How the cone development works
Let the finished bottom and top radii be R and r, axial height be h, and slant height be s. The slant is s = √(h² + (R − r)²). When the diameters differ, the flat pattern is an annular sector with outer radius sR/(R − r), inner radius sr/(R − r), and sector angle 360°(R − r)/s. Those values make each developed arc exactly match its finished circumference.
A top diameter of zero collapses the inner arc to an apex. Equal diameters have no finite sector center, so the correct development is a rectangle: circumference by height. The calculator handles all three cases and keeps the optional seam tab outside the finished seam line.
Measure the shape consistently
Enter diameters and height for the same finished reference surface. For thin paper or sheet, outside dimensions may be adequate for a mock-up. With thicker material, rolling and forming happen around a neutral surface that depends on material, tooling, and process. Mixing outside diameters with a neutral-axis slant can create a systematic fit error.
Slant height is measured along the side, perpendicular to both circular edges—not diagonally around the shell. The station lines are generators along that same direction. Build a paper or inexpensive-material test before committing valuable stock.
Print and assemble accurately
The browser print uses CSS paged media with physical page dimensions, while the standalone SVG uses millimeter width and height. The W3C paged-media specification defines page-size control, but browser, PDF, driver, and printer settings can still rescale output. Match the selected paper/orientation, print at 100%, and measure the check line.
Align adjacent tiles with both registration crosses in their shared 10 mm region. Join the two theoretical seam edges after accounting for the selected tab and your fastening method. The tab is a simple straight allowance; it does not design rivet spacing, lock seams, hems, or weld preparation.
Cutting and fabrication safety
Cutting, grinding, brazing, and welding can create fire, fumes, fragments, noise, ultraviolet radiation, and burn hazards. Secure the work, remove or isolate combustibles and fuel sources, use guarded equipment, ensure ventilation and fire protection, and select PPE from a proper hazard assessment. OSHA’s hot-work guidance summarizes major hazards and controls.
Do not use this pattern alone for pressure vessels, structural parts, exhaust or fuel systems, guarding, or other safety-critical fabrication. Follow drawings, codes, material specifications, qualified procedures, and competent review.
Frequently asked questions
Is this a cone pattern calculator or a frustum calculator?
Both. Enter top diameter 0 for a full cone, a smaller positive top diameter for a frustum, or the same top and bottom diameter for a cylinder rectangle.
Does seam allowance change the cone diameter?
No. The orange dashed line is the finished seam. The allowance adds material beyond one edge for overlap; it is not included in either circumference.
Should I enter vertical height or side length?
Select whichever you measured. Axial height is parallel to the centerline. Slant height follows the straight side from one circular edge to the other. The calculator solves the remaining height.
Does this include sheet-metal thickness or bend allowance?
No. It develops an ideal reference surface. Thick stock may require neutral-axis dimensions and process-specific compensation established from tooling data or trials.
Why does my nearly cylindrical cone have a very large pattern radius?
A slight taper develops as a narrow sector of a very large circle. That is mathematically expected. The exported drawing is cropped to the actual cut outline, so the distant theoretical center is not included.
How can I verify the result?
Check that outer pattern radius × sector angle in radians equals the bottom circumference, and likewise for the top. On paper, measure the 100 mm scale and both developed arcs before cutting stock.
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