Birdsmouth Cut Calculator

To cut a birdsmouth, first mark the plumb line at the outside face of the wall on your rafter. Set your framing square to the roof pitch and draw the level seat-cut line back toward the ridge; its horizontal length is the seat cut. Then draw the plumb heel-cut line down from the top edge at the wall line. Example: on a 6/12 pitch with a 2x8 rafter and a 3 inch seat cut, the heel cut is exactly 1-1/2" deep and the height above plate is 6-5/8". Cut the triangular notch out with a circular saw, finishing the corner with a handsaw so you do not overcut. This page is a birdsmouth cut rafter layout tool that does every one of these steps for you.

The seat cut vs heel cut distinction is simple: the seat cut is the level (horizontal) face of the birdsmouth that sits flat on top of the wall plate, while the heel cut is the plumb (vertical) face that bears against the outside edge of the plate. Carpenters size a birdsmouth by the heel-cut depth, because that is the dimension the building code limits. The two cuts and the rafter's bottom edge form a right triangle where heel depth equals seat length times the tangent of the pitch angle.

Height above plate (HAP) is the vertical distance from the top of the wall plate to the top edge of the rafter, measured at the outside face of the wall (the heel plumb line). It is computed as rafter depth divided by cos(pitch angle), minus the heel-cut depth. For a 2x8 (7-1/4 in actual) on a 6/12 pitch, rafter depth over cos is 8-1/8"; with a 1-1/2" heel cut the HAP is 6-5/8". Raising the HAP shallows the birdsmouth, which is the standard fix when a heel cut fails the code limit.

IRC rafter notch limits come from IRC R802.7.1, which points to R502.8.1: notches at the ends of a member, which includes the birdsmouth at the plate, shall not exceed one-fourth the depth of the member. That gives a max birdsmouth depth (heel cut, plumb) of 1-3/8" for a 2x6, 1-13/16" for a 2x8, 2-5/16" for a 2x10, and 2-13/16" for a 2x12. On a 6/12 pitch with a 2x8, that caps the seat cut at 3-5/8". Always verify local code, because your inspector's amendments control.

A shed roof birdsmouth uses the exact same math as a gable roof: one birdsmouth per rafter where it bears on the high wall (the low end typically lands on a ledger or a second birdsmouth). Example: 4/12 pitch, 2x8 rafter, 3 inch seat cut gives a 1" heel cut, 6-5/8" HAP, and passes the IRC one-fourth-depth check. Because shed roofs are often low-slope, watch the heel depth: shallow pitches need longer seat cuts to reach the same heel depth, and the seat must still fit on the plate.

Roof pitch to angle is arctangent of rise over run: angle = atan(pitch/12). Common conversions: 4/12 is 18.4°, 6/12 is 26.6°, 8/12 is 33.7°, and 12/12 is 45.0°. A roof pitch calculator also needs the slope factor, which is the hypotenuse per foot of run: 1.1180 for 6/12, so each foot of horizontal run is 1.1180 ft of rafter. The calculator above shows pitch to degrees live as you type.

Common rafter length is run times the slope factor, measured along the top edge from the ridge plumb line to the heel plumb line at the wall. Run is half the span minus half the ridge-board thickness. Example: 24 ft span, 6/12 pitch, 1-1/2 in ridge board gives a run of 11' 11-1/4" and a rise of 5' 11-5/8". Rafter length is 13' 4-3/16", the 12 in overhang tail adds 1' 1-7/16", for 14' 5-9/16" overall. A rafter length calculator must deduct the ridge before multiplying, which this roof rafter calculator does.

A hip rafter calculator works per foot of common run: hip length per foot is the hypotenuse of 17 and the unit rise (16.97 in is the diagonal of a 12 in square). On a 6/12 pitch that is 18.03 in per foot, so a 10 ft run gives a 15' 1/4" hip. The hip pitch angle is 19.4°, the cheek cut angle on the top face is 43.3°, and the backing angle is 18.4°. A valley rafter calculator uses identical math. Jack rafters step down by 17-7/8" at 16 in on-center (26-13/16" at 24 in). A jack rafter calculator table is built into the Hip & Valley tab.

Framing layouts use 16ths fraction because a 1/16 in graduation is the finest mark most carpenters can reliably transfer with a tape and pencil, and it keeps rounding error under about 1/32 in per mark, which does not accumulate visibly across a roof. All inch outputs on this page round half-up to the nearest 16th, for example a heel cut of 1.5 in shows as 1-1/2 in and a HAP of 6.604 in shows as 6-5/8". Metric mode switches every output to millimetres.

No. The one-third rule you see on older calculators is a rule of thumb, not code: some tools cap the heel cut of a birdsmouth 2x8 at one-third of rafter depth. The actual IRC limit for an end notch like a birdsmouth is one-fourth (see the max birdsmouth depth table above). Related trade guidance from the Journal of Light Construction says to leave roughly two-thirds of the rafter width intact, measured square to the board, to support an overhang; for a birdsmouth 6/12 roof framed with 2x8 rafters and a 3 in seat cut, the remaining section is 5-15/16" versus the two-thirds line of 4-13/16". When rules disagree, the code wins and the inspector decides.

Yes. Switch the unit toggle to Metric and every input and output becomes millimetres: seat cut, HAP, heel-cut depth, rafter lengths, and hip dimensions. Pitch stays in x/12 form because it is unitless, and the IRC one-fourth-depth check is a ratio so it is identical in any unit system. Fractions to 16ths only apply to imperial inches; metric rounds half-up to 0.1 mm.

This tool is a geometry layout aid, not structural design. Conventional light-frame roofs inside the IRC prescriptive tables generally do not need an engineer, but the code limits here (notch depths, spans, connections) are minimums, and local amendments, snow, wind, and seismic loads can change everything. Verify local code with your building department, and hire a licensed structural engineer for anything outside prescriptive framing: long spans, heavy loads, engineered lumber, or repairs to cut structural members.