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Category Construction & Repair

Pitch Input Mode

Rise (per 12 run)

Roof Angle (°)

Unit System

Rafter Lumber Size

Rafter Depth Rafter Width

Birdsmouth Depth (optional) Leave blank for maximum allowed (⅓ of depth)

Top Plate Width (optional) For seat cut bearing check

Quick Presets:

Enter rafter dimensions and pitch, then press Calculate.

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About

A birdsmouth (or bird's mouth) is a notch cut into a rafter where it bears on the wall top plate. The notch consists of two cuts: a horizontal seat cut (or heel cut) that rests flat on the plate, and a vertical plumb cut that aligns with the outer face of the wall. Incorrect geometry here means the rafter load transfers through a point contact instead of a bearing surface. This concentrates stress, splits the rafter tail, and in extreme cases causes the roof to spread outward under snow or wind load. IRC Section R802.6 limits the birdsmouth depth to no more than ⅓ of the rafter depth for this reason.

This calculator derives the seat cut length, plumb cut height, and Height Above Plate (HAP) from your roof pitch and rafter dimensions using basic trigonometry. It enforces the one-third depth rule and flags violations. The rendered diagram is drawn to scale on a canvas element so you can verify proportions visually before marking lumber. Note: the tool assumes dimensional lumber with rectangular cross-section and does not account for compound angles in hip or valley rafters.

Formulas

Given a roof pitch angle θ and rafter lumber of depth D and width W, the birdsmouth dimensions are computed as follows:

Seat Cut Length = dsin(θ)

Plumb Cut Height = dcos(θ)

HAP = D − d

Where d is the birdsmouth depth measured perpendicular to the rafter edge. The constraint from IRC R802.6 requires:

d ≤ D3

The rafter length factor per foot of run is:

Rafter Factor = √1 + tan²(θ)

Where θ = roof pitch angle in degrees, D = full rafter depth (e.g., 5.5″ for a 2×6), W = rafter width (e.g., 1.5″ for dimensional lumber), d = birdsmouth notch depth perpendicular to rafter length, and HAP = Height Above Plate (remaining rafter depth above the seat cut).

Reference Data

Roof Pitch	Angle (°)	Rise per Foot	Rafter Factor	Common Use
2/12	9.46°	2″	1.0138	Low-slope membrane roofs
3/12	14.04°	3″	1.0308	Minimum shingle slope
4/12	18.43°	4″	1.0541	Standard residential
5/12	22.62°	5″	1.0833	Standard residential
6/12	26.57°	6″	1.1180	Common residential
7/12	30.26°	7″	1.1577	Steeper residential
8/12	33.69°	8″	1.2019	Steep residential, colonial
9/12	36.87°	9″	1.2500	Steep gable
10/12	39.81°	10″	1.3017	Steep gable, A-frame
11/12	42.51°	11″	1.3566	Very steep
12/12	45.00°	12″	1.4142	45° gable
14/12	49.40°	14″	1.5366	Gothic, steep dormers
16/12	53.13°	16″	1.6667	Mansard upper slope
18/12	56.31°	18″	1.8028	Mansard, decorative

Frequently Asked Questions

Removing more than one-third of the cross-section at the bearing point reduces the effective bending strength of the rafter below the design capacity assumed in span tables. The remaining two-thirds (the HAP) must carry the full bending moment from roof loads. Exceeding this limit can cause the rafter to split horizontally along the grain at the notch under concentrated bearing stress.

As pitch angle θ increases, sin(θ) increases, so the seat cut length decreases for the same notch depth d. At a 4/12 pitch (18.43°), a 1.5″ deep notch produces a seat cut of about 4.74″. At 12/12 (45°), the same notch depth gives only 2.12″. Steeper roofs naturally produce shorter seat cuts.

Generally no. Engineered lumber manufacturers prohibit field-notching because the lamination layers or web/flange structure cannot tolerate the stress concentration. LVL, TJI, and similar products require proprietary connector hardware (e.g., Simpson hangers) instead of birdsmouth cuts. Always check the manufacturer's installation guide.

The full rafter depth D applies along the unnotched span. At the birdsmouth, the effective structural depth is the HAP (D − d). Span tables are calculated assuming the rafter is unnotched. The one-third rule ensures the HAP retains at least 66.7% of the original depth, which preserves approximately 44% of the section modulus at the bearing point.

The seat cut should be at least as long as the top plate width (typically 3.5″ for a 2×4 wall or 5.5″ for a 2×6 wall) to provide full bearing. A shorter seat cut concentrates the load on a partial area, which can crush the plate. If your calculated seat cut is shorter than the plate width, you must either increase the notch depth (within the one-third limit) or add a beveled bearing block.

Set a framing square with the rise on the tongue and 12 on the blade. Draw the plumb line along the tongue. Then flip the square to draw the level line (seat cut) perpendicular to the plumb line. The intersection depth from the bottom rafter edge must equal your calculated notch depth d. Use a circular saw for the straight cuts and finish the inside corner with a handsaw to avoid overcutting.