Calculate rafter birdsmouth notch dimensions (seat cut, heel cut, HAP height above plate), theoretical rafter line lengths, plumb cuts, overhangs, and IRC building code safety checks.
Vertical Heel Cut is within structural limits, preserving required shear load resistance at the support plate.
In traditional roof stick-framing, an angled roof rafter cannot simply balance on the narrow corner edge of a wall plate. A Birdsmouth Cut (or bird's mouth notch) is a triangular cutout on the underside of the rafter that provides a solid, level bearing platform:
The horizontal bottom face of the notch that rests directly on the top wall plate. Under the International Residential Code (IRC), wood rafters must have a minimum bearing length of at least 1.5 inches on wood and 3.0 inches on masonry.
The vertical cut that sits flush against the outside edge of the top plate. The depth of this cut dictates the remaining vertical lumber thickness (HAP) left to resist bending and shear forces.
Over-notching a rafter is one of the most common reasons residential roof framing fails building inspections. When you cut into the bottom tension edge of a rafter, you reduce its effective beam depth:
| Nominal Lumber | Actual Depth | Max 1/3 Heel Cut (IRC Code) | Conservative 1/4 Cut (Snow Zones) |
|---|---|---|---|
| 2×4 Lumber | 3.50 in | 1.17 in (1-3/16") | 0.88 in (7/8") |
| 2×6 Lumber | 5.50 in | 1.83 in (1-13/16") | 1.38 in (1-3/8") |
| 2×8 Lumber | 7.25 in | 2.42 in (2-7/16") | 1.81 in (1-13/16") |
| 2×10 Lumber | 9.25 in | 3.08 in (3-1/16") | 2.31 in (2-5/16") |
| 2×12 Lumber | 11.25 in | 3.75 in (3-3/4") | 2.81 in (2-13/16") |
HAP (Height Above Plate, also called "Stand" or "Heel Height") is the vertical thickness of wood remaining directly above the heel cut up to the top rafter edge:
If one rafter has an HAP of 4.5" and another has 4.25", your roof plywood decking will develop visible humps and valleys, and the eave subfascia will wave unevenly along the wall.
When framing hip roofs, the hip rafter sits at a shallower slope ($6/17$ vs $6/12$). Carpenters must calculate the hip birdsmouth so its center line matches the common rafter HAP exactly.
Why does a notched rafter fail when overloaded? Softwood lumber (Douglas Fir, Hem-Fir, Southern Pine) has strong longitudinal grain fibers but weak cross-grain tension resistance:
The 90° internal corner where the seat cut meets the heel cut acts as a major stress riser. Under downward bending, tensile forces concentrate at this microscopic apex point.
Horizontal shear stress is calculated strictly using remaining uncut lumber depth ($d_{\text{eff}} = d_{\text{rafter}} - d_{\text{heel}}$). An overnotched rafter can experience sudden horizontal split failure along the grain line.
Toenailing (3× 8d nails) provides minimal uplift resistance ($~150\text{ lbs}$). Engineered hurricane ties (Simpson H2.5A) provide $500–1,000\text{ lbs}$ of seismic and wind uplift restraint.
Hip and valley rafters run diagonally at $45^\circ$ relative to the exterior walls. Because the diagonal run across a 12-inch square is $\sqrt{12^2 + 12^2} = 16.97\text{"} \approx 17\text{"}$, hip rafters have a shallower pitch than common rafters:
A common rafter with a 6/12 pitch has a corresponding hip rafter with a 6/17 pitch (19.4° vs 26.6°). Plumb and level cuts on hip rafters are marked using 17 on the framing square body rather than 12.
Because the hip rafter is thicker and sits at a shallower angle, its center edge would poke above the common rafter plane if unadjusted. Master carpenters deepen the birdsmouth seat cut by 1/4" to 3/8" (dropping the hip) or bevel the top edges (backing the hip) so roof sheathing lies completely flat.
A birdsmouth cut (or bird's mouth joint) is a triangular notch cut into the underside of a roof rafter that allows it to rest securely and flat on the top wall plate. It consists of two intersecting cuts: (1) The Seat Cut (a horizontal, level cut resting on top of the plate) and (2) The Heel Cut (a vertical, plumb cut sitting flush against the exterior face of the wall plate). This joint transfers roof vertical dead loads and snow loads directly down through the wall studs.
Under the International Residential Code (IRC Section R802.7.1) and general structural engineering standards, the vertical heel cut depth of a birdsmouth notch must NOT exceed 1/3 of the total rafter depth (and no more than 1/4 depth in heavy snow load or engineered framing jurisdictions). For example, on a 2x6 rafter (actual depth 5.5 inches), the maximum legal heel cut is 1.83 inches (5.5 / 3 = 1.83"). Over-notching severely reduces the lumber's cross-sectional shear capacity at the support bearing point.
HAP (Height Above Plate, also known as 'Stand' or 'Heel Height') is the vertical distance measured along a plumb line from the top of the wall plate to the top edge of the rafter directly above the birdsmouth notch. HAP = (Rafter Depth / cos(Pitch Angle)) - Heel Cut Depth. Maintaining an identical HAP across all common rafters, hip rafters, and valley rafters is vital so that roof sheathing lies in a perfectly flat plane and exterior fascia/soffit heights align uniformly.
The trigonometry of a birdsmouth cut is governed by roof slope: (1) Pitch Angle θ = arctan(Rise / 12); (2) If full bearing on a 3.5-inch wall plate is used, Seat Cut = 3.5 inches; (3) Vertical Heel Cut = Seat Cut × tan(θ) = 3.5 × (Rise / 12). For example, on a 6/12 pitch roof with a 2x4 wall (3.5" plate), the Heel Cut = 3.5 × (6 / 12) = 1.75 inches, leaving a full 4.40-inch HAP on a 2x6 rafter.
Wider wall plates (such as a 2x6 exterior wall with a 5.5-inch top plate vs. a 2x4 wall with a 3.5-inch plate) require wider bearing surface. However, cutting a full 5.5-inch seat cut on steep roof pitches (8/12 or higher) on 2x6 rafters can easily violate the 1/3 maximum heel cut code limit. In such cases, carpenters cut a partial seat cut (e.g., 3.5 inches) or step up to 2x8 or 2x10 rafter stock to maintain adequate HAP and structural shear strength.
To lay out a birdsmouth cut: (1) Using a Swanson Speed Square, align the pivot point on the bottom edge of the rafter and rotate until the roof pitch number (e.g., 6 on the Common scale) aligns with the rafter edge; (2) Draw the vertical Plumb Line for the heel cut; (3) Measure your calculated Heel Cut Depth along this line; (4) Align the square at 90 degrees to the plumb line (or level) and scribe the horizontal Seat Cut line to the bottom edge; (5) Cut with a circular saw, stopping exactly at the corner intersection, and finish with a hand saw to avoid overcutting.
