What is a birdsmouth cut?

A birdsmouth (seat cut) is the triangular notch where the rafter rests on the wall's top plate. The seat cut angle equals the pitch angle, and the opposing plumb cut equals 90° minus the pitch angle. Keep the notch depth to a quarter of the rafter depth or less.

What pitch should a lean-to roof have?

Most lean-to and shed roofs use between 2:12 and 6:12. Below 2:12 you must switch to a waterproof membrane instead of shingles; steeper pitches shed water faster but add height and material cost. A 3:12 to 4:12 pitch is a common all-round choice for asphalt shingles.

Shed Roof Pitch Calculator

Calculate single-slope lean-to pitch, wall height differences, birdsmouth cuts, and rafter lengths.

Shed Dimensions

Shed Span / Width (Wall to Wall)

High Wall Height

Low Wall Height

High Overhang

Low Overhang

Rafter Spacing

Mono-Slope Elevation

Rise: 2 ft

Rafter Lumber: 2x4 (16" o.c.) or 2x6 (24" o.c.) • Total Cut: 12' 2 7/8"

2.4:12

Shed Pitch

11.3°

Roof Angle

12' 2 7/8"

Total Rafter Cut

2 ft

Wall Height Diff

Shed Rafter Cutting & Birdsmouth Specifications

Framing Element	Dimension / Angle	Carpentry Instructions
Plumb Cut (Top & Bottom Ends)	78.7°	Mark square from top edge using speed square set to 2.4:12.
Seat Cut (Birdsmouth Notch)	11.3°	Rest flush on 2x4 (3.5") or 2x6 (5.5") top plate. Notch depth ≤ 1/4 rafter depth.
Base Rafter (No Overhang)	10.2 ft	Center-to-center distance between high and low exterior wall top plates.
Recommended Lumber Size	2x4 (16" o.c.) or 2x6 (24" o.c.)	Based on 16" spacing and span under standard 30psf snow / 10psf dead load.

Shed Roof Terms and How the Calculator Works

A shed roof — also called a mono-pitch or lean-to roof — is a single sloping plane that runs from a taller high wall down to a shorter low wall. Its pitch comes entirely from the wall height difference: rise ÷ span, normalized to a 12-inch run. That is why the calculator only needs the wall-to-wall span and the two wall heights to produce the full cutting layout.

Span

Horizontal distance from the outside of the high wall to the outside of the low wall, wall to wall.

Rise

Vertical difference between the high-wall and low-wall top plates. Rise per 12" of span is the pitch (X:12).

Plumb cut

The vertical end cut on the rafter, set to 90° minus the pitch angle so the rafter edge stands plumb.

Seat cut (birdsmouth)

The notch resting on the top plate, angled at the pitch angle. Keep notch depth to ¼ of the rafter depth or less.

Rafter factor

Multiplier giving true rafter length per foot of run: √(1 + (rise/12)²). Example: a 4:12 shed roof = 1.054.

Overhang (tail)

Extension past the wall forming the eave. Add overhang × rafter factor to the base rafter for total cut length.

How to use it: enter the shed span and both wall heights (any units — fractional inches work), add the front and rear overhangs you plan, and pick 16" or 24" rafter spacing. The calculator returns the pitch ratio, angle, plumb and seat cut angles, the total rafter cut length including overhangs, and a suggested lumber size for the span at standard 30 psf snow / 10 psf dead loads. Always confirm final sizing against your local code and, for long spans or heavy snow regions, a framing table or engineer.

Related Roofing Tools

Frequently Asked Questions

Subtract the low wall height from the high wall height to get the vertical rise, then divide the wall-to-wall span by that rise and normalize to 12. For example, a 10 ft span with a 2 ft height difference rises 24 inches over 120 inches of run — a 2.4:12 pitch (11.3°).