafter] – [Heel (plumb) cut]
- Heel cut as share of plumb depth = [Heel (plumb) cut]÷[Plumb depth of rafter]×100
- Ridge height above plate (top of rafter) = [Rafter run]×[Roof pitch (rise per 12)]÷12 + [Height above plate]
Example values
How the main result changes when Building width changes and everything else stays at the example values above:
| Building width (outside of plates) (ft) | Rafter length incl. overhang (ft) |
|---|---|
| 12 | 7.756 |
| 18 | 11.11 |
| 24 | 14.465 |
| 30 | 17.819 |
| 36 | 21.173 |
| 48 | 27.881 |
Formula
θ = atan(pitch ÷ 12); run = W/2 − ridge/2
Rafter length = (run + overhang) ÷ cos θ
Seat cut = plate width; heel cut = seat × tan θ
Plumb depth = rafter depth ÷ cos θ; height above plate = plumb depth − heel cut
Worked example
Inputs: Building width (outside of plates): 24 ft; Top plate width (seat cut): 2×4 wall – 3½ in; Roof pitch (rise per 12): 6 /12; Overhang (horizontal): 12 in; Rafter size (actual depth): 2×8 – 7¼ in; Ridge board thickness: 1.5 in.
Results: Roof angle = 26.57 °; Rafter run = 11.938 ft; Rafter length incl. overhang = 14.465 ft; Rafter length (ft-in) = 14 ft 5 9/16 in; Seat cut = 3.5 in; Heel (plumb) cut = 1.75 in; Plumb depth of rafter = 8.106 in; Height above plate = 6.356 in; Heel cut as share of plumb depth = 21.6 %; Ridge height above plate (top of rafter) = 6.498 ft.
Key terms
- Seat cut
- The level cut of a birdsmouth that rests on the top plate.
- Heel cut
- The plumb (vertical) cut of a birdsmouth against the outside of the wall.
Frequently asked questions
How deep should a birdsmouth cut be?
The heel cut should not exceed about one-third of the rafter depth; a full plate-width seat cut is ideal.
What is height above plate (HAP)?
The vertical distance from the top of the wall plate to the top edge of the rafter. It sets the ridge height and fascia line.
Does the seat cut have to be the full plate width?
It should bear on the full plate where possible; on steep pitches the seat may be shortened to keep the heel within limits.