Birdsmouth Cut Calculator

Work out birdsmouth seat and plumb cuts, notch depth, HAP, rafter length, and ridge height with our free calculator. Checks IRC notch limits.

Unit System
Roof Geometry
ft
ft
/12
in
in
Rafter Details
in
in
in
in
Birdsmouth Cut
Birdsmouth rule: The perpendicular notch depth (material removed from the rafter's bottom edge) must not exceed 25% of the rafter depth for structural safety. For steeper pitches with a wide plate, reduce the seat cut length to stay within the limit.
Additional Materials
Cost Details
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$
$
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Rafter & Birdsmouth Summary
Birdsmouth: —
Roof Geometry
Building Span—
Run (ridge to wall)—
Rise—
Pitch (Rise:12)—
Pitch (Percent)—
Pitch (Degrees)—
Rafter Line Length—
Total Rafter Length (with overhang)—
Height at Ridge (top of rafter)—
Birdsmouth Cut
Seat Cut Length (horizontal bearing)—
Plumb Cut Height (vertical)—
Perpendicular Notch Depth—
Max Notch Allowed—
Notch Compliance—
Height Above Plate (HAP)—
Remaining Rafter Depth at Notch—
Materials
Number of Rafters—
Actual Rafter Spacing—
Total Rafter Lumber Length—
Ridge Board Length—
Collar Ties—
Collar Tie Length (each)—
Collar Tie Lumber (total)—
Hurricane Ties—
Cost Breakdown
Rafter Lumber Cost—
Ridge Board Cost—
Collar Tie Cost—
Connectors / Hardware—
Material Subtotal—
Labor Cost—
Additional Cost—
Estimated Total Cost—
ComponentValueUnit

Enter details and calculate to see breakdown.

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Faiq Ur Rahman is a web designer, digital product developer, and Founder of Techraxy, a growing platform of online calculators and utility tools. He specializes in building structured, user-friendly tools focused on finance, health, conversions, productivity, and everyday problem-solving. He is passionate about developing practical digital solutions that make complex tasks simpler for users worldwide.

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What is a birdsmouth cut?

A birdsmouth is a V-shaped notch cut into the bottom of a rafter where it meets the wall plate. It has two faces: a horizontal seat cut that bears on the plate, and a vertical plumb cut that runs up the inside face of the plate. The cut lets the rafter transfer the roof load straight down onto the wall instead of sliding off.

Every rafter has one critical cut: the birdsmouth. It’s the notch where the rafter meets the wall plate. Cut too deep and you’ve removed so much material that the rafter loses strength. Cut too shallow and the rafter rocks on the plate instead of bearing flat. This calculator takes your building span, pitch, and plate width and returns the exact seat cut and plumb cut dimensions. It also checks whether the perpendicular notch depth stays within the 25% IRC limit, since that’s the number that fails inspections. Rafter length, HAP, ridge height, and total rafter count come out of the same inputs. Framers use it on layout day. Owner-builders use it to sanity-check a set of plans before cutting a single board. Imperial and metric both work.

 

How to Use the Birdsmouth Cut Calculator

  1. Pick your unit system. Imperial uses inches and feet. Metric uses millimeters and meters.

  2. Enter the building span and length. Span is wall-to-wall across the ridge. Length is along the ridge.

  3. Choose your pitch format. Rise:12 is the standard way to express roof slope in the US. Percent and degrees work too.

  4. Enter the rafter spacing, typically 16 or 24 inches on center.

  5. Pick a rafter size or enter a custom width and depth. Depths run from 4 inches (2×4) up to 12 inches (2×12).

  6. Set the wall plate width and the horizontal roof overhang.

  7. Choose seat cut mode. Most codes want the seat cut equal to the plate width. You can override it.

  8. Pick a notch depth limit. IRC uses 25%. Some codes go to 33%. A conservative 20% is also available.

  9. Add collar ties and connectors if your design needs them, then enter unit costs and read the result.

 

How the Birdsmouth Cut Calculator Formula Works

The birdsmouth math runs from run and pitch. Run is half the span after subtracting the ridge board. Rise is run times pitch. The rafter line length and every birdsmouth dimension follow from those two numbers.

Formula: Run = (Span − Ridge Thickness) ÷ 2

Formula: Rise = Run × Pitch Ratio

Formula: Rafter Line Length = Run ÷ cos(atan(Pitch Ratio))

Formula: Total Rafter Length = (Run + Overhang) ÷ cos(atan(Pitch Ratio))

Formula: Plumb Cut Height = Seat Cut × tan(atan(Pitch Ratio))

Formula: Perpendicular Notch Depth = Seat Cut × sin(atan(Pitch Ratio))

Formula: Height Above Plate (HAP) = Rafter Depth ÷ cos(atan(Pitch Ratio))

The perpendicular notch depth is the number that matters most for code. It’s the vertical thickness of material removed from the rafter’s bottom edge. IRC caps that at 25% of the rafter depth. A 2×10 with a 9.25-inch depth gives a max notch of 2.31 inches. If your seat cut produces a deeper notch than that, you either reduce the seat cut or step up to a bigger rafter.

Plumb cut height is the vertical length of the cut on the wall side of the birdsmouth. It’s what sets how high the rafter sits above the plate. HAP is measured from the top of the plate to the top edge of the rafter. Together, plumb cut height and HAP position the rafter for the rest of the roof.

Rafter count comes from building length and spacing. A 40-foot building at 16 inches on center needs 31 rafters per side, so 62 total. The tool rounds up and reports the actual spacing, which is usually a fraction less than the target.

 

Worked Example

A garage with a 26-foot span, 36-foot length, and an 8:12 pitch. 2×10 rafters at 16 inches on center. Wall plate is 3.5 inches wide. 18-inch overhang. Standard seat cut equal to plate width.

Step 1 — Run. (26 − 0.125) ÷ 2 = 12.94 ft.

Step 2 — Pitch angle. 8:12 = 0.6667 ratio. atan(0.6667) = 33.69°.

Step 3 — Rise. 12.94 × 0.6667 = 8.63 ft.

Step 4 — Rafter line length. 12.94 ÷ cos(33.69°) = 12.94 ÷ 0.832 = 15.55 ft.

Step 5 — Total rafter length. (12.94 + 1.5) ÷ 0.832 = 17.35 ft.

Step 6 — Plumb cut height. 3.5 in × tan(33.69°) = 3.5 × 0.6667 = 2.33 in.

Step 7 — Perpendicular notch depth. 3.5 × sin(33.69°) = 3.5 × 0.5547 = 1.94 in.

Step 8 — Notch check. 1.94 ÷ 9.25 = 21% of rafter depth. IRC limit is 25%, so the cut passes.

Step 9 — HAP. 9.25 ÷ cos(33.69°) = 9.25 ÷ 0.832 = 11.12 in.

Step 10 — Rafter count. 36 ft at 16 in on center: 28 spaces, 29 rafters per side, 58 total. Actual spacing 15.72 in.

Step 11 — Ridge board. 36 + 2 × 1.5 = 39 ft.

Interpretation: The birdsmouth passes IRC without adjustment. You need 58 rafters at 17.35 feet each, 610 feet of total rafter lumber, and a 39-foot ridge board. Notch depth stays 1.94 inches, well within the 2.31-inch limit.

Frequently Asked Questions

How do I cut a birdsmouth on a rafter?

Mark the plumb cut at the wall side first, then mark the seat cut horizontally from the same corner. The seat cut should match the plate width, usually 3.5 inches. Cut both lines with a circular saw, then clean the corner with a handsaw. The notch depth should stay under 25% of the rafter depth.

 

What is the maximum notch depth for a rafter?

25% of the rafter depth under IRC. A 2×10 with a 9.25-inch actual depth allows a 2.31-inch perpendicular notch. Some codes allow 33%, and many framers use 20% as a conservative target. Anything deeper needs a bigger rafter or a shallower seat cut.

 

How do I calculate the seat cut length?

Start with your wall plate width. A standard 2×4 top plate measures 3.5 inches, so the seat cut is 3.5 inches long. You can go wider for more bearing surface, but wider seat cuts produce deeper notches at steep pitches.

 

What is HAP in roof framing?

Height above plate. It’s the vertical distance from the top of the plate to the top of the rafter. Calculate it by dividing rafter depth by the cosine of the pitch angle. A 2×10 at an 8:12 pitch gives an 11.1-inch HAP.

 

How many rafters do I need?

Divide building length by spacing, add one, and double the result. A 40-foot building at 16 inches on center needs 62 rafters total. The calculator reports the actual spacing after the count rounds up.

 

How do I calculate rafter length?

Divide run by the cosine of the pitch angle. Run is half the span minus half the ridge thickness. Add the overhang to the run before dividing for the total rafter length including the tail.

 

What is a good roof pitch?

Between 4:12 and 9:12 for standard residential roofs. 6:12 is the most common. Below 4:12 you need special underlayment. Above 9:12 is considered steep and needs fall protection during installation.

 

Why is my birdsmouth notch too deep?

A wide seat cut at a steep pitch. The same 3.5-inch seat that passes at 4:12 can fail at 10:12. Reduce the seat cut length, step up to a bigger rafter, or add a rake-side connection detail to avoid a deep notch.

 

Do I need collar ties?

They’re required in the upper third of the attic space when the roof pitch is above a threshold (typically 3:12) and the ridge doesn’t have a structural beam. Collar ties resist wind uplift, not the roof’s weight. Ridge straps or a structural ridge can substitute.

 

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

The seat cut is the horizontal bearing surface on the wall plate. The plumb cut is the vertical face along the inside edge of the plate. Together they form the birdsmouth. A third cut, the ridge cut, angles to meet the ridge board.

 

Can I use this calculator for a shed roof?

Partially. A shed roof has one rafter run instead of two, so the “run” is the full span, not half. Enter the span as double the actual run and divide the rafter count in half, or treat it as a single-sided calculation. The birdsmouth math is the same.

Disclaimer

This calculator provides geometric and code-reference estimates. It doesn’t replace a structural engineer’s review, a permit inspection, or your local building code. Rafter spans depend on species, grade, and load, none of which are modeled here. The birdsmouth check only verifies notch depth, not whether the rafter itself is adequate for the span. Verify all dimensions, materials, and connection details with a qualified engineer or inspector before construction. Cost figures reflect the unit prices you enter and won’t match every market.

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