Scissor Truss Calculator
Cathedral ceilings are bought with structural effort: every inch of lifted bottom chord adds thrust at the walls and force in the chords. This tool prices that trade in numbers — clearance, chord lengths, and a thrust index for your exact span and pitches.
Cathedral Clearance Calculator — Scissor Truss Geometry
Enter span and both chord pitches to see the ceiling space a scissor truss buys — and what it costs in thrust.
Ridge height
6 ft 0 in
top chord above wall plate
Cathedral rise
3 ft 0 in
ceiling lift at center
Center gap
3 ft 0 in
the tool's Truss Depth
Top chord length
13 ft 5 in
per side, no overhang
Bottom chord length
12 ft 4 in
per side, heel to center
A King Post truss on the same walls shows 0 kip thrust — every pound of scissor thrust here is new demand on your wall plates.
Balanced scissor geometry: bottom pitch at or below half the top pitch keeps forces moderate.
How This Scissor Truss Calculator Works
A scissor truss replaces the flat bottom chord of a King Post with two members that climb from the heels toward the centerline. That single change drives every number on this page. The calculator takes three inputs you can measure or choose on paper — building span, top-chord pitch, and bottom-chord pitch — and resolves the geometry the same way a truss designer’s layout software does:
- 1Ridge height = (span ÷ 2) × top pitch ÷ 12. A 24 ft span at 6/12 puts the peak 6 ft above the wall plates.
- 2Cathedral rise = (span ÷ 2) × bottom pitch ÷ 12. This is the ceiling height you gain at the center of the room — the entire reason anyone orders a scissor.
- 3Center gap = ridge height − cathedral rise. This is the vertical daylight between the two chords at midspan — the value the Structural Analysis tab calls Truss Depth.
- 4Chord lengths follow from the pitch ratios through Pythagoras, giving the per-side lengths you need for material takeoffs before overhangs are added.
The fifth output — the thrust index — is the one most ceiling truss calculators omit. It estimates the horizontal force the finished truss delivers to each wall plate, using the standard arch relation H ≈ wL²/(8·rise) with a uniform roof load of 1 kip per foot. Because a King Post’s flat bottom chord produces zero thrust, the index is effectively a measure of what the scissor geometry costs you in wall design.
Ceiling Truss Design: Clearance vs. Wall Thrust
The defining tension in ceiling truss design is that the two things you want move in opposite directions. Raise the bottom chord for a roomier cathedral ceiling and the roof becomes more arch-like: member forces climb and the wall plates feel more push. Flatten it for easier structure and the ceiling flattens with it. The bars below show the thrust index at a 6/12 top pitch for a 1 kip/ft uniform load — the scissor’s cost of admission grows in a straight line with span, because thrust scales with L² divided by a rise that itself scales with L.
💡 Tip: if the thrust index at your span looks intimidating, remember it assumes both truss ends rigidly held. Real resistance comes from the wall itself, the floor diaphragm tying the two walls together, and ceiling ties — which is why scissor trusses below about 32 ft usually pass without special wall design, while longer ones deserve a conversation with your truss manufacturer.
What Truss Depth Does to Scissor Truss Member Forces
“Truss Depth” in the Structural Analysis tab is the vertical gap between the top chord and the rising bottom chord at midspan — the center-gap output of the calculator above. Shrink it and the ceiling climbs, but the chords must work harder. The table below is not a hand estimate: each row was solved with the actual stiffness-method engine behind the calculator, using a 24 ft span, 6 ft wall height, and a 2 kip point load on every top-chord joint.
| Truss Depth (ft) | Cathedral Rise (ft) | Top Chord Force (kip) | Bottom Chord (kip) | Peak Web (kip) | Load Level |
|---|---|---|---|---|---|
| 1.0 | 5.0 | −53.67 (compression) | +52.00 (tension) | +43.82 | High |
| 1.5 | 4.5 | −35.78 (compression) | +34.18 (tension) | +27.71 | Moderate |
| 2.5 | 3.5 | −21.47 (compression) | +20.00 (tension) | +14.67 | Low |
| 3.5 | 2.5 | −15.33 (compression) | +14.01 (tension) | +8.89 | Lowest |
Read the ratios, not just the rows: going from a 2.5 ft depth to a 1.0 ft depth buys 2.5 extra feet of ceiling rise but multiplies the top-chord compression by roughly 2.5× (−21.47 → −53.67 kip). The same run in the other direction — from the 1.5 ft default to 3.5 ft — cuts peak chord force by 57% while surrendering 2 ft of cathedral height. This is the page’s core trade in one sentence: every inch of clearance is purchased with member force, at an exchange rate that worsens as the gap closes.
Open model at 1.5 ft depth →
The Scissor preset, 24 ft × 6 ft, preloaded in the Structural Analysis tab. Watch the force table as you shrink the depth input.
Compare at 2.5 ft depth →
Same span and loads with a deeper center gap — the member forces drop by about a third, and the ceiling drops with them.
⚠️ Warning — the shallower limit: as the center gap approaches zero, the two chords converge and the web forces explode nonlinearly. Below roughly 1 ft of depth on a 24 ft span, the numbers in this table stop being conservative and the geometry starts behaving like a pair of crossing beams rather than a truss. If your dream ceiling needs a depth under about span/24, budget for an engineered design rather than a prescriptive one.
Interior Clearance by Span: A Ceiling Trusses Reference Table
The most common way people shop for ceiling trusses is by span: “what will a 24 ft great room feel like?” The table below answers with the standard balanced geometry — a 6/12 top chord and a 3/12 bottom chord — and assumes 8 ft wall plates. Cathedral height is measured to the highest ceiling point at the room’s centerline; the slope means walls-side ceilings stay at the traditional 8 ft.
| Span (ft) | Ridge Height (ft) | Cathedral Rise (ft) | Ceiling at Center (ft)* | Thrust Index (kip) | King Post Ceiling |
|---|---|---|---|---|---|
| 16 | 4.0 | +2.0 | 10.0 | 16 | No cathedral (flat at 8 ft) |
| 20 | 5.0 | +2.5 | 10.5 | 20 | No cathedral (flat at 8 ft) |
| 24 | 6.0 | +3.0 | 11.0 | 24 | No cathedral (flat at 8 ft) |
| 28 | 7.0 | +3.5 | 11.5 | 28 | No cathedral (flat at 8 ft) |
| 32 | 8.0 | +4.0 | 12.0 | 32 | No cathedral (flat at 8 ft) |
| 36 | 9.0 | +4.5 | 12.5 | 36 | No cathedral (flat at 8 ft) |
| 40 | 10.0 | +5.0 | 13.0 | 40 | No cathedral (flat at 8 ft) |
*With 8 ft wall plates; add your wall height difference directly.
The space the bottom chord buysPhoto: UnsplashReading the table like a designer
- ▸ Ceiling height at center grows only 0.5 ft per 4 ft of extra span — the 3/12 bottom pitch is a gentle climb, which is why these rooms feel expansive rather than tunnel-like.
- ▸ The thrust index grows linearly (16 kip at 16 ft → 40 kip at 40 ft), so wall and tie-down demands escalate exactly in proportion to span at fixed pitches.
- ▸ For comparison, the King Post column is structurally identical at every span: flat 8 ft ceiling, zero thrust. The scissor premium is constant relative to geometry, not span.
Scissor vs. King Post: Choosing the Right Ceiling Truss
Both shapes span the same room with the same top chord — the entire difference lives below the rafters. This comparison is the decision sheet for a truss ceiling, quantified for a 24 ft span at 6/12 pitch with the balanced 3/12 scissor bottom chord.
| Property | Scissor Truss (3/12 bottom) | King Post Truss (flat bottom) |
|---|---|---|
| Ceiling shape | Cathedral, +3.0 ft at center | Flat at wall-plate height |
| Peak chord force (24 ft, 2 kip/joint) | ≈ −35.8 kip top / +34.2 kip bottom | ≈ −24 kip top / +24 kip bottom |
| Horizontal thrust at walls | ≈ 24 kip shared (arch action) | 0 kip (vertical reactions only) |
| Web layout | Zig-zag diagonals, longer webs | Single king post, shortest webs |
| Best for | Great rooms, dining halls, churches | Bedrooms, garages, attics below |
| Wall design implication | Ties or engineered walls advised ≥ 32 ft | Standard wall framing |
❌ Don’t: don’t specify a scissor truss for every room on the plan because it looks good in the great room. Each scissor imports the thrust problem into that wall line, and mixing scissor and flat-bottom trusses on the same bearing wall produces uneven deflection that shows up as cracked drywall at the transition. Confine them to the rooms that earn them.
Scissor Truss Calculator FAQ
What does a scissor truss calculator actually tell me?▼
A scissor truss calculator answers three questions at once: how much cathedral ceiling space the bottom chord creates at midspan, how long each top and bottom chord is so you can order material, and how the geometry redistributes forces compared with a flat-bottomed truss. This page's calculator adds a thrust index — the horizontal push a scissor truss delivers to both wall plates, which a King Post truss never produces. For full member-by-member forces, the Structural Analysis tab preloaded with the Scissor preset gives every axial force, displacement, and reaction.
How much ceiling height does a scissor truss add?▼
The cathedral rise at the centerline is half the span times the bottom-chord pitch divided by 12. A 24 ft room with a 3/12 bottom chord gains 3 ft of ceiling height at the center relative to a flat ceiling at the wall plates. At a 6/12 top pitch, that 3/12 bottom chord is exactly half — the balanced default most manufacturers assume. Every row of the span table above shows the paired numbers so you can read the gain for your span directly.
What is the best pitch for ceiling trusses?▼
For a truss ceiling that feels spacious without overloading walls, keep the bottom-chord pitch between one-third and one-half of the top-chord pitch. A 6/12 top with a 3/12 bottom is the residential workhorse: it lifts the ceiling 25% of the half-span while keeping chord forces within about 15% of an equivalent King Post. Steeper bottom chords (above 3/4 of the top pitch) push thrust and member forces up steeply and usually need heavier plates or a heel tie engineered in.
Do scissor trusses push the walls outward?▼
Yes — that is the defining trade-off of this ceiling truss design. When both truss ends are fixed to the walls (the real-world condition), the sloped bottom chord acts like an arch and delivers a horizontal thrust estimated by H ≈ wL²/(8·rise). At 24 ft span, 3/12 bottom pitch, and a 1 kip/ft roof load, that is about 24 kip of outward push shared between the two wall plates. The calculator's Structural Analysis tab models a pin and a roller, which is the statically determinate textbook setup: it isolates member forces cleanly, and the thrust appears in the real building instead.
How is a scissor truss different from a King Post truss?▼
A King Post truss has a flat bottom chord, so it produces a flat ceiling and vertical-only reactions. A scissor truss raises that bottom chord into two sloping members, trading structural efficiency for open space: chord forces increase, webs re-arrange into a zig-zag, and horizontal thrust appears at the supports. The comparison table above quantifies the difference — at identical span and pitch, expect roughly 20–60% higher peak chord forces depending on how aggressive the bottom chord pitch is.
Can I open the calculator with a scissor truss already loaded?▼
Yes. Every 'Open in the Structural Analysis tab' button on this page carries an encoded link that preloads the Scissor preset — one at 1.5 ft truss depth and one at 2.5 ft — so you can compare member forces between the two depths without re-entering anything. The model, loads, and units rebuild instantly on any device from the link alone.
Scissor geometry, hoisted and bracedPhoto: UnsplashRelated Guides & Calculators
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