A birdsmouth is the notch that lets a sloping rafter sit flat on a wall plate. It has two faces: a horizontal seat that bears on the plate, and a vertical heel or plumb cut that meets the outside face of the wall. The two are locked together by the pitch, so once you fix the seat length the plumb cut follows, and so does the amount of rafter depth you have removed. The birdsmouth cut calculator above works all of that out, and prints the notch against the depth limit you supply so you can see the margin rather than a bare answer.
This is a preliminary layout and teaching tool published by Arb Digital. It is not a structural design, it is not stamped, and it does not replace a licensed engineer, an architect or the building department. Notching a rafter removes material from a member that is carrying load, and how much may be removed, and where, is decided by the code adopted in your jurisdiction — not by a web page and not by a rule of thumb. Read the section on limits before you cut anything.
What This Birdsmouth Cut Calculator Does
It solves the geometry of the notch and reports six related quantities. The plumb cut height is the vertical face of the notch, equal to the seat length multiplied by the tangent of the pitch angle. The notch depth square to the rafter is what actually matters structurally, and it is the seat length multiplied by the sine of that angle — always smaller than the plumb height, which is why quoting the plumb figure makes a notch look deeper than the code check treats it, and quoting the perpendicular figure when the code wants a plumb measurement makes it look shallower. The remaining depth is what is left of the rafter above the notch. The height above plate is the plumb dimension from the seat to the top edge, which is the number that sets your ridge height and has to be identical on every rafter in the roof.
The tool then divides the notch depth by the rafter depth and compares it against a limit you enter, printing the limit and the actual value side by side. It does not decide whether the notch is acceptable. It shows you the ratio and leaves the judgement where it belongs.
Which Standard Governs, and Why No Table Appears Here
In much of the United States, rafters in dwellings are framed under the International Residential Code and larger buildings under the International Building Code, both published through the ICC Digital Codes library. Those codes carry the provisions for cutting, notching and boring structural members, and they reference the National Design Specification for Wood Construction for the engineering behind them. Which edition applies, and what has been amended, is decided locally: states, provinces and municipalities adopt different editions and add their own changes, and other countries use entirely different standards.
For that reason this page publishes no notching table. A limit typed into a web page would be wrong for a great many readers, because it varies with the member type, with the position of the notch along the span, and with the code edition in force. The notch limit is an input for exactly the same reason our breaker size calculator publishes no ampacity table: where a figure is jurisdictional, the honest thing is to ask for it rather than invent it.
Two further points are worth stating plainly. Engineered members are not covered by rafter notching rules at all: an I-joist, an LVL, a truss or a structural composite rafter may only be cut where the manufacturer's own literature permits, and cutting the flange of an I-joist destroys it. The APA – The Engineered Wood Association publishes the technical documentation for many of those products. And a roof truss must never be notched, drilled or altered in any way without the truss designer's written approval, because every member in it is sized for a specific force path.
How to Use It
- Enter the real pitch. Measure it on the frame if the drawing and the building disagree, because the birdsmouth is unforgiving of a pitch error.
- Set the seat length to the actual bearing you have. Usually the dressed width of the plate, and never more than the plate is wide.
- Use actual rafter dimensions. Nominal sizes overstate the depth and make the notch ratio look better than it is.
- Enter the notch limit that applies to your job, from the building department, the engineer or the manufacturer. Do not use the loaded default as though it were an answer.
- Cut one rafter, offer it up, then use it as the pattern. The height above plate has to be the same on every rafter or the roof plane will not be flat.
The Formula / How It's Calculated
Let the pitch angle be θ, the seat cut length S and the actual rafter depth D measured square to its faces. From a rise of R per 12 of run, θ = arctan(R / 12).
The plumb cut height is H = S × tan θ. The notch depth measured square to the rafter is N = S × sin θ. The plumb depth of the rafter itself, measured vertically through the section, is D / cos θ, so the height above plate is HAP = D / cos θ − H, and the depth remaining square to the rafter is D − N. The sloping tail beyond the seat, for a horizontal overhang O, is O / cos θ.
Worked example with the loaded values. A 6 in 12 pitch is arctan(0.5) = 26.565 degrees. With a 3.5 seat cut, the plumb cut height is 3.5 × tan 26.565° = 1.75, and the notch depth square to the rafter is 3.5 × sin 26.565° = 1.5652. On a 2×8 rafter of actual depth 7.25, the remaining depth is 7.25 − 1.5652 = 5.6848, and the notch is 1.5652 / 7.25 = 21.6 per cent of the depth, against the 33.33 per cent limit loaded as an example. The plumb depth of the rafter is 7.25 / cos 26.565° = 8.1057, so the height above plate is 8.1057 − 1.75 = 6.3557. A 16 horizontal overhang gives a sloping tail of 16 / cos 26.565° = 17.889.
Why the Pitch Makes This Harder Than It Looks
The notch grows with the pitch, and it grows faster than most people expect. Hold the seat length constant at the width of a 2×4 plate and the plumb cut height rises from a little under an inch at 3 in 12 to nearly two and a half inches at 8 in 12 and past three and a half at 12 in 12. On a shallow roof that is a trivial notch in a deep rafter. On a steep roof in a shallow rafter, the same seat length can remove a serious fraction of the section.
That is the tension at the heart of birdsmouth layout: bearing and section pull in opposite directions. A longer seat gives more bearing area on the plate, which is good for compression perpendicular to the grain, but it cuts deeper into the rafter, which is bad for what is left. A shorter seat preserves section but reduces bearing. There is no universally correct answer, which is precisely why the limits live in code and in engineering judgement rather than in a formula.
Steep roofs also change where the load goes. As the pitch increases, more of the rafter thrust turns into horizontal force at the plate, and the tie that resists it — ceiling joists acting as a collar, a ridge beam that removes the thrust altogether, or a designed tie — becomes the thing that keeps the walls from spreading. None of that is calculated here. Our rafter length calculator handles lengths and cut angles, the roof pitch calculator converts between slope expressions, and the beam load calculator and wood beam span calculator carry the load work, all with the same limits stated.
Getting It Right on the Frame
Three practical points make the difference between a roof plane that is flat and one that is not. First, height above plate is the controlling dimension, not the notch. Every common rafter must have the same HAP, or the top edges will not lie in one plane no matter how carefully the ridge is set. Cut one, check it, then use it as the pattern for the rest and check the pattern again halfway through the run.
Second, the seat cut must not run past the inside face of the wall. A seat that overshoots leaves the rafter bearing on nothing at its inner end and creates a stress riser exactly where the section is already reduced. The plumb cut should land on the outside face of the wall, and if it does not, the layout dimension is wrong somewhere.
Third, overcutting at the inside corner of the notch is a real and under-appreciated problem. A circular saw cutting to the line on the face has already cut past it on the far side, and that overrun sits at the corner where the two faces meet — the point of highest stress in the whole notch. Finish the corner with a handsaw or a jigsaw rather than running the circular saw past the mark. Our angle cut calculator covers the geometry of the angled cuts on the tail, and the roofing calculator the covering above.
What This Page Does Not Tell You
It does not tell you whether a notch is acceptable. It reports the ratio and prints your limit next to it, and the decision belongs to the code official and to whoever designed the roof. It does not check bearing stress, which is compression perpendicular to the grain at the seat and depends on the species and grade of the timber and on the reaction at the support. It does not check shear at the notch, which is the mechanism that actually governs many notched-member failures because a notch acts as a crack initiator in the tension zone. It does not check the rafter for bending, deflection or the loads on it, and it says nothing about connections, ties, uplift or the wall below.
Nor should any output be treated as a specification. A birdsmouth in a real roof is part of a designed system, and if you are notching close to a limit, notching an engineered member, altering an existing roof or working on anything other than straightforward new framing to a published detail, the right move is a conversation with a licensed engineer or the building department before the saw comes out.
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Browse Free Tools Talk To Arb DigitalCommon Mistakes to Avoid
- Measuring the notch plumb instead of square to the rafter — the two differ by the cosine of the pitch angle, and the wrong one misstates how much section has gone.
- Using nominal rafter depth — a 2×8 is 7.25 deep, not 8, and the notch ratio changes accordingly.
- Running the seat cut past the inside face of the wall — the inner end of the rafter then bears on nothing, at the weakest point of the member.
- Overcutting the inside corner with a circular saw — the overrun lands exactly where the stress concentrates. Finish the corner by hand.
- Notching an engineered rafter or a truss — I-joists, LVL and trusses may only be cut where the manufacturer or the truss designer permits in writing, and often not at all.
Related Free Tools From Arb Digital
Work out the rafter itself with the rafter length calculator, convert the slope with the roof pitch calculator, and take the loads through the beam load calculator, the wood beam span calculator and the floor joist calculator. The roofing calculator covers materials above and the angle cut calculator the angled cuts. Everything we publish is listed on the free online tools hub.
Frequently Asked Questions
That is set by the building code adopted where you are building, and it varies with the member, the position along the span and the code edition. This page takes the limit as an input and prints your notch against it rather than publishing a figure of its own.
Both are reported, because they are different numbers. The plumb heel cut is the seat length times the tangent of the pitch; the depth square to the rafter is the seat length times the sine. Check which one your code provision or your engineer means.
It is the plumb distance from the seat cut to the top edge of the rafter. It sets the ridge height, and it must be identical on every common rafter or the roof plane will not be flat.
Only where the manufacturer's literature explicitly allows it. Cutting the flange of an I-joist destroys the member, and engineered rafters are outside the notching provisions written for sawn lumber.
No, not without the written approval of the truss designer. Every member in a truss is sized for a specific force, and cutting any of them alters the whole system.
Because bearing and section pull against each other. More seat length gives more bearing area on the plate but removes more rafter depth. Where the balance falls is an engineering judgement, not a rule that a calculator can settle.
No. It is geometry. It performs no bending, shear, deflection or bearing check, and it takes no account of loads. A rafter must be designed by a qualified person under the code in force.
Because the plumb cut height is the seat length times the tangent of the pitch angle, and the tangent rises quickly. The same seat length that barely touches a rafter at 3 in 12 removes several times as much at 12 in 12.
This tool computes birdsmouth geometry from dimensions you supply, for preliminary layout and education only. It is not a structural design, it is not stamped, it performs no bending, shear or bearing check, it publishes no notching limit of its own, and all roof framing must be designed and approved by a licensed engineer or the building department in accordance with local code.
