How to use this cone pattern calculator
- Choose millimetres or inches, then enter the large end diameter, the small end diameter and the vertical height between the ends.
- Say whether your diameters are to the inside, outside or centre of the metal. For inside or outside, enter the material thickness so the pattern is developed on the mean diameter.
- Optionally add a seam allowance, split the pattern into several equal pieces, or add roll guide lines.
- Check the preview. The outer and inner radii, sweep angle and chord are shown on it.
- Download the PDF and print it at 100% / Actual size. Measure the 100 mm and 4 in rulers on the first page before cutting anything, then trim and tape the pages together using the registration marks.
- Or download the DXF (for CAD, plasma, laser or waterjet) or SVG (for vinyl and craft cutters, Inkscape or Illustrator).
How the flat pattern is calculated
The side of a right circular cone unrolls into a flat annular sector: the region between two arcs that share a centre (the cone's apex). With large-end radius R, small-end radius r and vertical height H:
Two quick checks: the outer arc length L × θ (in radians) equals the circumference of the large end, π × D, and L − ℓ equals the slant length. A full cone is the special case r = 0, so the inner radius is zero. When both diameters are equal the formulas break down, and the calculator switches to a cylinder, whose pattern is a rectangle π × D by H.
Worked example: D = 600 mm, d = 300 mm, H = 400 mm gives R − r = 150 mm, s = √(400² + 150²) = 427.2 mm, L = 427.2 × 300 ÷ 150 = 854.4 mm, ℓ = 427.2 mm and θ = 360° × 150 ÷ 427.2 = 126.40°.
The calculator's geometry is checked by automated tests against independent reference calculations, a published worked example, and a numerical model that unrolls a finely triangulated 3D cone.
Inside, outside or centre of the metal?
When plate is rolled, the outside stretches and the inside compresses. The mid-thickness keeps its length, so fabricators lay the pattern out on themean diameter: inside diameter + thickness, or outside diameter − thickness. Laying out thick plate from the inside diameter is a classic mistake: the finished cone comes out small.
This calculator applies that standard shop rule to both ends. It is exact for a cylinder. For a steep-sided cone rolled from thick plate, the diameter "at the edge" also depends on how you measure it and how the edge is cut, so the calculator warns you when that difference could exceed about 0.5 mm. For very thick plate relative to the diameter, the neutral axis moves towards the inside of the bend; allow for a trial roll.
Printing the full-size template
The PDF splits the pattern across as many pages as needed, with the page count shown before you download. The first page has instructions, the key dimensions, a map of the pages, and two calibration rulers (100 mm and 4 in). Every pattern page has its own 50 mm or 2 in check bar.
- Print at 100%, "Actual size" or "No scaling". Never use "Fit to page".
- Measure the ruler with a steel rule. If it is not exact, fix the printer setting before cutting.
- Adjacent pages overlap by 15 mm. Trim the margin along the grey border of each page's left and top edges where it overlaps a neighbour, lay it over that neighbour so the circled cross marks line up, and tape.
- Paper can stretch slightly with humidity. For large parts, check the chord and diagonal dimensions against the table before cutting metal.
DXF and SVG downloads
- DXF (AutoCAD R12 format, the most widely accepted): the arcs are true ARC entities and the edges are LINE entities, with no splines or approximations. Layers:
CUT(outline),SEAM(seam or lap line) andMARK(roll guide lines). Units are declared in the file (millimetres or inches, whichever you chose). The lower-left corner of the part is at the origin. - SVG: drawn at full size, with the width and height in mm or inches. The same three layers become groups. Text labels are off by default so the file can go straight to a cutter.
- Each file contains one piece. If you split the pattern, cut the stated number of identical pieces.
Seam allowance, pieces and roll lines
A seam allowance adds a strip of constant width parallel to the seam edge, ending on the extended arcs, for lap joints or grooved seams. The red dashed line marks the true edge. Pieces splits the development into equal segments. This is useful when the pattern is larger than your sheet or almost a full ring. Roll guide lines are straight elements of the cone, drawn at equal angles; keep them parallel to the rolls to avoid a twisted cone.
For a very shallow cone the pattern approaches a full circle. If a seam allowance would make a one-piece pattern overlap itself, the calculator says so and tells you how many pieces to use.
Limitations
- Right circular cones only: both ends are circles perpendicular to the same axis. Eccentric (offset) reducers and oblique cones are not supported yet. They need a triangulation layout, which will be a separate tool.
- The pattern is geometric. It does not include weld gaps, kerf, springback or allowances for flanges or joints beyond the seam strip.
- Always confirm critical dimensions before cutting expensive material.
Frequently asked questions
- What is the sweep angle?
- It is the angle of the flat pattern at the apex, the "slice" of a full circle the pattern occupies. It depends only on how steep the cone is: 360° × sin(half apex angle).
- Why is the pattern less than a full circle?
- A flat disc would need 360°. The steeper the cone, the smaller the sweep angle; a nearly flat cone approaches 360°.
- How do I make a pattern bigger than my printer paper?
- The PDF tiles it across as many sheets as needed. You can also split it into pieces, or use the chord-offset table to mark it out directly on the metal without swinging a huge radius.
- Can I share a pattern?
- Yes. The page address updates as you type, so bookmarking or sharing the link reopens the same dimensions.
- Is anything I enter sent to a server?
- No. The calculation, preview and file generation all run in your browser.