Gambrel Roof Calculator

Gambrel Rafter Length Calculator

Solve both rafter segments, then turn the theoretical lengths into the numbers you actually mark on the lumber.

ft
°
°
%
% of the half-span, from the eave
in
Actual dressed depth — a 2×8 is 7.25"
in
A 2× ridge board is 1.5"
in
Horizontal bearing length on the wall plate

Cut lengths

Lower rafter (R1) Upper rafter (R2)

R1 centreline
12.00 ft
12′ 0″ · 60.0° · 20.8:12
R1 physical cut
12.00 ft
12′ 0″ · no knuckle deduction (mating cut)
Seat notch depth
4.33 in
plumb depth at the seat cut
R2 centreline
6.62 ft
6′ 7 7/16″ · 25.0° · 5.6:12
R2 physical cut
6.55 ft
6′ 6 5/8″ · ridge deduction 0.83 in
Remaining above notch
4.92 in
53% of rafter depth

Design aid, not a stamped engineering drawing — verify pitch, seat length and lumber grade against your local code before cutting.

Centreline length vs. physical cut length

The main gambrel calculator solves a triangle: given the span, the lower pitch theta, the upper pitch phi and the knuckle position, it returns R1 and R2 — the straight-line, point-to-point distances from eave to knuckle and from knuckle to ridge. Those are centreline lengths. They describe the geometry perfectly and they are exactly what you need to size a roof, but they are not, by themselves, what you mark on a board.

A physical rafter has to stop somewhere at each end, and what it stops against matters. At the ridge, it butts against an actual ridge board with real thickness. At the wall plate, it gets notched to bear on the plate. At the knuckle, it meets its partner rafter directly, or through blocking, or against a gusset — a framing choice, not a geometry constant. Every one of those junctions can shorten, or leave unchanged, the board you actually cut relative to the centreline number the triangle produced.

This page starts from the same R1/R2 the main calculator produces and applies two adjustments: a ridge-end deduction on the upper rafter, and a seat-cut notch depth on the lower rafter, reported separately so you can see exactly what changed and why. Nothing here overrides the geometry on the pitch calculator or the main tool — it consumes their output.

Worked example, the calculator's own defaults: a 24 ft span at 60° lower and 25° upper pitch, split evenly at the knuckle, gives R1 = 12.00 ft and R2 = 6.62 ft. Those are the numbers a framing square or an online span table would hand you. The physical cut lengths below are what actually go on the saw.

The two deductions, and why each one works this way

Only two junctions change the cut length in this model. The knuckle does not, because the mating cut there is assumed to be a direct plumb joint with no board between the members — state that assumption plainly, because not every framer builds the knuckle that way.

Ridge-end deduction (upper rafter, R2)

deduction = (ridgeThickness / 2) / cos(phi)

netR2 = R2 − deduction

ridgeThickness in the same units as R2; phi is the upper pitch angle, measured from horizontal, the same convention gambrel.ts uses everywhere (R = run / cos(angle)).

Half the ridge board's thickness is a horizontal setback — the rafter's ridge-end run gets shorter by that much, because the board takes up space between the two opposing rafters. But the rafter itself travels along a slope, and length along a slope is always run divided by cos(angle). A horizontal shortening of X therefore becomes a slope-length shortening of X / cos(phi), not X. At phi = 25°, cos(phi) ≈ 0.906, so the true deduction runs about 10% larger than the flat half-thickness figure — small at low pitches, not negligible once phi climbs into the 30s and 40s.

Seat-cut notch depth (lower rafter, R1)

notchDepth = seatLength × tan(theta)

seatLength is the horizontal bearing length you want on the wall plate; theta is the lower pitch. This is the same formula used on the birdsmouth and framing pages — one seat-cut model, three pages.

A birdsmouth's seat cut has to be horizontal so the rafter bears flat on the plate, but the rafter above it is sloped at theta. Cutting a horizontal shelf into a sloped board means the notch gets deeper, measured straight down, as the seat gets longer — the exact relationship is seatLength times the tangent of the pitch. This depth does not shorten R1's centreline length; it only removes material locally. See the birdsmouth calculator for the full treatment, including the 1/3-depth structural limit.

Worked example — 24 ft span, 60°/25°, 2x10 rafters, 2x ridge board
  1. R1 = 12.00 ft, R2 = 6.62 ft — straight from the two-pitch triangle.
  2. Ridge deduction: (1.5 / 2 / 12) / cos(25°) = 0.0690 ft ≈ 0.83 in.
  3. Net R2 = 6.62 − 0.069 = 6.55 ft — the length that actually goes on the saw.
  4. Net R1 = 12.00 ft — unchanged, under the plumb-knuckle assumption.
  5. Seat cut, 2.5" horizontal: notch depth = 2.5 × tan(60°) = 4.33 in, leaving 4.92 in of a 9.25" rafter above the notch (53%).

Design aid, not a stamped engineering drawing. Verify pitch, ridge thickness, seat length and lumber grade against your local code and an engineer's sign-off before you cut a full set of rafters.

Ridge deduction and notch depth by pitch

Both deductions scale with pitch, not with span — the numbers below hold for any width. Ridge deduction assumes a standard 1.5" (2x) ridge board; notch depth assumes a 2.5" horizontal seat cut.

Ridge-end deduction and seat-notch depth by pitch angle
Pitch angle Rise-in-12 Ridge deduction (2x board) Seat notch depth (2.5" seat)
15° 3.2:12 0.78 in 0.67 in
20° 4.4:12 0.80 in 0.91 in
25° 5.6:12 0.83 in 1.17 in
30° 6.9:12 0.87 in 1.44 in
35° 8.4:12 0.92 in 1.75 in
45° 12.0:12 1.06 in 2.50 in
60° 20.8:12 1.50 in 4.33 in

Read the bottom row carefully: at 60°, a 2.5" seat cut already removes over 4 inches, measured plumb — more than a third of a typical 2x10's depth. That is exactly the tension the framing guide and the birdsmouth calculator both work through: steep gambrel lower slopes need either deeper stock or a shorter seat, not a bigger saw.

Marking and cutting, in order

The sequence below turns the numbers above into cuts on real lumber, for one lower/upper rafter pair. Once that pair test-fits, every other pair at the same span and pitch is identical.

  1. Solve the triangle

    Run the span, both pitches and the knuckle position through the calculator (or the two-pitch/half-circle triangle by hand) to get the centreline lengths R1 and R2 — the point-to-point distances the geometry actually produces.

  2. Decide the ridge deduction

    Pick your ridge board thickness. Halve it, convert to feet, and divide by cos(phi) to get the length the upper rafter loses at the ridge end. Subtract that from R2 to get its net physical cut length.

  3. Leave the knuckle end alone

    Under a plumb mating-cut joint, the lower and upper rafters meet directly with no board between them, so neither R1 nor R2 loses anything at the knuckle end in this model.

  4. Mark the seat cut

    Choose a horizontal seat-cut length and multiply by tan(theta) to get the notch depth, measured plumb. Mark that depth on the rafter at the wall-plate line before you touch a saw.

  5. Square-cut and test-fit one pair

    Cut one lower and one upper rafter to their net lengths, dry-fit them at the knuckle and the seat, and check the ridge gap before you batch-cut the rest of the run.

  6. Batch-cut the remainder

    Once the test pair fits, cut the rest of the lower and upper rafters to the same two net lengths — every pair on a given span and pitch combination is identical.

Rafter length FAQ

Why is the physical cut length different from the centreline length?
The centreline length (R1 or R2) is the theoretical, point-to-point distance the geometry produces — top edge to top edge, with zero material in the way. The physical cut length subtracts what actually sits at each end: a ridge board at the ridge, nothing at a plumb-cut knuckle joint, and nothing at the seat cut end (the notch removes bearing material, not length). Cut to the centreline number and your ridge line will be too high by roughly half the ridge board thickness.
Why divide by cos(phi) instead of just subtracting half the ridge thickness?
Half the ridge thickness is a HORIZONTAL setback, but the rafter runs along a slope. Length along a slope equals run divided by cos(angle), so a horizontal deduction of X becomes a slope-length deduction of X / cos(phi) — always slightly more than X once phi is greater than zero. At a 25° upper pitch that factor is about 1.10, so skipping it under-deducts by roughly 10% of the true amount.
Does the knuckle joint really need no deduction?
Only under the plumb mating-cut model used here — the lower rafter's top edge and the upper rafter's bottom edge meet at a single point, held together by a gusset plate on the face rather than a board sandwiched between them. If your framing detail runs the upper rafter past the joint, adds blocking, or uses a different splice, add that thickness back in yourself; the calculator does not assume any one method is universal.
Should the seat-cut notch reduce the rafter length I cut?
No. The notch removes material from the UNDERSIDE of the rafter at one point along its length — it changes bearing and shear capacity, not the top-edge centreline distance you are cutting to. Keep the length calculation and the notch-depth calculation separate, as this page does; see the birdsmouth calculator for the full notch-depth and IRC 1/3-depth check.
How much does the ridge deduction change with a thicker ridge board?
It scales linearly. A 1.5" (2x) ridge board deducts about 0.75" / cos(phi) from R2; a 2.5" (glulam or doubled) ridge board deducts about 1.25" / cos(phi) — roughly 67% more. At a 15° upper pitch that difference is only a few hundredths of an inch either way; at a 45° upper pitch it starts to matter for a tight ridge fit.