Count the trusses for a gable roof, find the center height and top chord length from span and pitch, and estimate the lumber volume and delivered cost.
📋 What's on this page: Use the free calculator above to get the truss count, the center height at the peak, the top chord length, the lumber per truss, the total board feet, and the delivered cost. Then scroll down for the full guide, the truss vs rafter comparison, the anatomy of a truss, a height and chord table, the spacing options, truss types, a worked example, the ordering checklist, and 6 truss mistakes that cost you.
Roof Truss Calculator
Enter span, pitch, length, spacing and lumber to find count, height, chord length & cost
Inputs
Wall to wall, the width each truss covers.
Rise in inches per 12 inches of run.
Length along the ridge, for counting trusses.
Delivered price, set to 0 to skip the cost total.
Results
21
Trusses Needed
4.67 ft
Center Height
14.76 ft
Top Chord Length
51 bd ft
Lumber per Truss
1,063 bd ft
Total Lumber
$2,520
Estimated Truss Cost
How to Use This Roof Truss Calculator
Enter the building span in feet (the wall to wall width the truss covers), the roof pitch as rise over 12, and the building length along the ridge. Pick the truss spacing and lumber size, and optionally enter a cost per truss. The calculator returns the number of trusses for the whole roof, the center height at the peak, the top chord length, the board feet of lumber in each truss, the total lumber volume, and the delivered cost.
The math behind each result, where span is S, pitch is P, and building length is L:
Run = S ÷ 2
Center height = run × P ÷ 12
Top chord length = √(run² + height²)
Truss count = L in inches ÷ spacing, rounded up, plus 1
Lumber per truss = (2 × top chord + bottom chord + web allowance) × lumber factor
Trusses vs Rafters: The Two Ways to Frame a Roof
Roofs are framed two ways. Rafters are single sloping boards cut on site, one pair per roof bay, each rafter running from the wall to the ridge. Trusses are prefabricated triangular frames built in a factory and delivered whole. Each truss combines a pair of sloping top chords, a horizontal bottom chord, and a pattern of web members, all joined with toothed metal connector plates.
The web triangle is what changes the game. A plain rafter is a beam that bends, so it needs a deep section to span a wide roof. A truss turns the roof load into tension and compression running through the web, which lets a much lighter 2x4 frame carry the same span. That is why production houses use trusses, they arrive pre-engineered, go up fast, and let framers skip the measuring and cutting that stick framing requires. The rafter length calculator covers the stick-framed route, and this one covers trusses.
Anatomy of a Roof Truss: Chords and Webs
Every truss has three parts. The top chords are the two sloping members that form the peak and carry the roof sheathing. The bottom chord is the horizontal member that ties the two top chords together and usually doubles as the ceiling joist. The webs are the internal members arranged in a triangle pattern that carry the compression and tension between the chords.
The most common residential design is the Fink truss, also called the W truss, where the webs form a W between the chords. The Howe truss uses a lattice of diagonals and is better for longer spans and heavier loads. A scissor truss has a raised bottom chord that slopes, which creates a vaulted ceiling under the roof. An attic truss has a raised bottom chord with a wider flat section, forming a small storage room or bonus space inside the roof. All of them share the same geometry, the height and top chord length come from the span and pitch, no matter which web pattern you pick.
How Truss Height and Top Chord Length Are Calculated
The peak height of a truss follows the same pitch math as a rafter. The run is half the span, and the rise over that run comes from the pitch. Center height = run × pitch ÷ 12. A 28-foot span at 4/12 has a 14-foot run, so the center rises 14 × 4 ÷ 12 = 4.67 feet above the top plate. That number sets both the ceiling height under the truss and the attic space above it.
The top chord is the hypotenuse of the triangle formed by the run and the center height, so top chord length = √(run² + height²). For the same 28-foot truss at 4/12, the chord is √(14² + 4.67²) = √217.8 = 14.76 feet. The table below gives the center height and top chord length for a 28-foot span across common pitches, the two numbers the truss plant needs to lay out the frame.
Pitch
Center Height
Top Chord Length
Pitch
Center Height
Top Chord Length
3/12
3.50 ft
14.43 ft
7/12
8.17 ft
16.21 ft
4/12
4.67 ft
14.76 ft
8/12
9.33 ft
16.83 ft
5/12
5.83 ft
15.17 ft
10/12
11.67 ft
18.24 ft
6/12
7.00 ft
15.65 ft
12/12
14.00 ft
19.80 ft
Steep pitches grow the top chord fast. From 4/12 to 8/12 the chord only grows about 2 feet, but from 8/12 to 12/12 it grows another 3 feet for the same 28-foot span. That is why a steep truss carries noticeably more lumber and a taller gable wall, the peak keeps climbing while the base stays put.
Truss Spacing: 24, 19.2, and 16 Inches
Trusses sit on top of the walls at a set interval, measured on center like wall studs. 24 inches on center is the residential standard. It balances truss count, lumber cost, and the span ratings of the roof sheathing above, and it is what most truss plants quote first. 19.2 inches on center, the five-in-six layout, places a truss every five stud bays and saves roughly one truss in six, which trims the bill on a long building at the cost of a tighter layout to frame around. 16 inches on center is rare for trusses, the prefabricated frame simply does not need it for normal residential loads, and it roughly doubles the count over 24-inch spacing.
The spacing choice is part of the truss design, not just the count. The truss plant engineers the chords and webs for the spacing you give them, wider spacing means a stronger truss and a thicker floor or roof package on top. Tell the plant the spacing up front, and tell your sheathing supplier too, because OSB and plywood carry different span ratings at 19.2 and 24 inches.
How Many Trusses Do I Need?
The count comes straight from the building length and the spacing. Convert the length to inches, divide by the spacing, round up to a whole number, and add one for the end truss. A 40-foot building at 24-inch spacing has 480 inches divided by 24, or 20 intervals, so 21 trusses. The same building at 19.2-inch spacing has 25 intervals and 26 trusses, and at 16-inch spacing it has 30 intervals and 31 trusses.
The extra truss is the one that frames the end wall. The first truss sits flush with the outside face of the end wall, then the rest follow at the spacing interval, so the number of intervals always needs the plus-one. Add a couple of spares to the order if you expect any to arrive damaged, and confirm the truss drawings for a gable-end overhang, some trusses carry a piggyback extension for the rake.
Common Truss Types and When to Use Them
The Fink truss is the workhorse of residential framing, its W-shaped web carries light to medium spans economically and it is what most gable roofs use. The Howe truss swaps in a lattice of small diagonals and holds up better on longer spans and heavier snow loads, which is why it shows up on garages, workshops, and commercial buildings. The scissor truss raises and slopes the bottom chord to form a vaulted ceiling, a popular choice for great rooms. The attic truss raises the bottom chord into a flat platform, turning the roof into a storage room or a bedroom with knee walls.
Each type changes the usable space under the roof and the price of the truss. A scissor truss costs more than a Fink because of the extra fabrication, and an attic truss costs the most because it carries a floor load across the raised platform. Pick the type for the room you want below, then let the plant engineer it, the span and pitch math on this page is the same for every type.
2x4 or 2x6? Choosing Truss Lumber
Most residential trusses frame in 2x4 lumber. The triangle geometry does the structural work, so a 2x4 top chord carries a 30-foot span at 24-inch spacing without complaint, which is why 2x4 is the default at most truss plants. Step up to 2x6 chords when the span runs long, when the roof carries heavy loads, when the truss spacing widens past 24 inches, or when the local snow load calls for it. The plant also uses bigger lumber in the bottom chord of an attic truss because that member becomes a floor joist.
The calculator applies the lumber factor, 0.667 board feet per linear foot for a 2x4 and 1.0 for a 2x6, to the total length of chords and webs in one truss. The per-truss volume also feeds the delivery weight, a 2x6 truss weighs roughly half again as much as the same truss in 2x4, which matters for the crane and the crew on the ground. When in doubt, let the truss plant recommend the size, they price the exact engineered frame at no extra cost to you.
Worked Example: A 28-Foot Garage Roof
Take a 28-foot-wide garage at 4/12 pitch, 40 feet long, with trusses on 24-inch centers. The run is 14 feet. The center height is 14 × 4 ÷ 12 = 4.67 feet, so the ridge peaks 4.67 feet above the wall plates. The top chord is √(14² + 4.67²) = 14.76 feet, and each truss carries two of them plus the 28-foot bottom chord and the Fink webs, about 76 linear feet of lumber before the size factor. In 2x4 that works out to roughly 51 board feet per truss.
For the count, 40 feet is 480 inches, divided by 24 gives 20 intervals, so 21 trusses. The whole roof frames with about 21 × 51 = 1,063 board feet of lumber. At a delivered price of $120 per truss, the framing package runs 21 × $120 = $2,520, which is where the estimate on this page comes from. Add the sheathing and roofing on top, the roofing calculator turns the same footprint into squares and bundles, and the roof pitch calculator does the area conversion if you only know the pitch.
Ordering Trusses: What the Plant Needs From You
Trusses are engineered to order, so the plant needs accurate numbers before they cut a single board. Give them the span, the pitch, the spacing, the count, and your local snow and wind loads. Tell them the truss type you want and whether the ceiling below will carry a drywall load, a storage load, or just an open attic. The more detail you give, the closer the quote comes to the delivered reality.
Delivery day is where truss projects fail. The truck needs a level, clear spot to park and a crane or a strong crew to unload, a 28-foot truss is awkward to carry by hand. Set trusses on stickers off the ground, keep them dry, and brace them plumb as they go up. The bracing pattern comes with the truss drawings, follow it, an unbraced row of trusses can domino in the wind. The framing calculator handles the wall framing below the trusses, and the decking calculator estimates the sheathing that stiffens the roof plane on top.
6 Truss Mistakes That Cost You
Ordering before the walls are framed. Trusses arrive on a delivery date you set. If the walls are not built and braced, the truck shows up with nowhere to put the load and you pay a re-delivery fee or the trusses sit on wet ground.
Giving the plant the wrong span. The span is the wall to wall width, not the length along the ridge and not the diagonal of the roof. A truss is built to its exact span, a few inches of error means the bottom chord does not land on both plates.
Forgetting the load numbers. Truss plants design for the snow and wind load you declare. Understating it to save money on lumber produces a truss that may not pass the building inspection or survive a heavy winter.
Skipping the bracing. A bare row of trusses has no lateral stability until the sheathing goes on. Without the bracing the drawings call for, one truss can roll and pull the whole row down in a gust.
Walking on top chords before sheathing. The top chord of a bare truss is not a ladder. A point load on an unbraced chord can buckle it. Work from a plank spanning several trusses or wait for the sheathing.
Cutting or notching truss members. The chords and webs are engineered as a unit. Cutting a web to run a vent or notching the bottom chord for a pipe changes the load path and voids the truss design. Plan the penetrations with the plant before they build.