About this calculator
This calculator helps compute a rafter's length and cut angles from the span, roof pitch, and overhang length — useful for roof-framing planning before cutting timber. The calculator is purely geometric: it computes the rafter's dimensions and cut angles, not its load-bearing capacity or cross-section size.
Formula
The calculator converts the span, overhang, ridge board thickness, and birdsmouth depth to whole units, then:
run (horizontal projection) = (span − ridge thickness) / 2
rise (vertical) = run × tan(pitch)
common rafter length = run / cos(pitch)
total rafter length (incl. overhang) = (run + overhang) / cos(pitch)
overhang tail cut length = total length − common rafter length
plumb cut angle (at the ridge) = pitch
seat cut angle (at the wall plate) = 90° − pitch
The run is measured from the ridge's own theoretical centreline (span/2), pulled back by half the ridge board's own thickness — so the rafter's plumb cut rests against the ridge board's face, not the building's own centreline. Rafter length is measured along the top edge (the way rafter tables or a framing square would measure it), not the board's own centreline — there is no rafter width or thickness input, so there is nothing to compute a centreline offset from. The birdsmouth depth is not part of these formulas at all — it only affects the rafter's bottom edge and is shown only in the drawing, as an illustration, not as a calculation variable.
Worked example
Defaults: span 6 m, pitch 30°, overhang 450 mm, ridge thickness 38 mm, birdsmouth depth 38 mm.
run = (6000 mm − 38 mm) / 2 = 2981 mm
rise = 2981 mm × tan(30°) = 2981 × 0.57735... ≈ 1721.08 mm
common rafter length = 2981 mm / cos(30°) = 2981 / 0.86603... ≈ 3442.16 mm
total rafter length (incl. overhang) = (2981 + 450) mm / cos(30°) = 3431 / 0.86603... ≈ 3961.78 mm
overhang tail cut length = 3961.78 − 3442.16 ≈ 519.62 mm
plumb cut angle = 30°
seat cut angle = 90° − 30° = 60°
For these inputs the calculator returns exactly this: run 2981 mm, rise ≈1721.08 mm, common rafter length ≈3442.16 mm, total rafter length (incl. overhang) ≈3961.78 mm, overhang cut length ≈519.62 mm, plumb cut angle 30°, and seat cut angle 60°.
FAQ
Why is rafter length measured along the top edge, not the centreline? Because the calculator has no rafter width or thickness input from which a centreline offset could be computed — top-edge length is what rafter tables and a framing square use, so it was chosen as the standard convention.
Does the birdsmouth depth change the rafter length calculation? No. The birdsmouth only removes material from the rafter's bottom edge, and every length this calculator computes is measured along the top edge, which the birdsmouth doesn't touch. This dimension is used only in the drawing, as an illustration.
Why does the calculator warn about a low pitch? When the pitch is below about 18.43° (a 4:12 ratio) — a general guideline, not a specific standard's requirement — a warning is shown, because the minimum allowed pitch for a specific roofing material depends on the chosen material, which this purely geometric calculator does not evaluate.
Does the calculator check whether the rafter can carry the load? No. It computes only geometry — length and cut angles. Determining load-bearing capacity and cross-section size depends on Eurocode 5's national annexes and is separate work, outside this calculator's scope.
What's shown in the 3D view, if the calculator doesn't know the rafter's cross-section? The 3D model uses a fixed, illustrative cross-section (184×38 mm, matching a nominal "2×8" sawn profile) — this is not a value you entered, it was chosen only so the 3D view has a realistic thickness.
Assumptions and limits
This calculator is purely geometric — no standard was found for rafter length or cut-angle
calculation, since it's plain trigonometry, not an engineering calculation. Load-bearing
capacity and cross-section sizing depend on Eurocode 5's national annexes and are outside
this calculator's scope, so meta.standards is deliberately left empty.
The low-pitch warning threshold (~18.43°, a 4:12 ratio) is a general guideline, not a specific roofing material's requirement — the minimum allowed pitch depends on the chosen roofing material, which this calculator has no input for.
The birdsmouth depth doesn't affect any length or angle calculation — it only affects the rafter's bottom edge and is shown in the drawing as a schematic illustration (a small notched cut), not an exact cut profile. The 3D model's rafter cross-section (184×38 mm) is a fixed illustrative constant, not a dimension derived from input — the calculator has no rafter width or thickness input field.