Roof Truss Calculator — Rafter Length & Pitch Geometry
Find the key dimensions of a roof truss — rafter length, peak rise, pitch angle and overhang rafter length — from the building span and pitch.
ft
/12
ft
Structural rafter from wall plate to ridge board, excluding overhang
- 1
Half span (run)
30 ÷ 2 = 15 - 2
Peak rise
(6 ÷ 12) × 15 = 7.5 - 3
Rafter length
√(15² + 7.5²) = 16.77Pythagorean theorem: √(run² + rise²) gives the sloped rafter from wall plate to ridge.
How does this calculator work?
Rafter length = √((span/2)² + rise²), where rise = (pitch/12) × (span/2). For a 30-ft span at 6/12 pitch, each side has a 15-ft run and 7.5-ft rise, giving a rafter of √(15²+7.5²) ≈ 16.77 ft. Add the overhang the same way.
Formula
How this is calculated
A common roof truss is a right triangle. One half of the building span forms the horizontal run (the base), the peak rise is the vertical height, and the rafter is the hypotenuse. Given the pitch as rise-per-12-inches-of-run (e.g. 6/12 means 6 inches up for every 12 inches across), the peak rise is (rise/12) × half-span. The rafter length from wall plate to ridge follows directly from the Pythagorean theorem: √(run² + rise²). The pitch angle in degrees is arctan(rise ÷ run).
The pitch factor sqrt(1 + (rise/12)²) relates the sloped rafter length to the horizontal run — it is also used when estimating roofing material, because it converts flat footprint area to true sloped area.
Eave overhang extends the rafter tail horizontally beyond the wall. The full rafter length (used for cutting lumber) adds the overhang run to the half span before applying the same Pythagorean formula. All results are in the same unit as the span input (feet here, but the formula works in any consistent unit). These are geometric dimensions; structural sizing (lumber species, grade, span tables) requires consultation with an engineer or local building code.
Frequently asked questions
A 6/12 pitch rises 6 inches for every 12 inches of horizontal run. So on a 30-foot span, the run per side is 15 feet (180 in), giving a peak rise of 6/12 × 180 = 90 in (7.5 ft). The resulting pitch angle is about 26.6°.
The pitch factor sqrt(1 + (rise/12)²) multiplies the flat footprint length to give true sloped length. It is used both to find rafter length and to convert plan-view roof area to actual roof surface area when ordering shingles.
No — the calculator gives the theoretical rafter length from the centre of the ridge. In practice you deduct half the ridge board thickness (usually ¾ in) from the rafter seat cut. For engineered trusses, the manufacturer's cut list accounts for this automatically.
Also known as
TG we-Calculate Editorial Team. (2026). Roof Truss Calculator — Rafter Length & Pitch Geometry [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/roof-truss-calculator
TG we-Calculate Editorial Team. "Roof Truss Calculator — Rafter Length & Pitch Geometry." TG we-Calculate. 2026. https://we-calculate.com/calculator/roof-truss-calculator.
TG we-Calculate Editorial Team, "Roof Truss Calculator — Rafter Length & Pitch Geometry," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/roof-truss-calculator
@misc{wecalculate_roof_truss_calculator, title = {Roof Truss Calculator — Rafter Length & Pitch Geometry}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/roof-truss-calculator}}, year = {2026}, note = {TG we-Calculate} }
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