Birdsmouth Cut Calculator

Calculate birdsmouth notch dimensions including seat cut depth, heel height, plumb cut angle, and HAP for any rafter size and roof pitch

Calculate birdsmouth seat cut and heel height by rafter size and pitch

Quick presets

Count

27 pieces

24" spacing • 16.1 ft length

PRO

Professional Calculator

Extended parameters for precise calculations

sq ft

Estimated Materials

60 bundles

Roof Area

1,792 sq ft

Squares

17.9

Detailed Breakdown

Roof Area1,792 sq ft
With Waste1,971 sq ft
Roofing Squares17.9
Bundles60
How to Use This Calculator
The Birdsmouth Cut Calculator helps you determine the exact notch dimensions for your rafter-to-wall-plate connection, ensuring a structurally sound and code-compliant joint.

Dimensions tab: Enter your rafter lumber size, roof pitch, and wall plate width to calculate the birdsmouth notch geometry. The calculator determines the seat cut depth (how deep the horizontal cut goes into the rafter), the heel height (HAP — Height Above Plate), and verifies that the notch does not exceed the IRC one-third rule. If the seat cut requires a deeper notch than allowed, the calculator warns you and recommends a larger rafter size. This tab is the starting point for anyone laying out birdsmouth cuts for the first time or checking that a particular rafter-and-wall combination works structurally.

Layout tab: This tab provides the cutting angles and measurements you need at the saw. Enter your rafter size, pitch, eave overhang distance, and ridge board thickness to get the plumb cut angle in degrees, the seat cut length, the rafter tail length along the slope, and the ridge shortening amount. The plumb cut angle is the angle you set on your circular saw or speed square to make the vertical cut of the birdsmouth and the ridge cut at the top. The tail length accounts for the slope factor applied to your horizontal overhang distance — for example, a 12-inch horizontal overhang at 8/12 pitch requires a 14.4-inch tail along the rafter.

Materials tab: Enter the roof ridge length, building span, pitch, rafter spacing, and lumber size to estimate the total number of rafters and board feet of lumber needed. The calculator determines the rafter run (half the building span), applies the pitch factor to get the rafter length, adds overhang, and multiplies by the number of rafter pairs plus a waste factor. This is useful for material ordering and cost estimation before cutting begins.

The Formula
The birdsmouth cut calculator uses these formulas:

Pitch Angle = arctan(rise / 12) Example at 5/12 pitch: arctan(5/12) = 22.62°

Seat Cut Depth = Wall Plate Width × sin(Pitch Angle) Example: 3.5" × sin(22.62°) = 1.35" notch depth

Heel Height (HAP) = Rafter Depth - Seat Cut Depth Example for 2x8: 7.25" - 1.35" = 5.90" HAP

Maximum Notch Depth (IRC) = Rafter Depth / 3 Example for 2x8: 7.25" / 3 = 2.42" maximum

Plumb Cut Angle = arctan(rise / 12) = pitch angle from horizontal Example at 8/12: arctan(8/12) = 33.69°

Rafter Tail Length = Eave Overhang × Pitch Factor Pitch Factor = sqrt(1 + (rise/12)²) Example at 5/12 with 12" overhang: 12" × 1.0833 = 13.0" tail length

Ridge Shortening = (Ridge Board Thickness / 2) × cos(Pitch Angle)

Rafter Count = ((Roof Length × 12) / Rafter Spacing + 1) × 2 Example: ((40 ft × 12) / 16 + 1) × 2 = 62 rafters
Example Calculation
Example: 2x8 Rafters on 2x4 Walls at 5/12 Pitch — 28 ft Span Ranch House

Dave is stick-framing a 40-foot-long ranch house addition with a 28-foot span and 5/12 pitch roof using 2x8 rafters on 2x4 exterior walls with 12-inch eave overhangs.

Step 1: Dimensions — Birdsmouth Geometry
• Rafter: 2x8 (actual depth 7.25")
• Pitch: 5/12 → pitch angle = 22.62°
• Wall plate width: 3.5" (2x4)
• Seat cut depth: 3.5" × sin(22.62°) = 1.35"
• Maximum notch allowed: 7.25" / 3 = 2.42" — PASS (1.35" < 2.42")
• HAP: 7.25" - 1.35" = 5.90 inches (well above 3.5" minimum)

Step 2: Layout — Cutting Angles
• Plumb cut angle: 22.62° from vertical (set speed square to 5)
• Seat cut length: 3.5" (matches wall plate width)
• Pitch factor at 5/12: sqrt(1 + (5/12)²) = 1.0833
• Rafter tail: 12" × 1.0833 = 13.0" along the slope
• Ridge shortening: (1.5" / 2) × cos(22.62°) = 0.69"

Step 3: Materials — Lumber Order
• Rafter run: 28 ft / 2 = 14 ft (half the span)
• Rafter length along slope: 14 ft × 1.0833 = 15.17 ft
• Plus 1.08 ft tail overhang = 16.25 ft per rafter → order 18-ft 2x8s
• Rafter count: ((40 × 12) / 16 + 1) × 2 = 62 rafters
• With 10% waste: 62 × 1.10 = 69 pieces of 18-ft 2x8 lumber
• Board feet: 69 × 18 × 1.5 × 7.25 / 144 = 935 board feet
• Estimated lumber cost at $1.10/BF (2026 pricing): ~$1,029

Frequently Asked Questions

What is a birdsmouth cut and why is it needed on rafters?
A birdsmouth cut is a V-shaped notch cut into the bottom edge of a rafter where it sits on the wall top plate. It consists of two cuts: the seat cut (horizontal, resting on the plate) and the plumb cut (vertical, against the outside edge of the plate). The birdsmouth provides a stable, load-bearing connection that prevents the rafter from sliding off the wall and transfers the roof load directly downward into the wall framing. Without a birdsmouth, the rafter would rest on only a single point of contact, creating a weak connection prone to splitting and lateral movement. Per IRC Section R802.6, birdsmouth cuts are required on site-framed rafters bearing on wall plates.
What is the maximum birdsmouth notch depth allowed by building code?
The IRC (International Residential Code) Section R802.7.1 limits the birdsmouth notch depth to no more than one-third of the rafter depth at the bearing point. For a 2x8 rafter with an actual depth of 7.25 inches, the maximum notch is 2.42 inches. For a 2x10 (9.25 inches actual), the maximum is 3.08 inches. For a 2x12 (11.25 inches actual), it is 3.75 inches. Exceeding this limit weakens the rafter and can cause splitting or failure under load. If your wall plate width requires a deeper notch than one-third of the rafter depth, you must either use a larger rafter size or use a different connection method such as a structural ledger or metal rafter connector.
What is HAP (Height Above Plate) and what is the minimum required?
HAP stands for Height Above Plate, which is the vertical distance from the top of the wall plate to the top edge of the rafter measured at the birdsmouth location. It represents how much rafter material remains above the notch after the birdsmouth is cut. Most building codes and structural engineers require a minimum HAP of 3.5 inches (equivalent to the depth of a 2x4 on the flat) to maintain adequate structural capacity. In high-wind zones or areas with heavy snow loads, engineers may require a larger HAP. A shallow HAP means a deeper notch, which weakens the rafter, while a taller HAP means more rafter material above the plate, providing greater load capacity but a higher effective roof plane at the eave.
How do I mark and cut a birdsmouth on a rafter?
To mark a birdsmouth, you need a framing square, pencil, and the pitch dimensions. Set the framing square on the rafter with the rise number on the tongue and 12 on the body. Mark the plumb cut line (along the tongue), then slide the square along the rafter edge to where the seat cut length meets the bottom edge, and mark the level cut line (along the body) for the seat cut. The seat cut length equals the wall plate width (3.5 inches for 2x4, 5.5 inches for 2x6). Cut with a circular saw, finishing the inside corner with a handsaw or reciprocating saw to avoid over-cutting. In 2026, many carpenters use speed squares or digital angle finders for faster layout, and some use jigs clamped to the circular saw for repeatable cuts across multiple rafters.
Can I use a birdsmouth on engineered lumber like LVL or I-joists?
No. You should never cut a birdsmouth into engineered lumber such as LVL (laminated veneer lumber), glulam beams, or manufactured I-joists. Notching engineered lumber voids the manufacturer warranty and destroys the structural integrity of the laminated layers or the engineered web. Instead, engineered rafters use proprietary metal connectors, bearing hangers, or sloped seat connectors that transfer loads without cutting into the member. Simpson Strong-Tie and MiTek both manufacture specialized rafter connectors for engineered lumber. If your roof design uses engineered rafters, consult the manufacturer installation guide or your structural engineer for the approved connection method at the wall plate.

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