# Scissor Truss Calculator

Scissor truss calculator for cathedral ceilings. Enter span, top and bottom chord pitch, and wall height to get interior ceiling height, peak height, chord lengths, and lumber.

## What this calculates

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.

## Inputs

- **Building Span** (ft) — min 12, max 60 — Exterior wall to exterior wall
- **Top Chord Pitch** (:12) — min 3, max 18 — Roof slope. 6:12 to 12:12 is typical for scissor trusses.
- **Bottom Chord Pitch** (:12) — min 1, max 10 — Ceiling slope. Rule of thumb: about 1/2 of top pitch.
- **Top Plate Wall Height** (ft) — min 7, max 20 — Finished ceiling height at the walls
- **Building Length** (ft) — min 8, max 200 — Length of building for truss count
- **Truss Spacing** (in) — min 16, max 48
- **Eave Overhang** (in) — min 0, max 36

## Outputs

- **Ceiling Height at Peak (interior)** (ft) — Highest interior ceiling point under the truss peak
- **Roof Peak Height** (ft) — Top of roof above top plate
- **Insulation Space at Peak** (in) — Vertical gap between top and bottom chord at center
- **Top Chord (Rafter) Length** (ft) — Each top chord including overhang
- **Bottom Chord Length** (ft) — Each half of the sloped bottom chord
- **Number of Trusses**
- **Total Lumber** (linear ft)

## Details

## 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.

## Frequently Asked Questions

**Q: What is the rule of thumb for scissor truss bottom chord pitch?**

A: The bottom chord pitch should equal about half the top chord pitch. An 8:12 top chord pairs with a 4:12 bottom chord; a 12:12 top pairs with a 6:12 bottom. Going much beyond half ratio creates weak geometry (the truss flexes excessively under load). Some engineers allow up to 2/3 ratio (8:12 top with 5.33:12 bottom) but most standard scissor truss designs stay at 1/2.

**Q: How much vaulted ceiling height do I gain from a scissor truss?**

A: The gain equals half the span times the bottom chord pitch ratio. For a 24 ft span with 4:12 bottom chord, that is 12 x (4/12) = 4 ft extra height at the center. If your walls are 9 ft, the center ceiling is 13 ft. For a 32 ft span with 6:12 bottom, you gain 8 ft for a 17 ft peak ceiling with 9 ft walls.

**Q: Are scissor trusses more expensive than regular trusses?**

A: Scissor trusses cost 15-30% more than a standard common truss of the same span because they use more lumber (both chords are long rather than just the top), more connector plates, and require more engineering time. However, they are still much cheaper than site-built cathedral ceilings, which require heavier lumber, collar ties, and either a structural ridge or ring tie-down.

**Q: Can I fit enough insulation in a scissor truss roof?**

A: That depends on the climate zone and the gap at the eaves. In cold climates requiring R-49 ceiling insulation, a standard scissor truss often cannot fit enough blown-in cellulose at the eaves. Solutions include: raised-heel (energy-heel) scissor trusses, closed-cell spray foam (R-6.5/in so 7-8 inches = R-49), or rigid foam board above the sheathing. Run the math before committing; many older scissor truss roofs are badly under-insulated at the walls.

**Q: What spans can scissor trusses handle?**

A: Residential scissor trusses are commonly used for 16-40 ft spans. Below 16 ft, a conventional truss or stick frame is cheaper. Above 40 ft, engineering becomes complex and lumber sizes grow fast; most truss plants cap scissor truss designs at 50 ft span. Commercial buildings use scissor trusses up to 70-80 ft with engineered wood or steel chords.

**Q: Do scissor trusses need a ridge beam?**

A: No. That is the whole point of a truss. The chord system is self-supporting and only bears on the two exterior walls. You do, however, need to resist the outward thrust at the wall plates. Most designs use a ring of connectors (LSTA straps, Simpson HDU tie-downs, or an engineered ring beam) to keep the walls from pushing outward under load. Your truss engineer will specify the exact hardware.

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Source: https://vastcalc.com/calculators/construction/scissor-truss
Category: Construction
Last updated: 2026-04-08