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Roof Framing Tools

Birdsmouth Calculator

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

Enter values above to calculate

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).

WALL PLATE Rafter Depth (D) SEAT CUT HAP Plumb (Heel) Cut

Step-by-Step Formulas

1. Pitch to Roof Angle

θ = arctan(Rise/Run)

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

Notch depth (vertical) = Seat length × tan(θ)

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 = (Rafter depth × cos(θ)) − Notch depth

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

Notch depth ≤ 1/3 of rafter depth

A common framing rule is to keep the birdsmouth notch shallower than one-third of the rafter depth to avoid weakening the rafter. Always follow local code and structural engineering requirements.

Worked Example

Standard framing: 2×8 rafter (184 mm depth), 6/12 pitch (~26.57°), 100 mm seat length.

Pitch angle θ = arctan(6/12) ≈ 26.57°
Notch depth = 100 mm × tan(26.57°) ≈ 100 × 0.50 ≈ 50 mm
Verification: 50 mm / 184 mm ≈ 27% (Safe, ≤ 33%)
HAP = (184 mm × cos(26.57°)) − 50 mm
HAP = (184 × 0.894) − 50 ≈ 164.5 − 50 = 114.5 mm

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.

Benefits of Using This Calculator

Notch Depth and HAP Reports both the heel cut depth and the resulting height above plate for layout.
Code Limit Check Flags when the notch exceeds a quarter of the rafter depth so you catch the problem before cutting.
Any Pitch and Rafter Size Works across the full range of common pitches and nominal rafter depths.
Cut Angles Gives the plumb and level angles for setting a square or saw.

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 limit = 7.25 ÷ 4 = 1.81 in — 1.75 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.

Heel depth = 3.5 × (12 ÷ 12) = 3.5 in

Notch limit = 5.5 ÷ 4 = 1.375 in

3.5 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 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

What is a birdsmouth cut?
A birdsmouth is a notch cut into the bottom of a rafter so it can sit flat on a wall plate. It typically includes a level (seat) cut and a plumb (heel) cut.
How much can I notch a rafter for a birdsmouth?
A common rule of thumb is to limit the birdsmouth notch depth to about one-third of the rafter depth. Requirements vary by jurisdiction and loading; follow local code or an engineer'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.

Assumptions & Reference Values

This tool returns estimates using standard financial formulas and the default parameters shown in the calculator inputs. Always consult a qualified financial advisor before making investment decisions.

Calculator Defaults:

  • Seat cut (level cut) length is measured horizontally across the top plate
  • Heel cut (plumb) depth = seat cut length × (pitch ÷ 12)
  • HAP (height above plate) = rafter depth ÷ cos(pitch angle) − heel cut depth
  • Notch depth should not exceed 1/4 of the rafter depth (IRC R802.7.1)
  • Pitch angle = arctan(rise ÷ 12) for a rise-per-12-inches pitch
  • Assumes a standard bearing on a nominal 2x top plate
  • Engineered I-joists and LVL rafters have their own notching rules — check the manufacturer

Disclaimer

All calculations are for informational purposes only. Past performance does not guarantee future results. Consult a licensed financial advisor for personalized advice.