Gambrel Roof Truss Design Calculator

Sweep angle, knuckle position, gusset plate dimensions, inner clearance, and usable cross-section: real-time half-circle geometry.

Building Width(ft)

Sweep Angle(°)

Rafter Thickness(in)

Gusset Base Length(in)

Lower Rafter R₁

12.00 ft

Upper Rafter R₂

6.21 ft

Knuckle Height

10.39 ft

Total Truss Height

12.00 ft

Inner Width at Plate

12.00 ft

Inner Height at Center

11.50 ft

Mid Gusset Size

12 × 12 in

Top Gusset Size

11 × 8 in

Cross-Section Area

98.35 ft²

Half-Circle Geometry

The half-circle truss inscribes both rafters in a semicircle of radius equal to half the building width. Every chord drawn from the wall plate to a point on the arc forms a right angle with the chord drawn from that point to the opposite wall plate (Thales' theorem). This is what guarantees the upper and lower rafters meet at the knuckle at exactly 90°, and what forces total height equal to W/2.

x₁ + x₂ = W/2, y₁ + y₂ = W/2 → R₁ = √(x₁² + y₁²), R₂ = √(x₂² + y₂²)x₁ = (W/2)(1 − tan β) / (tan α − tan β), where β = α − 45°

Why the Knuckle Is Structurally Sensitive

The knuckle absorbs the full thrust of the upper rafter. In a gable roof the rafter delivers thrust to the wall plate through a continuous load path; in a gambrel that load path bends at the knuckle, and the bend wants to straighten under load. Without reinforcement the knuckle hinges outward and the building width spreads. Three details solve this: continuous longitudinal purlins, plywood gusset plates on both rafter faces, and properly fastened collar ties near the ridge.

Gusset Sizing

Gusset plates are sized for two failure modes: nail pull-through and plywood shear. For 2× framing the working rule is ¾ in plywood, a minimum 12 in extension along each rafter from the joint centerline, and 8d common nails at 3 in on center around the perimeter. For spans over 30 ft, request an engineered drawing.

Span	Min Gusset Extension	Plywood Thickness	Nail Schedule
≤ 16 ft	12 in	½ in	8d @ 4 in
18–24 ft	12 in	¾ in	8d @ 3 in
26–30 ft	14 in	¾ in	8d @ 3 in
> 30 ft	Engineer required	N/A	N/A

IRC Requirements

IRC R802 governs rafter sizing; R802.5 lists allowable spans by lumber grade and species; R802.10 covers wood trusses, which must be designed, manufactured, and labeled in accordance with TPI 1. Field-built gambrel trusses do not qualify as engineered trusses and must use IRC rafter tables. For spans beyond the table, an engineered design is required.

Span Reference Table

Width	R₁ (ft)	R₂ (ft)	Height (ft)	Inner Width (ft)
12 ft	6.00	3.11	6.00	6.00
16 ft	8.00	4.14	8.00	8.00
20 ft	10.00	5.18	10.00	10.00
24 ft	12.00	6.21	12.00	12.00
30 ft	15.00	7.76	15.00	15.00
40 ft	20.00	10.35	20.00	20.00

Frequently Asked Questions

›What is the sweep angle in a gambrel truss?

Sweep angle is the angle of the lower rafter from horizontal, measured in degrees. In the half-circle truss method the sweep angle drives every other dimension: knuckle position, total height, upper rafter angle (sweep − 45°), and inner clearance. Common sweeps are 60°, 67.5°, and 75°.

›Where is the knuckle on a gambrel truss?

Knuckle horizontal position from the centerline equals R₁ cos(sweep), where R₁ is the lower rafter chord. Knuckle height above the wall plate equals R₁ sin(sweep). For a 24 ft truss at 60° sweep the knuckle sits about 6 ft inboard of the wall plate and 10.4 ft above it.

›How big should gambrel truss gusset plates be?

Plywood gussets at the knuckle should extend at least 12 in along each rafter from the joint, be the same nominal thickness as the rafter (¾ in plywood for 2× framing), and use a nailing schedule of 8d common at 3 in on center around the perimeter and 6 in in the field.

›What is the inner clearance at the wall plate?

Inner clearance equals the truss inner width: building width minus twice the lower rafter horizontal run at the wall plate. For a 24 ft building at 60° sweep that is roughly 12 ft of usable floor width before the inside roof line begins to slope inward.

›Can I use the half-circle method for any building width?

Yes. The half-circle method scales linearly. A 12 ft truss and a 40 ft truss with the same sweep angle have proportionally identical geometry. Practical limits come from lumber spans, not from geometry. Once R₁ exceeds 14 ft, single-piece 2× rafters become hard to source.