The birdsmouth is the notch that lets a rafter sit flat and solid on the wall plate. Get it right and the roof load lands squarely on the wall; get it wrong — too deep, too shallow, or a seat that overhangs the plate — and you have weakened the rafter at exactly the point where it carries the most load. This calculator works out the seat cut, the plumb depth of the notch, the depth removed from the board, and the height above plate (HAP) left standing over the wall, and checks the notch against the IRC one-quarter limit for your lumber size.
A birdsmouth has two cuts. The seat cut is the horizontal cut that rests on top of the wall plate — its length is the number you enter above, and on a standard 2×4 wall it usually runs the full width of the plate, 3.5 inches. The plumb cut is the vertical cut that bears against the inside face of the plate. Together they form a notch shaped, from the side, like an open bird's beak — which is where the name comes from.
The dimension that matters most after cutting is the HAP — height above plate: the vertical distance from the top of the plate to the top edge of the rafter, measured at the wall line. HAP is what sets the height of your ceiling and the top of your roof at the eaves, and it is what remains of the rafter to carry load over the wall. Two rafters with the same pitch and the same board can have different HAPs if their birdsmouths are cut differently, which is why HAP — not the notch — is the figure to record on a framing plan.
Everything follows from one input — the seat length — and the pitch angle. The vertical (plumb) depth of the notch is the seat length multiplied by the tangent of the pitch angle: at 6/12 the pitch angle is 26.57°, so a 3-inch seat drops 3 × 0.5 = 1.5 inches vertically. The depth actually removed from the board, measured perpendicular to its top edge, is the seat length times the sine of the angle — 3 × 0.447 = 1 5/16 inches at 6/12. That perpendicular figure is the one the one-quarter limit judges.
HAP is the mirror image of the notch. A board of actual depth D, tilted at the pitch angle, stands D ÷ cos(angle) tall measured vertically. Subtract the vertical drop of the notch and you have the height above plate: HAP = D ÷ cos(angle) − seat × tan(angle). The table below runs the numbers for a 2×8 (7.25 in actual) with a full 3.5-inch seat on a 2×4 wall — and shows how a steep pitch quietly pushes a full-width seat over the depth limit.
| Pitch | Seat | Notch depth (perp.) | Max allowed (¼ of 7.25 in) | HAP | Verdict |
|---|---|---|---|---|---|
| 4/12 | 3.5 in | 1 1/8 in | 1 13/16 in | 6 1/2 in | OK |
| 6/12 | 3.5 in | 1 9/16 in | 1 13/16 in | 6 3/8 in | OK |
| 8/12 | 3.5 in | 1 15/16 in | 1 13/16 in | 6 3/8 in | Over — shorten the seat |
| 10/12 | 3.5 in | 2 1/4 in | 1 13/16 in | 6 1/2 in | Over — shorten the seat |
| 12/12 | 3.5 in | 2 1/2 in | 1 13/16 in | 6 3/4 in | Over — shorten the seat |
The notch must not remove more than one-quarter of the board's actual depth, measured perpendicular to the top edge. That is the IRC's end-notch limit — R802.7.1 applies the R502.8.1 notching rules to rafters, and notches at the ends of a member are capped at one-quarter of its depth. Some framing guides quote a looser one-third rule of thumb; this calculator enforces the code figure. The reason is structural: the birdsmouth sits at the support, where shear forces in the rafter are highest. A notch deeper than the limit leaves too little wood above the plate to carry that shear, and the rafter can split horizontally from the inside corner of the notch — the classic birdsmouth failure, and one that usually happens under snow load, not during construction.
Note that the rule judges the perpendicular depth, not the vertical plumb depth and not the seat length. On a shallow pitch a long seat removes little depth; on a steep pitch the same seat removes a lot. If your notch is over the limit, the fixes, in order of preference, are: use the next lumber size up, shorten the seat so the notch shallows, or — on a remodel — check whether the plate can bear a raised-heel design instead. Never solve it by cutting deeper and hoping.
Both examples use a 6/12 pitch (26.57°) and a 2×8 with an actual depth of 7.25 inches, so the maximum permitted notch is 7.25 ÷ 4 = 1 13/16 inches. The first is a partial seat, the second the full plate width.
Seat 3 in. Plumb depth = 3 × tan 26.57° = 1 1/2 in. Perpendicular notch = 3 × sin 26.57° = 1 5/16 in. HAP = 7.25 ÷ cos 26.57° − 1.5 = 6 5/8 in.
Seat 3.5 in (full 2×4 plate). Plumb depth = 3.5 × 0.5 = 1 3/4 in. Perpendicular notch = 3.5 × 0.447 = 1 9/16 in. HAP = 8 1/8 in vertical board height − 1 3/4 = 6 3/8 in.
Mark the birdsmouth from the plumb line at the wall, not from the tail: lay out the rafter's plumb cut line at the building line first, then draw the seat cut level from the point where that line crosses the required depth. A framing square set to your pitch (rise on the tongue, run on the blade) draws both faces of the notch in two placements. Cut the seat first, then the plumb face, and finish the inside corner with a handsaw — a circular saw run past the corner overcuts into the board and starts the split the depth limit is trying to prevent.
The birdsmouth is one of three cuts that decide the finished rafter; the plumb cut at the ridge and the tail cut at the eave are the others. To see how the notch changes the overall board you need to cut — a deeper birdsmouth on a steep pitch can push you to the next stock length — run your numbers through the common rafter length calculator with the same pitch and lumber size. And because the plumb face of the birdsmouth is cut at the rafter's plumb angle, the rafter angle calculator gives you that angle and the saw setting for it directly from your pitch.
Every result on this page comes from the method described above, using standard framing geometry and the published data credited below. Found a number that looks wrong? Use Report an Error — every report is read.
At most one-quarter of the board's actual depth, measured perpendicular to the top edge — 1 13/16 in on a 2×8 (7.25 in actual). That is the IRC's end-notch limit: R802.7.1 applies R502.8.1 to rafters, and it caps notches at the ends of a member at one-quarter of its depth. Deeper than that, the rafter is weakened at the support where shear is highest, and it can split from the inside corner of the notch.
Ideally yes — full bearing is best, and on a 2×4 wall that means a 3.5 in seat. But on steep pitches a full seat can break the one-quarter limit; a slightly shorter seat with full depth of wood above it is the safer joint. Never let the seat overhang the outside of the plate.
HAP is the height above plate: the vertical distance from the top of the wall plate to the top of the rafter at the wall line. It sets eave and ceiling height, and because it depends on how the birdsmouth is cut, two otherwise identical roofs can have different HAPs. Record it on the plan so every rafter is cut to the same heel.
It doesn't change the theoretical line length, which is measured to the wall line regardless of the notch. But it does change the board you need in practice on steep pitches — a deep heel and a long tail together can push the cut length past a stock size.
No. Engineered I-joists and trusses must not be notched at the bearing unless the manufacturer publishes a specific detail for it. Birdsmouths are for solid sawn lumber; engineered members use hangers or bevelled plates instead.
The seat cut is the horizontal face that sits on the plate; the plumb cut is the vertical face that bears against the plate's inside edge. In this calculator you enter the seat length, and the plumb depth is derived from it and the pitch angle.
The full common rafter: length, angles, birdsmouth and materials.
Line and cut lengths and angles for the diagonal rafter on a hip roof.
Where two roof planes meet — valley length and its cut angles.
First jack length and the common difference for your spacing.
Single-slope rafters between two different wall heights.
Plumb, seat and cheek angles — plus the saw settings to cut them.
Convert pitch, rise/run, degrees and percent, both ways.
How far a board can span — IRC tables by species, grade and load.
The lumber size a span actually needs. The inverse of the span tool.
Two pitches, one roof — upper and lower rafter lengths.
The full pitch × run table, printable for the workshop wall.
Figure any rafter by hand — formula and framing-square methods.