How many roof trusses do I need?

How it works

The trusses are common (gable) trusses: a level bottom chord across the span, and two sloped top chords that meet at a peak in the middle.

• Trusses = building length ÷ spacing, rounded up to a whole number, + 1 (one truss at each end wall).
• Truss height (rise) = span ÷ 2 × pitch ÷ 12.
• Top chord with overhang (one side) = (span ÷ 2 + overhang) × √(1 + (pitch ÷ 12)²), by the Pythagorean theorem.
• Bottom chord = span.
• Roof angle = arctan(pitch ÷ 12), in degrees.
• Chord length in all trusses = trusses × (2 × top chord + bottom chord), in feet.
• Cost (when you type a price per truss) = trusses × price per truss.
• Lengths show in feet and in metres (1 ft = 0.3048 m exactly).

Exact arithmetic. Each size is read as the exact decimal you typed, in the unit you typed it in (24 in is exactly 2 ft). When you type in a unit, the page stores the size in metres and reads it back as the decimal with the fewest significant digits, in one of the box's units, that gives the same stored number (a feet-and-inches pair counts by its value in inches; on a tie the first unit in the menu wins). When no decimal of up to 17 significant digits in those units gives the stored number (a value that was not typed on the page), the stored number's own shortest decimal, in metres, is used. The truss count, height, bottom chord and cost are exact fractions, so 30 ft ÷ 24 in is exactly 15. The top chord is exact when 1 + (pitch ÷ 12)² is the square of a fraction (a 9/12 pitch gives exactly 1.25); otherwise it uses the square root as a decimal number. The angle uses arctan.

Output format. Trusses show as a whole number; lengths and the angle with at most 2 decimals; the cost in dollars and cents; each rounded half up from its value, with trailing zeros left off. In Metric the answer gives metres.

Assumptions

• Spacing: 24 in on center by default; from 0.1 m (about 4 in) to 10 m.
• Pitch: from 0.25 to 24 (inches of rise per 12 in of run); the same on both sides.
• The building length is from 0.1 m to 1,000 m, the span from 0.1 m to 100 m, the overhang from 0 to 10 m, measured level from the outside of the wall.
• Chord lengths are along the outside line of the roof, before any cut at the peak or the tail. Webs inside the truss are left out.

Worked examples by hand

A 30 × 24 ft building, 6/12 pitch, 1 ft overhang, 24 in spacing, $150 a truss. 30 ÷ 2 = 15, + 1 = 16 trusses, $2,400. Height 12 × 6 ÷ 12 = 6 ft. Top chord (12 + 1) × √(1 + 0.25) = 13 × 1.1180 = 14.53 ft. Bottom chord 24 ft. Angle arctan 0.5 = 26.57°.

A 40 × 32 ft building, 9/12 pitch, no overhang, 16 in spacing. 480 in ÷ 16 = 30, + 1 = 31 trusses. Height 16 × 0.75 = 12 ft. Top chord 16 × √(1 + 0.5625) = 16 × 1.25 = 20 ft (a 12-16-20 triangle). Chords in all trusses 31 × (40 + 32) = 2,232 ft.

A 10 × 8 m building, 6/12 pitch, 0.5 m overhang, 60 cm spacing. 10 ÷ 0.6 = 16.67 → 17, + 1 = 18 trusses. Height 4 × 0.5 = 2 m. Top chord 4.5 × √1.25 = 5.03 m.