Roof Truss Calculator: Member Lengths, Angles and Number of Trusses
Work out top chord, bottom chord and web lengths and angles for king post, queen post, Fink (W) and Howe trusses, plus truss count and lumber per truss.
How it works
Slope p = rise ÷ 12 (or tan of the pitch angle) · Rise h = (span ÷ 2) × p · Top chord = (span ÷ 2 + overhang) × √(1 + p²) · King post = h · Queen posts = 2h ÷ 3 · Fink short web = √((span ÷ 12)² + (h ÷ 2)²) · Fink long web = √((span ÷ 6)² + h²) · Howe diagonal = √((span ÷ 4)² + (h ÷ 2)²) · Trusses = ⌈building length ÷ spacing⌉ + 1
A common (gable) truss is two sloped top chords sitting on one level bottom chord, held in shape by webs. The rise is half the span times the slope, and each top chord is the hypotenuse of a right triangle with the half span and the rise as its legs. An eave overhang is measured level and stretched along the slope by the same factor √(1 + p²). The web layouts follow the usual panel points. A king post truss has one vertical from the bottom chord center to the peak. A queen post truss has two verticals at the third points of the span. A Fink (W) truss divides the bottom chord into thirds: short webs run from the midpoint of each top chord down to the nearest third point, and long webs run from each third point up to the peak. The Howe layout here has a center king post, verticals at the quarter points and two diagonals from the bottom chord center up to the quarter points of the top chords. Web angles are measured from the bottom chord. The truss count divides the building length by the on-center spacing, rounds up, and adds one so both gable ends get a truss. Lumber per truss adds both top chords, the bottom chord and all webs; board feet use nominal sizes. The closest calculator on this site, the roof rafter length calculator, sizes one rafter for a stick-framed roof. This one adds the bottom chord, every web member and its angle, the truss count and lumber totals. Lengths are working-line geometry for planning, ordering and shed or garage builds; trusses for a house must come from an engineered truss design.
Worked example
A 24 ft span Fink truss at 6/12 with a 12 in overhang, on a 40 ft building at 24 in spacing: the slope is 6 ÷ 12 = 0.5, so the pitch angle is arctan(0.5) = 26.57° and the rise is 12 × 0.5 = 6.00 ft. Each top chord from heel to peak is √(12² + 6²) = 13.42 ft, and with the 1 ft overhang it is (12 + 1) × √1.25 = 14.53 ft (14' 6-7/16"). The bottom chord is 24 ft. The short webs are √(2² + 3²) = 3.61 ft at 56.31°, and the long webs are √(4² + 6²) = 7.21 ft at 56.31°. One truss uses 2 × 14.53 + 24 + 2 × 3.61 + 2 × 7.21 = 74.70 linear ft of 2×4 (49.8 board ft). The building needs ⌈40 × 12 ÷ 24⌉ + 1 = 21 trusses, or 1,568.7 linear ft of lumber.
Sources: Calculover: Roof truss calculator (24 ft 6/12 king post and 16 ft 4/12 overhang examples) · Omni Calculator: Roof truss (truss count formula and 40 ft example) · BuildingClub: Wood roof truss calculator (truss types, spacing, overhang)
Frequently asked questions
How do I calculate how many roof trusses I need?
Divide the building length by the truss spacing, round up and add one for the second gable end. A 40 ft building at 24 in on center needs 40 × 12 ÷ 24 = 20, plus 1 = 21 trusses. At 16 in spacing the same building needs 31.
How long is the top chord of a truss?
It is the half span times √(1 + slope²), plus the overhang stretched along the slope the same way. For a 24 ft span at 6/12, the slope is 0.5, so the top chord is 12 × √1.25 = 13.42 ft from heel to peak, or 14.53 ft with a 12 in overhang.
What is the difference between a king post and a Fink truss?
A king post truss has a single vertical web from the bottom chord to the peak and suits short spans such as sheds and porches. A Fink truss uses four diagonal webs in a W shape, which supports the top chords at their midpoints and is the most common layout for house roofs.
What spacing are roof trusses?
Roof trusses are most often set 24 in (600 mm) on center, which matches common sheathing panel sizes. Heavy roofing, high snow loads or thin sheathing can call for 16 in or 19.2 in spacing; follow the truss design and local code.
Can I build my own roof trusses?
For sheds and small outbuildings many people do, using gusset plates and a jig. For a home, most building codes, including the US International Residential Code, require trusses designed by an engineer or the truss maker, with a stamped design for the loads in your area.
Related calculators
Truss geometry here is for planning and estimating only. Roof trusses carry structural loads: use an engineered truss design and follow your local building code.