Article — Roof Truss Calculator
Roof truss calculator: trusses, peak height, and rafter length
A roof truss is a triangulated wood frame that spans between exterior walls and supports roofing weight, snow, and wind loads. The count is floor(roof length / spacing) + 1, so a 40 ft roof at 24 in O.C. needs 21 trusses. Peak height equals span/2 times pitch/12, and rafter length comes from the Pythagorean theorem on rise and half-span.
Trusses dominate new residential construction in the US, Canada, and most of Europe because factory engineering plus volume manufacturing beats on-site stick framing on cost, speed, and quality control. The calculator handles the material take-off; final design still belongs to a licensed engineer or truss manufacturer's design department.
What is a roof truss?
A roof truss is a pre-engineered wood frame, usually 2x4 or 2x6 lumber connected with metal toothed plates (gang nails), that carries the roof load from ridge to bearing wall in pure compression and tension. The triangulated geometry means every member sees only axial load, no bending — that is why a 2x4 top chord can span 28 feet in a truss where a 2x4 rafter would sag immediately.
The top chords form the roof slope. The bottom chord is the ceiling joist and the tension tie that prevents the walls from spreading outward under roof load. Web members in between transfer load from top to bottom and prevent buckling of the long top chord. Most residential trusses are pitched (gable, hip, scissor) but flat-bottom trusses with parallel chords work for sheds and commercial roofs.
The factory-built wood truss as we know it dates to 1952, when the Florida-based Sanford Truss Company patented the metal toothed connector plate. Before that, trusses were assembled with bolts and gusset plates — slow, expensive, and limited to commercial applications. The toothed plate cut connection time by 80% and brought trusses to residential construction. Today over 80% of new US homes use roof trusses.
How to count roof trusses
N = floor(L / s) + 1, where L is roof length in feet and s is spacing in feet. The +1 accounts for trusses at both end walls. A 40 ft long roof at 24 inch (2 ft) on-center spacing needs floor(40/2) + 1 = 21 trusses. At 16 inch (1.333 ft) spacing the same roof needs 31 trusses, 50% more.
Hip roofs and complex geometries need additional trusses called girder trusses, jack trusses, and end jacks. A hip roof on a 40 by 28 ft rectangle adds 8-12 extra trusses for the corners. Order from a truss manufacturer's quote, not just the basic count, for any roof more complex than a simple gable.
N = floor(L/s) + 116 in O.C. = heavy load / tile / snow24 in O.C. = standard asphalt shinglepeak height = span/2 × pitch/12rafter = √(peak² + half-span²)Roof truss pitch and angle
Pitch is rise (inches) over 12 inches of run. 4/12 pitch means 4 inches of vertical rise for every 12 inches of horizontal run, giving an 18.4° slope angle. 6/12 is 26.6°, 8/12 is 33.7°, and 12/12 is exactly 45°. Pitches below 2/12 are flat roof territory and need special drainage detailing.
The minimum pitch for asphalt shingles is 2/12; below that, water can sit on the seams. Metal roofing handles down to 1/12 with proper detailing. Clay and concrete tile need at least 4/12 to shed water. Slate prefers 5/12 or steeper for the same reason — the steeper the roof, the less time water has to find a way past the lap joints.
- 2/12 pitch = 9.5° angle, minimum for asphalt
- 4/12 pitch = 18.4°, low-slope standard
- 6/12 pitch = 26.6°, walkable max for most workers
- 8/12 pitch = 33.7°, steep walk needs harness
- 12/12 pitch = 45°, very steep, sheds snow well
- Cathedral ceiling usually needs scissor trusses or stick framing
Roof truss spacing rules
24 inch O.C. is the conventional spacing for residential roofs with asphalt shingles and average snow load. The 2x4 top chord can span the 24 inch distance between trusses while supporting the sheathing and shingles, and the 2x4 bottom chord works as a ceiling joist for typical drywall ceiling.
16 inch O.C. spacing is required when roofing weighs more than about 20 psf (clay or concrete tile, slate) or snow load exceeds 50 psf. The closer spacing reduces tributary width by 33% and load per truss by the same. It also lets the top chord stay at 2x4 instead of stepping up to 2x6, which keeps truss depth and cost down.
If a truss design specifies 16 in O.C., changing to 24 in to save material increases load per truss by 50%. The truss may fail under design snow load. Same in reverse: 24 in O.C. trusses crowded to 16 in waste money. Spacing is engineered into the truss design and shows on the stamped drawing — do not change it on site.
Roof truss loads: dead, live, snow
Dead load is the permanent weight of materials: roofing, sheathing, insulation, drywall, and the truss lumber itself. Asphalt shingle assembly typically gives 12-15 psf total dead load. Metal roofing on purlins runs 6-8 psf (no sheathing needed). Clay tile climbs to 25-30 psf, slate 35-40 psf.
Live load is the temporary load during construction or maintenance — workers, tools, snow shoveling. Building codes require 20 psf live load on residential roofs regardless of slope. Snow load comes from ASCE 7 ground snow maps for your zone, reduced for slope and exposure. A 4/12 to 6/12 pitch carries the full ground snow load; above 6/12 the reduction factor drops the design value.
Roof truss cost in 2026
Premade trusses run $3-5 per linear foot of span for standard residential profiles. A 28 ft span at 6/12 pitch costs $90-140 per truss. The same roof in stick framing costs about $200 per opening (rafter, ridge, ceiling joist, ties) plus 4-6× the labor. For a 40 ft roof needing 21 trusses, truss material runs $1,900-2,900 plus delivery.
Delivery of trusses requires a flatbed truck and often a crane to set them onto the walls. Set fees run $300-800 for a small house, more for large or steep roofs. Total truss package (engineered drawings, manufacture, delivery, set) for a 1,500 sq ft home roof: $5,000-9,000 in 2026.
Stick framing vs roof trusses
Trusses win on cost, speed, and quality control for almost any new construction. A truss package arrives engineered, stamped, and pre-cut. A 1,500 sq ft house roof goes up in one day with a crane. Stick framing the same roof takes 5-10 working days, more lumber, more waste, and more variability in framing quality.
Stick framing still wins in three cases. First, additions and remodels where the existing roof connects in a complex pattern that prefab trusses cannot match. Second, very large clear spans (over 50 ft) where custom engineered timber framing or steel beats truss limits. Third, exposed cathedral ceilings where the homeowner wants visible structural lumber instead of the gusseted truss profile.
Building codes and truss design
The International Residential Code (IRC) requires truss designs to be performed by a licensed engineer or a Truss Plate Institute (TPI) certified designer. Designs must satisfy ASCE 7 minimum design loads for dead, live, snow, and wind. The truss manufacturer's design package includes a stamped engineering drawing for each truss profile, calling out lumber grades and connector plate sizes.
On site, trusses must be installed plumb, properly braced both temporarily (during construction) and permanently (per the truss drawing), and connected to top plates with appropriate hardware. The truss design drawing specifies hold-down requirements, lateral bracing positions, and any field cuts that are forbidden. Modifying a truss in the field (cutting through a web or chord) voids the engineering and is a building code violation.
Photograph the stamped truss drawing before installation. Inspectors will ask for it during framing inspection, and the homeowner will want it for permanent records. Some manufacturers email the drawings as PDFs; others only deliver a paper copy with the trusses.