Roof Framing Tools
Birdsmouth Calculator
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Calculate the exact notch depth and Height Above Plate (HAP) for your common rafters. Enter the material depth, roof pitch, and horizontal seat length (bearing on the plate) to ensure all rafters sit flat and provide a consistent roof plane.
Birdsmouth Cut Calculator
Estimate HAP and notch depth from pitch, rafter size, and seat length
Results
HAP (height above plate)
161.21 mm
Notch depth (vertical)
44.57 mm
IRC R802.7.1 limits the notch to 1/4 of the rafter depth, measured square to the rafter — this cut is within it.
Step-by-Step Calculation
Step 1 — Roof angle
θ = 26.60° (tan θ = 0.5008, cos θ = 0.8942)
Step 2 — Plumb cut height
184.00 mm ÷ 0.8942 = 205.78 mm
Step 3 — Heel (notch) depth
vertical: 89.00 mm × 0.5008 = 44.57 mm
square to the rafter: 89.00 × sin θ = 39.85 mm
IRC limit 184.00 ÷ 4 = 46.00 mm → within
Step 4 — Height above plate
205.78 − 44.57 = 161.21 mm
Step 5 — Rafter left above the notch
184.00 − 39.85 = 144.15 mm (78% of the depth)
Result — HAP 161.21 mm, heel cut 44.57 mm
Birdsmouth Cut Anatomy
The birdsmouth consists of a level seat cut and a vertical heel (plumb) cut. The leftover vertical material is the HAP (Height Above Plate).
Step-by-Step Formulas
1. Pitch to Roof Angle
Birdsmouth layout depends on the roof slope. The calculator converts pitch (rise over run) into an angle so it can translate the bearing seat length into a vertical notch depth.
2. Notch Depth from Seat Length
The seat cut length (the horizontal bearing on the plate) creates a run. Over that run, the roof rises by the tangent of the pitch angle, which determines the depth of the birdsmouth notch.
3. Height Above Plate (HAP)
HAP is the vertical height from the top of the wall plate to the top of the rafter at the outside edge of the wall. Keeping HAP consistent across all rafters ensures a flat roof plane.
4. Notch Depth Rule of Thumb
IRC R802.7.1 limits a notch at the end of a rafter to one quarter of its depth, measured square to the rafter. The calculator checks the depth the seat cut removes (seat length × sin θ) against that limit. Engineered lumber has its own, stricter rules.
Worked Example
Standard framing: 2×8 rafter (184 mm depth), 6/12 pitch (~26.57°), 100 mm seat length.
Maximum Notch Depth by Rafter Size
The IRC limits the birdsmouth to one quarter of the rafter depth. Heel depth is seat length × pitch ÷ 12:
| Nominal rafter | Actual depth (in) | Max notch (in) | Max pitch at 3.5 in seat |
|---|---|---|---|
| 2 × 6 | 5.50 | 1.38 | 4.7/12 |
| 2 × 8 | 7.25 | 1.81 | 6.2/12 |
| 2 × 10 | 9.25 | 2.31 | 7.9/12 |
| 2 × 12 | 11.25 | 2.81 | 9.6/12 |
The Notch That Sets the Roof
The birdsmouth is a small cut with outsized consequences for how the roof sits and how strong the rafter remains:
- HAP Sets the Roof Plane: Height above plate is what determines where the roof surface lands. Every rafter must share the same HAP or the roof plane will wave visibly along its length.
- Full Seat Bearing: The level cut should bear fully on the top plate so load transfers straight down into the wall. A partial seat concentrates load on the outer edge of the plate.
- Over-Notching Fails the Rafter: The IRC limits the notch to a quarter of the rafter depth. Cutting deeper removes material exactly where bending stress peaks and can fail inspection or the rafter itself.
Example Calculations
Three scenarios worked through step by step:
Example 1 — 2×8 Rafter at 6/12
2×8 rafter (7.25 in deep), 6/12 pitch, 3.5 in seat cut.
Pitch angle = arctan(6 ÷ 12) = 26.57°
Heel depth = 3.5 × (6 ÷ 12) = 1.75 in
Notch square to rafter = 3.5 × sin 26.57° = 1.57 in; limit 7.25 ÷ 4 = 1.81 in — passes
HAP = (7.25 ÷ cos 26.57°) − 1.75 = 8.108 − 1.75
HAP = 6.36 in
Example 2 — Steep Pitch Warning
2×6 rafter (5.5 in deep), 12/12 pitch, 3.5 in seat cut.
Notch square to rafter = 3.5 × sin 45° = 2.47 in
Notch limit = 5.5 ÷ 4 = 1.375 in
2.47 in far exceeds the limit — not permitted
Fix: shorten the seat cut or use a deeper rafter
A 2.75 in seat on a 2×10 would resolve it
Example 3 — Shallow Pitch
2×10 rafter (9.25 in deep), 4/12 pitch, 3.5 in seat cut.
Pitch angle = arctan(4 ÷ 12) = 18.43°
Heel depth = 3.5 × (4 ÷ 12) = 1.167 in
Notch square to rafter = 3.5 × sin 18.43° = 1.11 in; limit 9.25 ÷ 4 = 2.31 in — comfortably within
HAP = (9.25 ÷ cos 18.43°) − 1.167 = 9.752 − 1.167
HAP = 8.59 in
Layout Tip
Layout Tip
Set the seat cut length to match your top plate width — 3.5 in for a 2×4 wall, 5.5 in for a 2×6 — rather than picking a round number. A seat that overhangs the plate gains no bearing and only deepens the notch, while a short seat leaves the rafter perched on the plate edge.
Frequently Asked Questions
- How much can I notch a rafter for a birdsmouth?
- IRC R802.7.1 limits it to one quarter of the rafter depth, measured square to the rafter. Some jurisdictions and engineered products are stricter, so follow local code or the manufacturer’s guidance.
- What does HAP mean in roof framing?
- HAP stands for Height Above Plate. It is the vertical distance from the top of the wall plate to the top of the rafter at the outside edge of the wall.
- What is a birdsmouth cut?
- A right-angled notch cut into the underside of a rafter where it crosses the top plate. The level seat cut bears on the plate and the vertical heel cut sits against its outer face, locking the rafter in position and transferring load into the wall.
- How deep can a birdsmouth notch be?
- No more than one quarter of the rafter depth under IRC R802.7.1 — so 1.81 in on a 2×8 and 2.31 in on a 2×10. The notch removes material where bending stress is highest, which is why the limit is strict.
- What does HAP stand for?
- Height Above Plate: the remaining vertical depth of the rafter measured at the outer face of the wall plate. It sets where the roof plane sits and must be identical on every rafter, or the finished roof surface will not be flat.
- How do I calculate the heel cut depth?
- Multiply the seat cut length by the pitch ratio. A 3.5 in seat on a 6/12 roof gives 3.5 × 0.5 = 1.75 in. Steeper pitches produce deeper heel cuts from the same seat length, which is what pushes steep roofs past the notch limit.
- What if my birdsmouth exceeds the notch limit?
- Use a deeper rafter, shorten the seat cut, or switch to a structural connector that hangs the rafter without notching. On steep pitches with shallow rafters the notch limit is frequently the governing constraint.
- Should every rafter have the same birdsmouth?
- Yes. Cut one, verify its fit at both the ridge and the plate, then use it as a physical pattern for the rest. Identical HAP on every rafter is what produces a flat roof plane and a straight fascia line.
- Can I skip the birdsmouth entirely?
- Yes, using rafter hangers or a structural connector at the plate, which is common on steep pitches and with engineered lumber where notching is restricted or prohibited. The connector must be rated for the load and installed with the specified fasteners.