Formula
Rise is half the span times the pitch divided by 12. Each top chord, before any tail, is half the span times the rafter multiplier, √(1 + (pitch/12)²). A 6/12 is √1.25 = 1.118, so a 24 ft span has a 6 ft rise and a 13.416 ft top chord. A horizontal overhang adds overhang × that same multiplier on each end.
king = 2 top chords + bottom chord + the rise
Fink adds two verticals of rise/2 and two diagonals √((span/4)² + (rise/2)²)
Howe adds those quarter verticals, a center vertical of the full rise, and two diagonals √((span/4)² + rise²)
The Fink measured here is four bottom panels: joints at 0, span/4, span/2, 3×span/4, and the span. The diagonals run from the top-chord quarter points down to the center of the bottom chord. The Howe uses the same panel points, with diagonals from the peak down to the bottom quarter points. Neither drawing is a plate layout, a camber, or a load path. This page does not say the truss is adequate. Take the span and the pitch to a truss manufacturer or an engineer. The pitch itself is the roof pitch calculator. A common rafter of this span is the rafter calculator. Squares and bundles are the roofing calculator.
Worked examples
24 ft span, 6/12, no overhang, king post. Rise 6 ft. Two top chords at 13.416 ft, a 24 ft bottom chord, and a 6 ft king post. Four pieces, 56.833 ft of board.
The same span as a Fink. Seven pieces. The two half-height verticals add 6 ft. The two diagonals are each √(6² + 3²) = 6.708 ft. The total is 70.249 ft. There is no full-height king post in this Fink.
The same span as a Howe. The center vertical is the 6 ft rise. Each diagonal is √(6² + 6²) = 8.485 ft. Count the pieces on the drawing before you buy lumber.
Reference
Member list for a 24 ft span at 6/12 with no overhang. These are the coordinates used in the formula, not a catalog truss.
| Web | Members | Board, ft |
|---|---|---|
| king | 4 | 56.833 |
| fink | 7 | 70.249 |
| howe | 8 | 79.803 |
Questions
Will this truss carry the roof?
This page cannot tell you that. It adds up board lengths for one drawn skeleton. A truss has to be engineered. Order it from a truss manufacturer or ask an engineer. There is no span rating and no load check here.
Which Fink is this?
A four-panel Fink. Bottom joints at each quarter of the span. Two verticals of half the rise, and two diagonals from those top-chord points down to the center of the bottom chord. A shop drawing with a different web is a different truss.
Which Howe is this?
The same four panels. Verticals at the quarter points and a full-height vertical at the center. Diagonals run from the peak down to the bottom quarter points. It is not a manufacturer’s plate layout.
Sources
- Top-chord length uses the same pitch multiplier as the roof pitch and rafter calculators: √(1 + (rise per 12 / 12)²).
- Beam calculator for an educational deflection check of a prismatic member. It is not a truss design.
- King post, four-panel Fink, and four-panel Howe member lists are defined on this page. They are geometry. They are not a truss manufacturer’s shop drawing and they are not a structural design. Wall studs, plates, and header lengths are the framing calculator.