Scissor Truss Calculator
A scissor truss gives you a cathedral or vaulted ceiling without a separate framing crew to build a stick-framed ceiling. The top chord is the sloped roof and the bottom chord slopes upward from the wall plates to a peak, creating the vaulted interior. This scissor truss calculator lets you enter the span, top and bottom chord pitches, and wall height, and returns the interior ceiling height at the peak, the roof peak height, the chord lengths, and a rough lumber estimate.
How a Scissor Truss Works
Think of a conventional roof truss as a triangle with a flat bottom. A scissor truss replaces the flat bottom chord with a sloped bottom chord that rises toward the center, creating a V-shape on the underside. The two sloping chords look like the blades of a pair of scissors (hence the name) meeting at the peak.
The benefit: vaulted interior ceiling without site-built framing. The cost: less attic space for insulation and ductwork, and slightly higher lumber cost than a standard truss.
Key Scissor Truss Dimensions
- Span: building width, exterior wall to exterior wall
- Top chord pitch: the roof slope (rise per 12 in of horizontal run)
- Bottom chord pitch: the interior ceiling slope
- Wall height: finished ceiling height at the perimeter walls
The industry rule of thumb is that bottom chord pitch equals about 1/2 of top chord pitch. An 8:12 top with 4:12 bottom is the most common combination. A 12:12 top with 6:12 bottom creates a dramatic vaulted great room.
Scissor Truss Formulas
- Top chord rise = (span / 2) x (top pitch / 12)
- Bottom chord rise = (span / 2) x (bottom pitch / 12)
- Interior ceiling height at peak = wall height + bottom chord rise
- Roof peak height above top plate = wall height + top chord rise
- Attic space at peak = (top rise - bottom rise) x 12 inches
Example: 24 ft Span, 8:12 Top, 4:12 Bottom, 9 ft Walls
- Top rise = 12 x (8/12) = 8 ft
- Bottom rise = 12 x (4/12) = 4 ft
- Interior peak ceiling = 9 + 4 = 13 ft
- Roof peak above plate = 9 + 8 = 17 ft
- Attic space at peak = (8 - 4) x 12 = 48 inches for insulation and ductwork
- Top chord (rafter) length = sqrt(12^2 + 8^2) = 14.4 ft
- Bottom chord length = sqrt(12^2 + 4^2) = 12.65 ft each half
A cathedral great room with 13-foot ceilings at the peak dropping to 9 feet at the walls is a strong visual upgrade at modest added cost.
Insulation Space Consideration
The attic gap between top and bottom chords shrinks toward the walls. At the exterior wall, the gap is zero; at the center peak, it equals (top rise - bottom rise). Because of this, R-value drops toward the walls unless you use spray foam, closed-cell foam board, or a raised-heel truss variant.
If your climate requires R-49 ceiling insulation (most cold climates), a scissor truss with only 4-6 inches of gap at the walls cannot fit 14 inches of blown cellulose. Solutions:
- Energy-heel (raised-heel) scissor truss: extends the top chord above the wall to create an insulation chase at the eave
- Spray foam at the eaves (R-6.5/in closed cell) to hit R-49 in 7-8 inches
- Accept a lower R-value at the eaves if code allows (some jurisdictions permit this tradeoff)
Scissor Truss vs Cathedral Stick Framing
| Factor | Scissor Truss | Stick Frame Cathedral |
|---|---|---|
| Cost (labor + material) | Lower | Higher |
| Spans without supports | Up to 50 ft | Limited, usually needs center beam |
| Speed to install | 1-2 days | 4-7 days |
| Insulation depth | Compressed at eaves | Full depth available |
| Structural predictability | Engineered, stamped | Depends on builder |
For spans over 20 ft, scissor trusses are almost always the right choice. Below 20 ft, stick-framed cathedral with 2x12 rafters can compete.
When to Use This Scissor Truss Calculator
- Sizing a cathedral ceiling for a great room, master bedroom, or chapel
- Deciding between scissor, standard, or attic trusses for a design
- Pre-quoting lumber and truss count before calling a truss plant
- Verifying your architect's dimensions against the math
Always get final dimensions stamped by a licensed engineer. Scissor trusses generate outward thrust at the bearing points that must be resisted by a ring beam or hurricane tie-down system.