Roof Truss Calculator (king post & Fink truss member lengths)

Understanding the roof truss calculator — concept and principle

This calculator works out the member lengths of a simple king post or Fink (W) roof truss from the span, pitch and overhang, the timber in one truss, and the number of trusses and total timber for a building. Self-builders and students use it to understand truss geometry and to estimate material before getting an engineered design.

One Fink truss, then many: with the default inputs the result is 22.33 m per truss (18 trusses = 401.9 m).

How it is calculated

Half-span s = span ÷ 2; apex rise h = s × tan θ.
Top chord (wall to apex) = s ÷ cos θ; with overhang add overhang ÷ cos θ.
Bottom chord = span.
King post = h.
Fink: the bottom chord is split into thirds; short web = √((s/6)² + (h/2)²), long web = √((s/3)² + h²), two of each.
Trusses = ⌈building length ÷ spacing⌉ + 1.

The principle

A truss outline is two right triangles back to back, so trigonometry gives the rise and the sloping top chords. Inside, webs divide the triangle into smaller triangles; because a triangle cannot change shape without changing a side, the frame is stiff and carries the roof load to the walls mainly by tension and compression in its members. In a Fink truss, the webs run from the third points of the bottom chord to the middle of each top chord and to the apex, and each length follows from Pythagoras.

Worked example

Default inputs: span 7.2 m, pitch 25°, Fink, overhang 0.45 m, building 10 m, spacing 0.6 m.

s = 3.6 m; rise = 3.6 × tan 25° = 1.679 m.
Top chord = 3.6 ÷ cos 25° = 3.972 m; with overhang = 3.972 + 0.45 ÷ 0.906 = 4.469 m; bottom chord 7.2 m.
Short web = √(0.6² + 0.839²) = 1.032 m; long web = √(1.2² + 1.679²) = 2.064 m; king post not used (—).
One truss = 2 × 4.469 + 7.2 + 2 × 1.032 + 2 × 2.064 = 22.33 m.
Trusses = ⌈10 ÷ 0.6⌉ + 1 = 18; total timber = 22.33 × 18 = 401.9 m; pitch 25°.

Each point is the calculator re-run with only “Pitch” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Pitch	Rise at the apex (m)
6.25	0.394
12.5	0.798
18.8	1.222
25	1.679
31.2	2.185
37.5	2.762
50	4.29

How to read the result

Lengths are along member centre lines and ignore joint details, so cut lengths differ slightly. Add bracing, gable-end framing and fixings, which are not included. The truss count includes one at each end of the building.

Common mistakes

Treating these centre-line lengths as cut lengths.
Using inside wall dimensions for the span.
Forgetting lateral and diagonal bracing between trusses.
Building trusses without an engineered design.

Keep in mind: Roof trusses must be designed by an engineer or truss manufacturer for your loads, timber grade and connectors, and installed to local building codes. This calculator is for estimating and learning only.

Frequently asked questions

How do I calculate truss top chord length?

Divide half the span by the cosine of the pitch, and add the overhang divided by the same cosine.

How many trusses for a 10 m building at 600 mm spacing?

18, including one at each end.

What is a Fink truss?

A truss with W-shaped webs from the third points of the bottom chord, common for houses.

Sources: D. Zwillinger (ed.), CRC Standard Mathematical Tables and Formulas, 33rd ed. (2018), Geometry

Checked 9 Nov 2026. Right-triangle trigonometry of the truss outline; Fink layout with web points at the third-points of the bottom chord and the mid-points of the top chords (lengths by the Pythagorean theorem): D. Zwillinger (ed.), CRC Standard Mathematical Tables and Formulas, 33rd ed. (2018), §4.

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