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Rafter Birdsmouth Cut

Calculate standard common rafter plumb cuts, seat cut angles, line lengths, and tail overhangs based on the building span and roof pitch.

Roof Architecture

Total Span

Outside to Out

Roof Pitch

/ 12

Rise per ft

Ridge Thick.

Slightly shortens run

Overhang

Horiz. Eave

Cut Details

Total Min Board Length

160.16

inches

Does not account for scrap waste allowance

Top Plumb Cut

63.4

Degrees

Base Seat Cut

26.6

Degrees

Adjusted Run (w/ Ridge Deduction)	119.25"
Line Length (Ridge to Heel)	133.33"
Tail Length (Heel to Fascia)	26.83"

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What is Roof Rafter Geometry & Birdsmouths?

A common rafter relies on strict trigonometric geometry to form the pitch (slope) of a roof. Plumb cuts create the vertical mating surface against the ridge board, while the Birdsmouth seat cut creates a flat horizontal notch where the rafter rests securely on top of the exterior wall plates.

Mathematical Foundation

Adjusted Run

\text{Run} = \frac{\text{Total Building Span}}{2} - \frac{\text{Ridge Thickness}}{2}

Ridge Deduction

= Half the thickness of the ridge board must be subtracted because the rafter attaches to the face of it, not the mathematical center of the building.

Rafter Line Length (Hypotenuse)

\text{Line Length} = \frac{\text{Adjusted Run}}{\cos(\arctan(\frac{\text{Pitch}}{12}))}

\cos(\theta)

= Trigonometric expansion of the Pythagorean theorem, converting horizontal span into angled roof distance.

Laws & Principles

Framing Square Pitch Constant: Roof pitches in North America are designated by inches of rise per 12 inches of run (e.g. '6/12 pitch'). Base angles are derived from the arctan of (Pitch/12).
Birdsmouth Depth Limitation: Building codes (like the IRC) mandate that a birdsmouth notch can NEVER exceed more than 1/4 of the rafter depth. Cutting deeper weakens the lumber, leading to sagging roofs or structural failure.
Ridge Deduction Fallacy: Beginner framers often cut rafters to the exact mathematical center of the building. This is incorrect. You must subtract 3/4 inch (half of a standard 1.5-inch thick 2x ridge board) from the run so the rafter seats flush against the ridge face.

Step-by-Step Example Walkthrough

" Cutting common rafters for a shed spanning 240 inches (20 feet) across, using a standard 6/12 pitch roof, a 2x ridge board (1.5 inches thick), and a 24-inch horizontal overhang. "

1. Define Center: 240 inches / 2 = 120-inch Run.
2. Adjust for Ridge: 120 - 0.75 (half the 1.5-inch board) = 119.25-inch Adjusted Run.
3. Determine Angles: Arctan(6/12) gives a 26.56-degree pitch angle.
4. Calculate Line Length: 119.25 / Cos(26.56) = 133.32-inch Line Length (Ridge to Heel).
5. Add Tail: 24-inch overhang / Cos(26.56) = 26.83-inch Tail Length.
6. Final Board: 133.32 + 26.83 = 160.15 inches minimum board required.

Final Result: Source at least 14-foot lumber. Mark a top plumb cut of 63.4 degrees and measure down 133.3 inches to the birdsmouth heel point.

Quick Answer: How do you calculate rafter length and birdsmouth cuts?

To calculate a common rafter, divide the total building span by 2, subtract half the ridge board thickness, then divide the adjusted run by cos(arctan(pitch/12)) to get the line length from ridge to wall plate. The birdsmouth is a notch cut where the rafter meets the wall — its horizontal seat cut equals the wall plate width (typically 3.5 inches for a 2x4 wall), and its vertical plumb cut angle is found from the roof pitch. The IRC limits birdsmouth depth to one-quarter of the rafter depth.

Rafter Geometry Formulas

Adjusted Run = (Building Span ÷ 2) − (Ridge Thickness ÷ 2)

Line Length = Adjusted Run ÷ cos(arctan(Pitch ÷ 12))

Tail Length = Overhang Run ÷ cos(arctan(Pitch ÷ 12))

Pitch/12: North American convention — 6/12 means the roof rises 6 inches for every 12 inches of horizontal run.

Plumb Cut Angle: 90 − arctan(pitch/12). This is the angle you set on your circular saw or speed square.

Common Roof Pitch Reference

Pitch	Angle (degrees)	Multiplier per Foot of Run	Typical Application
2/12	9.46°	1.014	Low-slope commercial, membrane roofing
4/12	18.43°	1.054	Minimum for standard asphalt shingles
6/12	26.57°	1.118	Common residential, good attic space
8/12	33.69°	1.202	Colonial style, heavy snow regions
12/12	45.00°	1.414	Steep A-frame, maximum snow shedding

The multiplier converts one foot of horizontal run into actual rafter length along the slope. Multiply your total adjusted run by this factor to get the line length. For a 10-foot run at 6/12 pitch: 10 × 1.118 = 11.18 feet of rafter.

Rafter Cutting Failures

The Ridge Deduction Miss

A carpenter cuts 24 rafters using half the building span (120 inches) as the run. He forgets to subtract the 3/4-inch ridge deduction. Each rafter is 3/4 inch too long. When rafters from opposite sides meet at the ridge, they push each other apart by 1.5 inches total. The ridge board lifts off the king posts and the entire ridge line bows upward in a visible hump. All 24 rafters must be trimmed at the plumb cut.

The Over-Cut Birdsmouth

A framer notches a 2x8 rafter (7.25 inches deep) with a 3-inch deep birdsmouth to sit fully over the double top plate. This exceeds the IRC maximum of 1/4 depth (1.81 inches). Over winter, snow load pushes downward on the weakened heel point. The rafter splits horizontally along the grain at the birdsmouth, and the tail section snaps off the building, taking the fascia and gutter with it.

Rafter Layout Best Practices

Do This

✓Use a pattern rafter. Cut one rafter, test-fit it on the building, verify the plumb cut seats flush against the ridge face and the birdsmouth sits flat on the plate. Only after confirming the pattern should you gang-cut the remaining rafters using the pattern as a template.
✓Crown all lumber upward. Every dimensional board has a natural bow (crown). Place the crowned edge facing the sky so gravity loads push against the arch. A rafter installed crown-down will sag between the ridge and the wall under load.

Avoid This

✗Don't measure run to the building center. Always deduct half the ridge board thickness (3/4 inch for a 2x ridge) from the half-span. This is the most common error in rafter framing and causes the ridge to bow upward when opposing rafters push against each other.
✗Don't confuse pitch angle with plumb cut angle. A 6/12 pitch has a 26.57-degree roof angle, but the plumb cut on the speed square reads 63.43 degrees (the complement). Setting your saw to 26.57 degrees produces a level cut, not a plumb cut.

Frequently Asked Questions

What is a birdsmouth cut on a rafter?

A birdsmouth is a triangular notch cut into the bottom edge of a rafter where it meets the wall top plate. It consists of two cuts: the 'seat cut' (a horizontal cut that sits flat on the plate) and the 'heel cut' (a vertical plumb cut that faces the inside of the building). The notch creates a secure bearing surface that prevents the rafter from sliding off the wall under roof loads.

How deep can you cut a birdsmouth?

The International Residential Code (IRC) limits the birdsmouth depth to one-quarter of the rafter depth. For a 2x6 rafter (5.5 inches deep), the maximum notch depth is 1.375 inches. For a 2x8 (7.25 inches deep), the maximum is 1.81 inches. Exceeding this limit weakens the rafter at the bearing point and can cause the heel to split under snow or wind uplift loads.

Why do you subtract the ridge board thickness from the rafter run?

The rafter plumb cut bears against the face of the ridge board, not the mathematical center of the building. A standard 2x ridge is 1.5 inches thick, so the rafter stops 3/4 inch short of center. If you forget this deduction, opposing rafters from each side will push the ridge upward by 1.5 inches total, bowing the ridge line and creating visible roof humps.

What is the difference between a plumb cut and a level cut?

A plumb cut is vertical (plumb to the ground) when the rafter is installed at its roof angle. This is the cut at the ridge and the heel cut of the birdsmouth. A level cut is horizontal (level with the ground) when the rafter is installed. This is the seat cut of the birdsmouth. On a framing square, the plumb cut follows the rise side and the level cut follows the run side of the pitch triangle.