Cone / Frustum Configurator

A right circular frustum unrolls into an annular sector. Extending the cone to its apex gives the two development radii, and the included angle follows from requiring the developed arc to equal the true circumference of each end.

With large radius R1, small radius R2 and axial height H:

• Slant height L = √((R1 − R2)² + H²)
• Outer development radius Ro = R1 · L / (R1 − R2)
• Inner development radius Ri = R2 · L / (R1 − R2), so Ro − Ri = L
• Included angle θ = 2π (R1 − R2) / L
• Lateral surface area A = π (R1 + R2) L

Every calculation runs in millimetres internally and is converted on the way in and out, so millimetre and inch input produce identical geometry. A full cone is simply the case R2 = 0.

Dimension basis and thickness

With the basis on mid-surface, R1 and R2 above are your entered radii. Choose a finished face and they become neutral-layer radii instead, shifted by x = (t / 2) · cos(θw) where θw is the wall angle — added for an inside face, subtracted for an outside face.

Note what does not change: the developed angle θ depends only on (R1 − R2) / L, and both radii shift by the same amount, so the sector sweep is identical in all three bases. Ro − Ri also stays equal to the slant height. Only the radii move.

Press-brake faceting

A brake cannot bend continuously, so the cone is bump formed as N flat facets. Each facet keeps its apex angle δ = θ/N; intersecting the resulting pyramid with a unit sphere at the apex gives the bend angle:

• sin(γ) = sin(δ/2) / sin(Δ/2) where Δ = 360°/N
• cos(ψ) = tan(δ/2) / tan(γ)
• bend angle = 180° − 2ψ, the same for every line

Because the metal does not stretch, the facet polygon has exactly the developed perimeter — so it sits outside the nominal circle at each vertex and inside it at each facet midpoint. Both directions are reported as the out-of-round band.

What the DXF contains

A closed profile made of arcs and lines on layer CUT, written as DXF R12 (AC1009) for maximum compatibility. The CUT outline is identical for both forming methods. A seam allowance adds its strip to CUT and writes the original radial edge to BEND; press-brake mode adds short bend marks at each facet line, also on BEND, as separate geometry that never modifies the cut profile. The header records the units, and a comment records the generator version, dimension basis, thickness, forming method and material so an exported file can be traced back to exactly what produced it.