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Birdsmouth Cut Calculator
Calculate precise rafter seat cuts, plumb cuts, and Height Above Plate (HAP) heel dimensions conforming strictly to IRC Section R802.7.1 notch depth limits.
Calculates True AreaFactors in PitchIncludes Waste FactorSquares & Bundles
Example preview
ResultSeat Cut: 2.75" | Plumb Cut: 1.38"
- Seat Cut Length (Level)
- 2.75 inches (2.75")
- Plumb Cut Depth (Vertical)
- 1.38 inches (1.375")
- Height Above Plate (HAP)
- 4.77 inches
- Remaining Solid Wood
- 4.27 inches (78%)
- IRC Notch Compliance
- Restricted Cut (Max 1/4 Depth)
- Framing Square Setting
- 6" on Tongue, 12" on Body
Enter your values and press Calculate to see your result.
How the Birdsmouth Cut Calculator Works
Follow the exact steps to get your result instantly and privately.
Step 1: Select Roof Pitch
Choose your roof's rise-over-run pitch ratio (e.g. 4/12, 6/12, 8/12).
Step 2: Choose Lumber Dimension
Select 2×4, 2×6, 2×8, 2×10, or 2×12 nominal framing lumber to establish maximum allowable cut depths.
Step 3: Specify Top Plate Width
Input 3.5 inches for standard 2×4 exterior framing or 5.5 inches for 2×6 wall framing.
STEP 1
Step 1: Select Roof Pitch
Choose your roof's rise-over-run pitch ratio (e.g. 4/12, 6/12, 8/12).
IRC Section R802.7.1 Birdsmouth Cut Rules
A birdsmouth cut is the triangular notch cut into the underside of a common rafter allowing it to sit flat on an exterior wall top plate. It consists of two cuts: the horizontal 'seat cut' (which bears on the plate) and the vertical 'plumb cut' (which stands against the exterior wall sheathing). Under International Residential Code (IRC) Section R802.7.1, notches on the ends of rafters must not exceed one-fourth of the nominal rafter depth (D/4) to prevent horizontal shear failure.
Measuring Methods
- Seat Cut (Level Bearing): The horizontal surface resting on the wall plate. Under IRC R802.6, wood framing members must have a minimum bearing length of 1.5 inches on wood or 3 inches on masonry.
- Plumb Cut (Heel Notch): The vertical cut. Plumb Cut Depth = Seat Cut Length × Tan(Pitch Angle). Must never exceed 25% of actual lumber depth.
Pitch Angle (θ) = Arctan(Rise / 12)
Max Plumb Cut = Rafter Depth / 4 (IRC R802.7.1)
Plumb Cut = Min(Plate Width × Tan(θ), Max Plumb Cut)
Seat Cut = Plumb Cut / Tan(θ)
HAP = (Rafter Depth / Cos(θ)) - Plumb CutExample
For a 2×6 rafter (5.5" actual depth) on a 6/12 pitch with a 2×4 wall (3.5" plate): Max allowable cut = 5.5 ÷ 4 = 1.375 inches. Theoretical plumb cut = 3.5 × (6/12) = 1.75 inches. Because 1.75" > 1.375", the cut must be capped at 1.38 inches deep, producing a code-compliant seat cut of 2.75 inches with 4.77 inches of solid wood remaining.
Worked examples
Review these verified birdsmouth cut dimensions across common pitches and lumber sizes.
| Scenario | Calculation | Result |
|---|---|---|
| 2×6 Rafter on 4/12 Pitch (3.5" Wall Plate) | Plumb Cut = 3.5" × (4/12) = 1.17" (≤ 1.38" max). Seat Cut = 3.50". | Seat Cut: 3.50" | Plumb Cut: 1.17" | HAP: 4.63" |
| 2×6 Rafter on 6/12 Pitch (3.5" Wall Plate) | Plumb Cut restricted to 1.38" max. Seat Cut = 1.38 ÷ 0.50 = 2.75". | Seat Cut: 2.75" | Plumb Cut: 1.38" | HAP: 4.77" |
| 2×8 Rafter on 8/12 Pitch (3.5" Wall Plate) | Plumb Cut restricted to 1.81" max (7.25 ÷ 4). Seat Cut = 1.81 ÷ (8/12) = 2.72". | Seat Cut: 2.72" | Plumb Cut: 1.81" | HAP: 6.90" |
| 2×10 Rafter on 6/12 Pitch (5.5" 2×6 Wall Plate) | Plumb Cut restricted to 2.31" max (9.25 ÷ 4). Seat Cut = 2.31 ÷ 0.50 = 4.63". | Seat Cut: 4.63" | Plumb Cut: 2.31" | HAP: 8.03" |
Conversion reference
Reference table showing the maximum allowable plumb cut depth and resulting seat cut lengths across standard lumber dimensions.
| Lumber Size | Actual Depth | Max Allowable Plumb Cut (D/4) | Seat Cut (4/12 Pitch) | Seat Cut (6/12 Pitch) | Seat Cut (8/12 Pitch) |
|---|---|---|---|---|---|
| 2×4 | 3.50 inches | 0.88 inches (7/8") | 2.63 inches | 1.75 inches | 1.31 inches |
| 2×6 | 5.50 inches | 1.38 inches (1-3/8") | 3.50 inches | 2.75 inches | 2.06 inches |
| 2×8 | 7.25 inches | 1.81 inches (1-13/16") | 3.50 inches | 3.63 inches | 2.72 inches |
| 2×10 | 9.25 inches | 2.31 inches (2-5/16") | 3.50 inches | 4.63 inches | 3.47 inches |
| 2×12 | 11.25 inches | 2.81 inches (2-13/16") | 3.50 inches | 5.50 inches | 4.22 inches |
DID YOU KNOW?
Quick facts
- Over-cutting a birdsmouth notch beyond 1/4 the rafter depth is the most common residential framing inspection failure and reduces rafter span capacity by up to 50%.
- Height Above Plate (HAP) is the vertical measurement from the top of the wall plate to the top edge of the rafter; it must remain consistent across every rafter for the roof plane to be flat.
- A standard speed square or framing square is set using the pitch rise on the tongue (small arm) and 12 inches on the body (large arm) to scribe both cuts.
- IRC Section R802.6 requires a minimum 1.5 inches of continuous level bearing surface on wood wall plates for all common and hip rafters.
C.R. Vance, PE
Senior Structural & Building Envelope Engineer
- Professional Engineer (PE)
- ICC Certified Building Inspector
- NRCA Technical Consultant
C.R. Vance has spent over 22 years evaluating residential roof assemblies, structural load calculations, and building envelope waterproofing compliance across North America.
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Got Questions?
Frequently Asked Questions
Clear answers about roof square footage calculations, pitch slope factors, shingle bundles, and ordering materials.
Under IRC Section R802.7.1, notches on the ends of rafters cannot exceed one-fourth (1/4 or 25%) of the actual rafter depth. For a 2×6 rafter (5.5" actual), the maximum vertical plumb cut is 1.375 inches. For a 2×8 (7.25" actual), the maximum is 1.81 inches. Cutting deeper weakens the rafter at the reaction point and risks split failure under snow loads.
Height Above Plate (HAP) is the vertical distance measured from the level seat cut (the top plate of the wall) to the top edge of the rafter. HAP is the critical layout dimension that ensures all rafters sit at the exact same elevation so the roof decking forms a perfectly flat plane without dips or humps.
Under IRC Section R802.6, the minimum required bearing length for rafters on wood plates is 1.5 inches (38 mm). On masonry or concrete walls, the minimum bearing length is 3 inches (76 mm).
Place your framing square on the rafter with your pitch rise (e.g., 6) on the tongue and 12 on the body. Scribe the vertical plumb line along the tongue. Then slide the square to draw a 90-degree perpendicular line for the seat cut, measuring the horizontal seat length along the body.
NO. You must NEVER notch or cut a birdsmouth into an engineered roof truss. Trusses are engineered structural assemblies designed with specialized metal connector plates; cutting any notch into the bottom chord or top rafter chord voids the engineering stamp and causes immediate structural failure.
If a birdsmouth exceeds 1/4 the lumber depth, the cross-sectional area resisting horizontal shear and bending moment is compromised. Building inspectors will require the framing contractor to install structural sister rafters or replace the damaged members.
Under IRC Table R602.3(1), rafters can be toe-nailed to the top plate using three 16d common nails (or three 10d box nails). In high-wind and seismic zones, hurricane ties (such as Simpson Strong-Tie H2.5A clips) are required to resist wind uplift forces.
No. The plumb cut of the birdsmouth must align with the outside face of the exterior wall framing. The seat cut rests flat across the plate. If the plumb cut extends past the wall, the rafter is over-notched.
No. Hip and valley rafters run at a 45-degree angle to common rafters, which lowers their effective pitch. For example, a 6/12 common rafter corresponds to a 6/17 pitch on the hip. Hip rafters require a shallower seat cut and compound bevels (side cuts) at the plumb notch.
Use a circular saw to cut along both the seat line and plumb line, stopping just before the inner corner. Finish the intersection cleanly using a sharp hand saw or jigsaw. Never over-cut past the corner with a circular saw blade, as this creates a stress crack that causes lumber to split.
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