Carpentry & Timber Framing • IRC R802.4.1 Structural Code

Rafter Length & Birdsmouth Cut Calculator

Calculate true rafter line length, birdsmouth seat cut width, heel cut vertical plumb depth, overhang tail length, and bevel angles for roof framing.

Input Parameters

Building Span (Wall-to-Wall) building_span_ft

Total building out-to-out framing width

Roof Pitch (Rise per 12" Run) roof_pitch_in

in/12

e.g. 6/12 pitch = 26.57°

Rafter Timber Depth (Nominal Width) rafter_depth_in

2x6 is 5.5", 2x8 is 7.25", 2x10 is 9.25"

Wall Top Plate Width wall_thickness_in

2x4 wall top plate is 3.5"; 2x6 wall is 5.5"

Eave Overhang Horizontal Run overhang_run_in

Horizontal projection past outside of wall plate

Ridge Board Thickness ridge_thick_in

Standard 2x dimensional ridge board is 1.5"

Calculated Outputs

Rafter Line Length (Work Point to Work Point) —

Plumb Cut & Miter Angle —

Birdsmouth Seat Cut (Bearing Width) —

Birdsmouth Heel Cut (Plumb Depth) —

Overhang Tail Rafter Length —

Minimum Stock Lumber Board to Order —

Verified Mathematical Identity

Run = (Span - Ridge) / 2 | L_line = Run · √[ 1 + (Pitch/12)² ] | HeelCut = Seat · (Pitch/12) ≤ Depth / 3

Analytical Derivation & Methodology

1. Theoretical Horizontal Run

For a symmetrical gable roof, horizontal run is half the building span minus half the ridge board thickness: Run = (Span - Ridge / 12) / 2.

2. Pitch Hypotenuse Factor & True Line Length

Roof pitch angle is θ = arctan(Pitch / 12). The line length factor is sec(θ) = √[1 + (Pitch / 12)²]. The true rafter line length from ridge work point to wall plate work point is L_line = Run × sec(θ).

3. Birdsmouth Seat & Heel Cut IRC Limits

The horizontal seat cut rests on the wall plate (minimum 1.5 inches per IRC R802.4.1). For full plate bearing, Seat = WallThickness. The vertical plumb heel cut depth is H = Seat × (Pitch / 12). IRC R802.4.1 strictly prohibits notching rafters deeper than one-third of the lumber depth (H ≤ Depth / 3) to prevent shear split.

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Frequently Asked Questions

According to International Residential Code (IRC R802.4.1), the maximum vertical depth of a birdsmouth heel cut cannot exceed one-third (1/3) of the rafter depth. For a 2x8 (7.25" actual), the maximum heel cut is 2.41 inches.

Set your saw angle to the plumb angle θ = arctan(Pitch/12). For example, a 4/12 pitch is 18.4°, a 6/12 pitch is 26.6°, an 8/12 pitch is 33.7°, and a 12/12 pitch is 45.0°.

Total rafter board length equals the line length (from ridge cut to birdsmouth plumb line) PLUS the overhang tail length (from birdsmouth to fascia tail plumb cut) plus an allowance for square cuts.