Gambrel Roof Calculator

Birdsmouth Cut Calculator

Seat depth, heel height, and the structural limit that keeps a notched rafter from losing too much of itself.

Seat cut + heel cut, at the wall plate
°
in
Horizontal bearing length on the wall plate
in
Actual dressed depth — a 2×8 is 7.25"

Notch geometry

Seat-cut depth (plumb)
2.60 in
seatLength × tan(θ)
Plumb cut angle
60.0°
equal to θ
Heel height
13.30 in
plumb cut at the rafter tail
1/3-depth limit
Within limit
72% of depth remains (need ≥ 67%)
Remaining depth
6.65 in
above the notch, at the plate
Max seat length here
1.78 in
before the notch exceeds 1/3 depth

Design aid, not a substitute for an engineer's sign-off on unusual spans, species or loads.

Two cuts, meeting at a right angle

A birdsmouth is a small triangular notch cut into the underside of a rafter, right where it crosses the wall plate. It has two faces. The seat cut is the roughly horizontal face that actually bears on the plate — its length is a choice you make, not something fixed by the pitch. The heel cut is the plumb face that closes the notch, running from the inner end of the seat cut back up to the rafter's bottom edge.

Without a birdsmouth, a sloped rafter dropped onto a level plate only touches it along one edge, concentrating the entire reaction load onto a knife-edge of wood. The notch trades a small amount of the rafter's depth for a flat bearing surface — a good trade, as long as the amount you trade away stays small relative to what is left.

On a gambrel's lower rafter this trade gets tighter than it does on a typical gable roof, because the lower pitch is usually steep — 60° is this site's own default, the same one used on the main calculator and the rafter length page. Steep pitches make the notch deepen fast for the same seat length, which is exactly what the numbers below show.

The reaction over the wall — the point where the whole weight of that section of roof transfers down into the framing below — is also the point of highest shear in the rafter. Shear failure in wood runs along the grain, and a birdsmouth notch cuts directly across the grain right at that high-shear location, leaving a reduced cross-section to carry a load that has not gotten any smaller. That is the entire reason the 1/3-depth limit exists: it is not about how the rafter looks, it is about how much wood is left to resist splitting along the grain exactly where the load is heaviest.

Seat depth, heel height, and where "HAP" comes from

Seat-cut depth, measured plumb

notchDepth = seatLength × tan(theta)

A seat cut has to be horizontal to bear flat on the plate, but the rafter above it is sloped at theta — so a longer horizontal seat cut always means a deeper notch, measured straight down.

Heel height (HAP — Heel Amount Plumb)

remainingDepth = rafterDepth − notchDepth

heelHeight = remainingDepth / cos(theta)

Squaring a ruler across a sloped rafter to check remaining depth is awkward on the job. Framers instead mark the plumb line at the wall and measure straight down it by heelHeight — the same number, reached without ever leaving the plumb line. That is exactly what HAP tables on a rafter square give you.

The 1/3-depth limit

notchDepth ≤ rafterDepth / 3

remainingDepth ≥ (2/3) × rafterDepth

The widely used carpentry limit — matching the IRC's birdsmouth provisions and this site's own homepage framing note — is that a notch may not remove more than a third of the rafter's depth, leaving at least two-thirds intact above it.

Worked example — 60° lower pitch, 1.5" seat, 2x10 (9.25") rafter
  1. Notch depth = 1.5 × tan(60°) = 2.60 in.
  2. Remaining depth = 9.25 − 2.60 = 6.65 in, or 72% of the full depth — clears the 67% floor.
  3. Heel height (HAP) = 6.65 / cos(60°) = 13.30 in.
  4. Maximum seat length this stock allows at 60° before failing the 1/3 rule: 1.78 in — not much room above the 1.5" used here.

Push the seat cut out to a more generous 3.5" on lighter 2x8 (7.25") stock at the same 60° pitch and the notch reaches 6.06" — more than four times the 1/3-depth limit of 2.42", leaving only 16% of the rafter's depth above the cut. That combination fails outright; see the reference table below for where the line actually sits across pitches.

One more thing worth being explicit about: notch depth here is measured PLUMB (straight down, along the vertical), not square to the rafter (perpendicular to its top edge). The two conventions give different numbers at any pitch other than zero, and framing references do not always say which one they mean. This site measures plumb everywhere — on this page, on the rafter length page and on the framing guide — because it is the measurement a plumb bob and a speed square's plumb-cut line actually produce on the job, not because it is the only valid choice.

The 1/3 limit across pitch, fixed 3.5" seat on 2x10 stock

Same seat length and same rafter depth in every row — only the pitch angle changes, which is enough by itself to flip the result from comfortable to failing.

Birdsmouth notch depth and 1/3-depth check by pitch, 3.5" seat on 9.25" (2x10) stock
Pitch Notch depth Remaining depth % of depth remaining 1/3 check
30° 2.02 in 7.23 in 78% Passes
45° 3.50 in 5.75 in 62% Fails
60° 6.06 in 3.19 in 34% Fails
70° 9.62 in -0.37 in -4% Fails

By 45° the same 3.5" seat is already failing on 2x10 stock; by 60° the margin is not close. See the pitch calculator to convert any target rise-in-12 or slope ratio into the degree figure this table (and every other calculator on this site) uses.

When a combination fails, three fixes actually work and one does not. Shortening the seat cut works — it directly reduces notchDepth, though a seat too short may not give a hurricane strap or clip enough surface to bite into. Moving to deeper stock works — a 2x12 gives 50% more depth budget than a 2x8 for the same notch. Switching to a bearing detail that skips the notch entirely — a rafter hanger, a let-in strap let into the plate — works because it sidesteps the 1/3 rule altogether rather than satisfying it. What does not work is cutting the notch anyway and hoping the load never gets tested; shear failures at an over-notched heel tend to show up exactly when the roof is loaded hardest, not on a calm day.

Marking the notch, step by step

  1. Mark the plumb line at the wall

    Square the rafter to the wall plate and mark a plumb (vertical) line where the rafter crosses the plate's outer edge — every other mark on this notch is measured from that line.

  2. Step down by the heel height

    Measure down the plumb line by the heel height (HAP) the calculator returns, which is the remaining rafter depth divided by cos(theta) — this is the classic "Heel Amount Plumb" figure carpenters use instead of squaring a ruler across a sloped board.

  3. Mark the level seat line

    From that point, mark a level (horizontal) line running the seat-cut length back toward the ridge — this is the face that will actually bear on the top plate.

  4. Connect seat to heel

    The heel cut is the short plumb face connecting the inner end of the seat line back up to the rafter's bottom edge, closing the notch.

  5. Cut and test-fit before batching

    Cut one rafter, set it on the plate, and confirm full seat bearing and a tight heel before you cut the rest of the run to the same marks.

Birdsmouth FAQ

What is a birdsmouth cut?
A birdsmouth is a triangular notch cut into the underside of a rafter where it crosses the wall plate, made of two faces: a seat cut (roughly horizontal, bearing on the plate) and a heel cut (plumb, closing the notch). Together they let a sloped rafter sit flat on a level plate instead of only touching it at one point.
Why does a steeper pitch make the notch deeper for the same seat length?
Notch depth is seatLength × tan(theta), and tan(theta) grows fast as theta climbs. The same 3.5" seat cut removes about 2 inches at 30 degrees but over 6 inches at 60 degrees — on a typical 2x10, that second number already blows past the 1/3-depth limit before you have even checked bearing capacity.
What happens if the notch exceeds the 1/3-depth limit?
You have removed too much of the rafter's cross-section right at its highest-shear point — the reaction over the wall. The fix is not a bigger saw; it is a shorter seat cut, deeper rafter stock, or a bearing detail that does not rely on notch depth at all, such as a rafter hanger or a let-in strap that carries load without cutting into the rafter.
Is a birdsmouth required on a gambrel roof's lower rafter?
No single detail is mandatory everywhere — it depends on your local code and engineering. A birdsmouth is simply the most common way to seat a sloped rafter flat on a level plate. On steep gambrel lower slopes, where the notch math gets tight fast, some builders use a shorter seat, thicker stock, or a hardware-based bearing connection instead of pushing a full-depth notch to its limit.
How does this relate to the rafter length and framing pages?
This page is the deep dive on one joint. The rafter length calculator uses the same notch-depth formula as a quick check while it focuses on cut length; the framing guide uses the same seat and heel numbers while it focuses on truss count and raising sequence. One seat-cut model, three pages, on purpose.