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The width of the top plate the rafter's bird's mouth notch will seat on.
A standard 2x wall plate is 3.5 in wide (dressed); double top plates and different framing thicknesses will vary.
The roof's slope, expressed as inches of rise per 12 inches of horizontal run.
The pitch the rafter is actually cut to, because the bird's mouth is where that pitch meets a level plate: the seat cut is level and the heel cut is plumb, and both angles come from this number alone. Cut at the wrong pitch the notch will not sit flat — the rafter rocks on one edge of the seat and the heel opens a gap at the plate. Check it against a rafter already cut before committing the batch.
Heel cut height
1.75 in
- Seat cut length (= plate width)
- 3.5 in
They open the calculator with your figures already in it
Rafter Bird's Mouth Cut Calculator: 1.75 in — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
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How this was calculated
Formula source(s)
- Standard carpentry bird's mouth layout: seat cut length equals the wall plate width; heel cut height = wall plate width × tan(roof pitch angle)
Inputs used
- Wall Plate Width
- 3.5 in
- Roof Pitch (rise per 12)
- 6
Intermediate steps
- Seat cut length (= plate width)
- 3.5 in
What this calculation does not cover
- The seat cut length shown is the plate width measured horizontally, which is not the distance to mark along the sloping edge of the rafter. On a 3.5 in plate at 6/12 the notch spans 3.91 in along the rafter's underside, that being the plate width divided by the cosine of the pitch angle, and the page gives neither that layout dimension nor the position of the notch along the rafter.
- Nothing here tests the section of rafter left above the notch, and no rafter depth is asked for. The 1.75 in heel cut on a 3.5 in plate at 6/12 removes 1.57 in measured square to the rafter's edges rather than 1.75 in, so reading the heel cut height straight against a fraction of the rafter depth overstates the notch.
- Roof pitch is taken strictly as rise per 12 units of run and is never converted, even when the plate width is entered in millimetres. Entering 20 for a 20 degree roof returns 5.83 in instead of 1.27 in, over four times the correct heel cut, because 20 in 12 is a 59 degree slope and that value sits inside the accepted 1 to 24 range.
- The geometry is that of a common rafter meeting the plate square. A hip or valley rafter travels 16.97 in in plan for every 12 in of common run, so at 6/12 its heel cut is about 1.24 in rather than 1.75 in, its seat crosses the plate at the corner instead of sitting square across it, and dropping or backing the hip to line up with the jacks alters the seat cut again.
- A circular saw taken to the intersection of the two cuts overruns the inner corner on the far face of the rafter, so the notch as cut is deeper than these two dimensions describe unless the corner is finished with a handsaw. Saw kerf, a crowned or twisted top plate, and sheathing carried up past the plate are all outside the figures, as are the ridge plumb cut, the half ridge thickness deduction and the tail cut.
- Engineered rafters are a separate matter entirely. I-joists and structural composite lumber permit no bird's mouth beyond a manufacturer-detailed seat at the low bearing, with an I-joist flange never notched, so applying this plate width times tangent result to them is not a small error but a prohibited cut.
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Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.
Sources checked 2026-09-02 · in the site-wide review of 2026-09-06 · v1.0.1
Regulatory standards & verification citations1
- Standard carpentry bird's mouth layout: seat cut length equals the wall plate width; heel cut height = wall plate width × tan(roof pitch angle)
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