Fabrication tool
Cone Layout Generator
Create an exact flat pattern for a cone, reducer, diffuser or baffle section. Large patterns are automatically divided across numbered print pages with overlap and alignment marks.
Input
Cone dimensions
Dynamic drawing
FrustumFlat-pattern preview
Solid line: cut edge · dashed line: seam fold · numbered rectangles: print tiles · shaded strips: page overlap.
Calculated layout
Pattern dimensions
A4 portraitOne page
Print at 100% / Actual size. Disable “Fit to page”, browser headers and footers. Measure the 50 mm calibration line before cutting material.
Development method
Cone-layout formulas
A truncated cone becomes an annular sector when flattened. The generator calculates the true slant length, extends both cone sides to a virtual apex, and uses the required end circumferences to determine the sector angle.
1. End radii
r₁ = D₁ ÷ 2 · r₂ = D₂ ÷ 2
D₁ is the small-end diameter and D₂ is the large-end diameter. Enter finished internal diameters unless your fabrication method requires a neutral-line correction.
2. True slant height
s = √(h² + (r₂ − r₁)²)
The axial length h is not the flat-pattern width. The slant height s is the true material distance between the two circular edges.
3. Pattern radii
R₂ = s × r₂ ÷ (r₂ − r₁)
R₁ = s × r₁ ÷ (r₂ − r₁)
R₂ and R₁ are measured from the virtual apex to the large and small arcs of the flat pattern.
4. Sector angle
θ = 360° × (r₂ − r₁) ÷ s
The outer arc then equals 2πr₂ and the inner arc equals 2πr₁, preserving the exact finished circumferences.
5. Seam allowance
Cut edge = radial edge + selected tab
The allowance is added outside one radial edge. The original radial edge remains as a dashed fold or overlap line, so the calculated cone geometry is not enlarged.
6. Tiled pages
Step = printable area − overlap
If the pattern exceeds one sheet, the drawing continues on subsequent pages. Matching crosses, row/column labels and overlap bands show how the remaining parts align.
Fabrication questions
Cone layout FAQ
Will the printout be true size?
The generated SVG pages use physical millimetre dimensions and a zero-margin page definition. Select Actual size or 100% in the print dialog, disable Fit to page, and verify the supplied 50 mm calibration line before using the pattern.
What happens when the pattern is larger than the page?
The generator creates as many numbered row-and-column tiles as required. Adjacent sheets repeat the selected overlap area and include crosshair marks plus continuation labels for assembly.
Should I enter inside, outside or neutral diameters?
For thin exhaust sheet, fabricators commonly begin with finished internal diameters. For thick material or precision work, calculate the neutral-line diameter appropriate to the forming process before entering values.
What is axial length?
Axial length is the straight distance from the small-end plane to the large-end plane along the cone centreline. It is not the sloping side length.
Can this generate a full cone with a pointed apex?
Yes. Set the small-end diameter to zero. The inner pattern radius becomes zero and the development closes at the virtual apex.
What if both diameters are equal?
The shape is a cylinder rather than a cone. The generator automatically produces a rectangular wrap whose width is π times the diameter and whose height is the axial length.
How much page overlap should I use?
Eight to twelve millimetres works well for most office printing. Use a larger overlap when alignment is difficult, but remember that more overlap can increase page count.
Does the seam allowance change the finished cone size?
No. The allowance is a separate tab outside the calculated pattern. Fold or overlap at the dashed seam line to preserve the required geometry.
How should I transfer the tiled pattern to metal?
Verify scale, trim only the indicated page edges, align matching crosshairs, tape the sheets without stretching them, then transfer the assembled outline and fold line to the sheet.