Gambrel Roof Calculator

Gambrel Roof Rafter Length Calculator

Get upper and lower gambrel rafter cut lengths, plumb cut offsets, and net physical lengths from building width, pitch, and rafter thickness.

Lower Rafter Centerline
9.03 ft
Plumb Cut Offset δ₁
0.268 ft
δ₁ = t · tan α / 12
Seat Cut Offset δ₂
0.292 ft
δ₂ = plate / 12
Net Lower Rafter
8.47 ft
Upper Rafter Centerline
9.03 ft
Ridge Offset δ₃
0.069 ft
Knuckle Offset
0.058 ft
Net Upper Rafter
8.90 ft

Centerline vs Physical Cut Length

Every rafter geometry calculation starts from the centerline: the imaginary line down the middle of the lumber. The centerline is what the right-triangle math gives you: R = √(run² + rise²). But you do not cut on the centerline. You cut on the faces. Each angled cut shortens the physical rafter by an offset that depends on the cut angle and the rafter thickness.

For the lower rafter on a 65° pitch with 1½ in 2× framing, the plumb cut at the knuckle removes about 0.27 ft (3¼ in) of length. The seat cut at the wall plate removes another 0.29 ft (the wall plate width). Net cut length is centerline minus both offsets. Order lumber based on net length plus 6 in of safety margin per piece.

net_R₁ = R₁ − (t · tan α + plate_width) / 12 ft

Plumb and Seat Cuts

Plumb Cut Angle

The plumb cut at the wall-plate end and the knuckle end is set to the pitch angle itself. A 65° lower rafter takes a 65° plumb cut (measured from the rafter edge, which is the same as 25° from the rafter face). Set a sliding T-bevel from a framing square laid on the rafter at the rise/run ratio for the pitch.

Seat Cut Depth

Seat cut horizontal length equals wall plate width (3½ in for a 2×4 plate, 5½ in for 2×6). Seat cut depth is plate_width × tan(pitch). IRC R802.7 limits the total notch depth (heel height + seat depth) to one-third of the rafter depth. A 2×8 (7¼ in deep) rafter cannot be notched more than 2.4 in. See the dedicated birdsmouth calculator for the full check.

Pitch Reference for Common Gambrel Combinations

Lower PitchUpper PitchLower R per ft of widthUpper R per ft of width
60°15°0.5000.259
65°20°0.4230.342
67.5°22.5°0.3830.383
70°25°0.3420.423
75°30°0.2590.500

Frequently Asked Questions

›How do I calculate gambrel rafter length?
Lower rafter length R₁ = √(x₁² + y₁²), where x₁ solves (W/2)(1 − tan β)/(tan α − tan β) for lower pitch α and upper pitch β. Upper rafter R₂ = √(x₂² + y₂²), where x₂ = W/2 − x₁. Both runs add up to half the building width, and both rises add up to the same half-width. The calculator above does this in real time.
›What is the difference between centerline length and physical cut length?
Centerline length is the geometric hypotenuse measured along the middle of the rafter. Physical cut length is shorter because the plumb cut at the knuckle and the seat cut at the wall plate are taken on rafter faces. Subtract the plumb offset (≈ rafter thickness × tan pitch) at the knuckle and the seat offset (= wall plate width) at the bottom.
›How does rafter thickness affect the cut length?
A thicker rafter loses more length at each angled cut. A 2× rafter (1.5 in thick) on a 65° pitch loses about 3.2 in at the plumb cut; a 4× rafter loses about 7.5 in. Always work from the centerline length and then subtract the offsets. Never measure the offsets first.
›What is the plumb cut angle for a 65-degree lower rafter?
The plumb cut angle equals the pitch angle: 65° from the rafter edge, or 25° from the rafter face. Set a power miter saw to 25° or a sliding bevel to 65° from horizontal.
›Where does the seat cut sit on the rafter?
The seat cut is a horizontal notch at the bottom of the rafter that sits flat on the wall plate. Its horizontal length equals the wall plate width (3.5 in for a 2×4 plate); its vertical depth is plate_width × tan(pitch). IRC R802.7 limits this notch to one-third of the rafter depth.

Related Calculators

Full Gambrel Calculator

All twelve outputs plus a live diagram.

Open →
Truss Design

Knuckle position, gusset sizing, clearances.

Open →
Framing

Purlins, gussets, ridge, heel height.

Open →
Birdsmouth Cut

Seat depth and IRC notch check.

Open →