Roof Truss Calculator

Truss designer

Common truss types

All five types below are symmetric gable trusses with a bottom chord (ceiling tie), two top chords (rafters), and web members that carry the load to the walls. The calculator sizes every member for the type you pick.

• King post — the simplest truss: one central vertical post from tie beam to ridge. Best for short spans (up to ~16 ft) and steep pitches; cheap, leaves the most open space.
• Queen post — two vertical posts with a collar beam between them, leaving a clear center bay. Good for 16–24 ft spans and rooms where you want an open middle.
• Fink (W) — the workhorse of modern residential framing: a W of webs. Efficient for 20–36 ft spans at 24" spacing, which is why most manufactured trusses are fink-style.
• Howe — verticals plus diagonals in every panel. A heavier-duty pattern for 30–60 ft spans (barns, garages, light commercial).
• Fan — like a fink with extra webs fanning from the center. Used for 30–50 ft spans where you want more load paths and a busier, decorative web pattern.

Member names used below: top chord = the sloped rafter member (wall to ridge plus overhang tail); bottom chord = the horizontal tie across the span; webs = the interior members (posts and diagonals).

Reference: IRC rafter span table (planning aid)

The lumber recommendation above is read from 2018 IRC Table R802.5.1(1), Douglas fir-larch #2, ceiling joists not attached to rafters, 10 psf dead load, 20 psf snow/live load. "Span" is the horizontal projection of one rafter = half your building span. The tool picks the smallest size whose maximum span covers your half-span. Manufactured trusses are engineered products (TPI 1) — this table is a conservative planning reference, not a substitute for the full table or stamped design.

Source: 2018 IRC R802.5.1(1) via ICC Digital Codes and county-published rafter span tables. Spot-checked before publication; see SOURCES. "—" means the span exceeds 26 ft (beyond the prescriptive table).

Worked example

A 24 ft span garage, 6/12 pitch, 32 ft long, fink trusses at 24" on center, 1 ft overhang, ground snow 20 psf, dead load 10 psf, lumber at $1.25/board foot, 10% waste:

1. Run = 24 ÷ 2 = 12.00 ft; rise = (6/12) × 12 = 6.00 ft; angle = atan(6/12) = 26.57°.
2. Rafter (wall to ridge) = √(6.00² + 12.00²) = 13.42 ft. Overhang tail = 1 × √(1 + 0.5²) = 1.12 ft, so each top chord = 14.53 ft.
3. Truss count = floor(32 ÷ 2) + 1 = 17 trusses (both gable ends included).
4. Half-span 12 ft at 24" o.c.: 2×6 tops out at 11'-9", so the table recommends 2×8 top chords.
5. Fink members per truss: 2 top chords (14.53 ft), bottom chord 24 ft, king post 6 ft, 2 diagonal webs 6.71 ft each → 72.49 lin ft per truss.
6. Takeoff: chords 902.17 lin ft (1202.89 bf @ 2×8), webs 330.08 lin ft (220.05 bf @ 2×4) → 1422.95 board feet total.
7. Cost: 1422.95 bf × $1.25 = $1,778.68 materials; +10% waste → $1,956.55.
8. Load: balanced snow = 0.7 × 20 = 14.0 psf; design = 10 + max(20, 14.0) = 30.0 psf; per truss = 30.0 × 24 × 2 = 1,440 lb.
9. Heel check: required heel for 2×8 at 26.57° = 7.25 ÷ cos(26.57°) = 8.1"; a 9" heel clears it.

Every number above is computed by the engine on this page — change the inputs above and the calculator re-runs the same steps live.

How the math works

Every result comes from plain geometry plus the IRC reference table — no black boxes:

• Run = span ÷ 2. Rise = (pitch ÷ 12) × run. Angle = atan(pitch ÷ 12).
• Rafter (wall to ridge) = √(rise² + run²) — the Pythagorean theorem on the roof triangle.
• Overhang tail = overhang × √(1 + (pitch ÷ 12)²) — the same slope extended past the wall.
• Top chord per side = rafter + tail. Ridge height = rise.
• Truss count = floor(roof length ÷ spacing) + 1 — the +1 covers both gable ends.
• Balanced roof snow = 0.7 × ground snow Pg (simplified; assumes exposure, thermal and importance factors of 1.0). Design load = dead + max(20 psf roof live, balanced snow). Load per truss = design psf × span × tributary width (spacing in feet).
• Board feet = thickness(in) × width(in) ÷ 12 × length(ft). A 2×8 carries 16⁄12 = 1.33 bf per linear foot; a 2×4 carries 8⁄12 = 0.67 bf/ft.

Snow, dead and live loads

The IRC requires roofs to carry dead load (the permanent weight: shingles, sheathing, the truss itself — typically 10 psf for light roofing, 15–20 psf for tile) plus the larger of roof live load (20 psf minimum per IRC R301.6) and snow load. This tool uses the simplified balanced-snow formula p_s = 0.7 × P_g from ASCE 7 Chapter 7 with all adjustment factors at 1.0 — a reasonable planning number, but real snow design also checks drift, unbalanced sliding snow, and your local code's ground snow map (ASCE 7 Figure 7.2-1 or your building department).

Each truss carries a tributary strip of roof one spacing wide: at 24" on center, every truss supports a 2 ft wide strip of the full span. Multiply the design psf by span × tributary width to get the total pounds one truss must carry — that number is what you hand to a truss manufacturer or engineer.

Heel height, explained

The heel is the vertical height of the truss at the outside of the wall — where the top chord passes over the wall plate. Two things compete for that space:

• Bearing: the top chord needs enough heel for its birdsmouth seat cut. A quick check: required heel ≈ lumber depth ÷ cos(angle). For a 2×8 at 6/12 pitch that's 7.25 ÷ cos(26.57°) ≈ 8.1".
• Insulation: an "energy heel" (typically 9–12"+) leaves room for full-depth insulation over the wall plate, avoiding the cold compressed-insulation strip that causes ice dams.

Enter your heel height above and the tool flags it if it falls short of the bearing minimum for the recommended lumber size.

Manufactured vs. site-built trusses

Most residential trusses today are manufactured: designed per the Truss Plate Institute's TPI 1 standard, assembled with metal connector plates in a plant, and delivered with a stamped truss design drawing for your exact span, load and spacing. The lumber-size recommendation on this page follows the IRC prescriptive rafter table and is the right reference for site-built trusses (cut and assembled on site), but any site-built truss beyond the prescriptive tables still needs an engineer's stamp.

Use this calculator to plan — counts, member lengths, takeoff, budget — then take the numbers to a truss manufacturer or structural engineer for the final design.

Frequently asked questions