Gambrel Roof Calculator

Gambrel Truss Design Calculator

One truss at a time: the sweep angle, the knuckle joint's turn, and the gusset that has to hold it together.

Half-circle method · θ − φ = 45° always
ft
°
φ locks to θ − 45° automatically
in
Plate extension along each rafter face from the joint
in
Room needed at the joint for the purlin to seat

Knuckle joint & gusset

Sweep angle (eave to knuckle)
60.0°
central angle on the W/2 semicircle
Knuckle turn angle
45.0°
interior joint angle 135.0°
Gusset span (tip to tip)
22.17 in
plate footprint to lay out before trimming
Achieved inner clearance
4.59 in
meets your target
R1 / R2 / height
12.00 / 6.21 / 12.00 ft
20.8:12 lower · 3.2:12 upper
Usable cross-section, per truss
196.7 ft²
attic area in this truss's plane

Simplified planar gusset model for layout and lumber sizing — get truss-plate engineering signed off before you fabricate at scale.

A gambrel truss is more than a rafter

The rafter length calculator solves one rafter pair as a pair of straight lines. A truss is that same pair PLUS the joint that holds them at their new angle plus whatever ties the truss to its neighbors. On a gambrel, that joint is the knuckle, and it is the one place in the whole roof where the framing has to actively resist the rafters trying to straighten back out under load — everywhere else, wood in compression along its length does most of the work on its own.

Think of the knuckle as a hinge that has been welded shut. The lower rafter arrives at 60°; the upper rafter leaves at 15°. Nothing forces those two members to stay at that relative angle except the connection you build — a gusset plate nailed across both faces, a truss plate, or a bolted strap. Get that connection wrong and the roof does not fall down all at once; it slowly opens up at every knuckle until the ridge sags.

This page treats one truss in isolation: its sweep angle, its knuckle turn, and the gusset that closes the joint. The framing guide takes the same truss and repeats it along a building.

It helps to name the forces plainly. Every rafter is mostly in compression along its own length, pushing down and outward exactly the way a leaning ladder pushes against the ground and the wall. At a normal ridge, the two rafters lean into each other and cancel most of that outward push. At the gambrel's knuckle, the rafter changes direction partway through instead of running straight to a ridge, so the outward push from the lower rafter and the outward push from the upper rafter are no longer pointed the same way — the joint has to physically resolve that mismatch instead of the geometry doing it automatically. That mismatch is exactly what the gusset plate below is sized to carry.

The sweep angle and the fixed 45-degree turn

Every truss on this page uses the half-circle method: pick the lower pitch theta, and the upper pitch phi locks to theta minus 45 degrees automatically, because the knuckle and the ridge both sit on a semicircle struck from the centre of the wall-plate line. The main calculator proves this with an isosceles-triangle argument; the short version is that the semicircle's own geometry does the work, not a rule someone chose.

What the calculator is solving

phi = theta − 45°

sweep = 2 × (90° − theta)

"Sweep" is the central angle of the arc from the eave to the knuckle, on the W/2 semicircle. At the default theta = 60°, sweep = 60° and the knuckle turn (theta − phi) is fixed at 45° no matter what theta is.

That fixed 45° turn is the number every gusset calculation on this page runs from. Change theta and R1, R2 and the roof height all change — but the turn angle at the knuckle, and therefore the interior joint angle of 135°, never does, as long as you stay on the half-circle method.

Sizing the gusset: why a fixed turn angle makes this easy

Because the knuckle turn is always 45° under this method, the gusset math reduces to one triangle: two legs of length L (the gusset base you choose) meeting at a 135° interior angle. That triangle gives two numbers for free — the plate's overall tip-to-tip span, and how far the plate reaches into the joint along the angle bisector, which this page calls the inner clearance.

Gusset footprint (isosceles triangle, legs L, apex 135°)

gussetSpan = 2L × cos(22.5°) ≈ 1.85L

innerClearance = L × sin(22.5°) ≈ 0.383L

L is the gusset base length input, the distance the plate extends along each rafter face from the knuckle point. Both results are a direct consequence of the fixed 45° turn — no other pitch produces the 0.383 and 1.85 multipliers.

Worked example at the calculator's defaults: a 12" gusset base gives a 22.2" tip-to-tip plate — noticeably wider than 12" once the angle is folded in — and 4.59" of inner clearance. If a 3" clearance is the target for the purlin to seat properly, 12" clears it with room to spare; hitting exactly 3" would only need a 7.8" gusset base. Undersize the gusset and the plate simply will not reach far enough into the joint to do useful work; oversize it and you are just buying stiffness you did not need.

This is a simplified planar model for laying out lumber and estimating plate size — it is not a substitute for engineered truss-plate design on anything spanning further than a typical outbuilding or carrying unusual snow load.

Reference

Truss geometry by span, half-circle method at 60°

Every row below uses the same 60° lower pitch as the calculator's default, so phi locks to 15° and the knuckle turn is 45° throughout. Only R1, R2, height and the per-truss cross-section change with span.

Gambrel truss geometry, six common spans
Span R1 R2 Height Cross-section, per truss
12 ft span 6.00 ft 3.11 ft 6.00 ft 49.2 ft²
16 ft span 8.00 ft 4.14 ft 8.00 ft 87.4 ft²
20 ft span 10.00 ft 5.18 ft 10.00 ft 136.6 ft²
24 ft span 12.00 ft 6.21 ft 12.00 ft 196.7 ft²
30 ft span 15.00 ft 7.76 ft 15.00 ft 307.4 ft²
40 ft span 20.00 ft 10.35 ft 20.00 ft 546.4 ft²

Notice R1 and the height track the span almost exactly (both scale directly with the half-span at a fixed pitch); R2 grows more slowly, because the upper rafter only carries the last stretch to the ridge. Each span page works through material and cost specifics for that width — this table exists so the truss numbers you are looking at here match the numbers you will find there.

From cut lumber to a standing truss

The steps below assume you already have rafter cut lengths from the rafter length calculator and a target gusset size from the tool above.

  1. Fix the sweep

    Choose the lower pitch theta on the half-circle method. The upper pitch phi and the 45-degree turn at the knuckle both follow automatically — there is nothing left to set independently.

  2. Cut and stand the rafter pair

    Cut the lower and upper rafter for one truss (see the rafter length calculator for net cut lengths), then join them at the knuckle with the plumb mating cut.

  3. Fasten the gusset

    Nail or screw the plywood or OSB gusset plate to both rafter faces, spreading the fastener pattern across the full gusset base length rather than clustering it near the joint.

  4. Check the inner clearance

    Confirm the achieved clearance at the crook of the joint is at least what the purlin (or raised tie, in a custom layout) needs to seat properly.

  5. Repeat and stand the run

    Build the remaining trusses identically, stand them at the spacing set on the framing page, then run the knuckle purlins and collar ties through the whole line before sheathing.

Truss design FAQ

Why is theta minus phi always 45 degrees?
Because the half-circle method places the knuckle and the ridge on the same semicircle of radius W/2. That geometric construction — not a code rule, not a rule of thumb — forces the 45-degree gap between the two pitches for every knuckle position. See the main calculator for the full isosceles-triangle proof.
What is the gusset base length actually measuring?
In this model, it is how far the plate extends along EACH rafter face, outward from the knuckle point, symmetric about the joint. A 12" gusset base gives roughly a 22" tip-to-tip plate footprint once the 45-degree turn angle is folded in — the plate has to be wider than its own reach because the two rafters are not in line.
Why does a bigger gusset mean less inner clearance headroom, not more?
It does not — a longer gusset base gives you MORE inner clearance in this model, because clearance is measured as how far the plate reaches into the joint along the bisector. If your achieved clearance falls short of what you need for the purlin, the fix is a longer gusset base, which the calculator reports directly.
Does every gambrel truss need a gusset at the knuckle?
Every knuckle joint needs SOME positive connection, because the joint has to resist the two rafters trying to rotate away from each other under roof load. A plywood gusset on each face is the common light-frame answer; heavier trusses sometimes use steel truss plates or bolted straps instead, but the geometry — the 45-degree turn, the interior 135-degree joint angle — is identical either way.
How does truss design here relate to the framing page?
This page sizes ONE truss: the rafter pair, the knuckle joint and its gusset. The framing guide takes that truss and repeats it — spacing, truss count for a given building length, and the purlin/collar-tie runs that tie the whole line of trusses together.