FabLayout

Truncated cone flat pattern calculator

For a concentric reducer or hopper: enter the large diameter, the small diameter and the height. You get both pattern radii, the sector angle and a scale drawing.

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Enter your measurements

Your dimensions are measured to the

Truncated cone

Pinch or scroll to zoom, drag to move. Double-tap to fit.

Export from the Trueflat app

1:1 PDF and DXF files of this flat pattern are made in Trueflat, ready for print, plasma, laser or waterjet. It works offline on site.

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914.2 mm522.4 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Outer pattern radius

522.8mm

Exact geometry

Inner pattern radius
197.8 mm
Sector angle
138.46°
Seam
650.0 mm
Slant length
325.0 mm
Cut length
1,740.8 mm
Sheet size
914.2 × 522.4 mm

How to lay it out

  1. Swing the outer arc

    Set your trammel to the outer pattern radius and draw an arc from a centre point.

  2. Swing the inner arc

    From the same centre, draw a second arc at the inner pattern radius.

  3. Mark the sector angle

    Draw a radius line through both arcs, then measure the sector angle from it, or step the large circumference off along the outer arc.

  4. Close the pattern

    Draw the second radius line between the arcs. Add your seam allowance before you cut.

Good to know

  • FabLayout runs the same code as Trueflat; the result is exact geometry.
  • Source: Kittredge, The New Metal Worker Pattern Book (1917), Problem 123, pp. 250–251; Daugherty, Sheet-Metal Pattern Drafting (1922), Problem 43, p. 66

Method and formula

A truncated cone (frustum) unrolls into a ring segment between two arcs drawn from the apex of the full cone.

  • Slant length s = √((R − r)² + H²), where R and r are the large and small radii.
  • Outer pattern radius L₁ = s × R ÷ (R − r).
  • Inner pattern radius L₂ = s × r ÷ (R − r) = L₁ − s.
  • Sector angle φ = 360° × (R − r) ÷ s.

With sheet thickness, both radii are taken to the middle of the sheet; the sector angle does not change.

Worked example

Large diameter 60 mm, small 30 mm, height 20 mm: R − r = 15, s = √(15² + 20²) = 25, L₁ = 25 × 30 ÷ 15 = 50 mm, L₂ = 25 mm, φ = 360° × 15 ÷ 25 = 216°.

When the two diameters are almost equal the apex is very far away and the arcs need a long trammel. Then the triangulation method, which Trueflat also offers, is easier to lay out by hand.

Questions

Is a reducer the same shape as a truncated cone?

A concentric reducer is. If the small end is off-centre, it is an eccentric reducer, which needs a different pattern.

Why is my outer radius so large?

The radius goes back to the apex of the full cone. When the large and small diameters are close, the apex is far away and the radius grows quickly.

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