Birdsmouth Cut Calculator

Bird's Mouth Cut Calculator

Calculate the precise seat and heel cuts for roof rafters to ensure a perfect fit on the top plate of your wall.

Last updated: March 2026

e.g., 6 for a 6/12 pitch

2x6 = 5.5", 2x8 = 7.25"

2x4 = 3.5", 2x6 = 5.5"

Seat Cut
3.5
in
Heel Cut
1.75
in
HAP
4.399
in
Plumb Angle
26.57°

What is a Bird's Mouth Cut?

A bird's mouth cut is a notch cut into the bottom of a rafter that allows it to sit securely and flat on the top plate of a wall. This cut is essential in roof framing because it provides two critical functions: a horizontal bearing surface (seat cut) for the rafter to rest on, and a vertical surface (heel cut) that prevents the rafter from sliding outward under roof load.

The bird's mouth consists of two perpendicular cuts: the seat cut (horizontal) matches the width of the top plate, and the heel cut (vertical) is calculated based on the roof pitch. The HAP (Height Above Plate) is the remaining vertical thickness of the rafter after the cuts are made—this must be adequate to maintain the rafter's structural integrity.

A critical rule in carpentry is never to cut more than one-third of the rafter's depth for the bird's mouth. Cutting too deeply weakens the rafter and can lead to structural failure under snow load or high winds.

How to Calculate Bird's Mouth Cuts

The Calculation Process

Follow these steps to determine accurate bird's mouth cuts:

Step 1: Calculate roof pitch angle: arctan(Rise ÷ 12) = Angle in radians
Step 2: Seat Cut = Top Plate Width (typically 3.5" for 2×4, 5.5" for 2×6)
Step 3: Heel Cut = Seat Cut × tan(Angle)
Step 4: HAP = (Rafter Width ÷ cos(Angle)) - Heel Cut
Step 5: Verify HAP is at least 1/3 of rafter width (minimum structural requirement)

Key Terms

Seat Cut:
The horizontal cut where the rafter rests on the plate. Width equals the plate thickness.
Heel Cut:
The vertical cut perpendicular to the seat cut, calculated based on roof pitch and geometry.
HAP:
Height Above Plate—the remaining vertical height of the rafter after the bird's mouth is cut.

Example: Calculate Bird's Mouth for a 6/12 Roof

Roof framed with 2×6 rafters (5.5" actual width) on 2×4 top plate (3.5" actual width) with 6/12 pitch:

Step 1:
Calculate pitch angle:
arctan(6 ÷ 12) = arctan(0.5) = 26.57°
Step 2:
Seat cut = top plate width:
Seat Cut = 3.5"
Step 3:
Calculate heel cut:
Heel Cut = 3.5" × tan(26.57°) = 3.5" × 0.5 = 1.75"
Step 4:
Calculate HAP:
HAP = (5.5" ÷ cos(26.57°)) - 1.75" = (5.5" ÷ 0.894) - 1.75" = 4.48"
Result:
Seat Cut: 3.5"
Heel Cut: 1.75"
HAP: 4.48" ✓ (4.48" > 1.83" minimum)

Disclaimer: This calculator provides geometric guidance for birdsmouth cuts based on standard roof framing relationships. Results are for reference and planning purposes only. It does not constitute a full structural assessment or account for all design considerations, regional code variations, or installation-specific factors. Cutting rafters incorrectly can weaken structural integrity and cause roof failure. Always follow local building codes and consult a qualified builder, structural engineer, or licensed contractor before cutting. Never cut more than 1/3 of the rafter depth.

Frequently Asked Questions

How deep should the bird's mouth be?

The heel cut should never exceed 1/3 of the rafter's width. Cutting too deep significantly weakens the rafter and violates building codes.

What is HAP and why does it matter?

HAP (Height Above Plate) is the remaining vertical thickness after cutting. It must be adequate to maintain structural integrity—generally at least 1/3 of original rafter width.

Does seat cut have to match plate width exactly?

Yes, the seat cut should match the plate width for maximum bearing surface and code compliance. Use actual dimensions (3.5" for 2×4, 5.5" for 2×6).

How do I mark the cuts on the rafter?

Use a framing square set to the roof pitch. Mark the plumb line first, then measure the seat cut horizontally from that line using the calculated dimensions.

Can I use bird's mouth with engineered lumber?

Not recommended. Engineered rafters (LVL, truss components) may have specific fastening requirements. Consult manufacturer instructions before cutting.

What if my calculations show HAP less than 1/3?

If HAP is insufficient, use a higher-grade lumber (larger rafter), reduce roof pitch, or use raised heel trusses to maintain structural integrity.

How accurate are these notch measurements?

These calculations are geometric and suitable for field layout. Always check fit with a test rafter and adjust for saw kerf and actual lumber dimensions before cutting all pieces.

Can I use a birdsmouth on engineered roof trusses?

Engineered trusses are factory-designed and often should not be altered in the field. Consult the truss manufacturer or a structural engineer before modifying.

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