FabLayout

Cone flat pattern calculator

Enter the base diameter and height of a cone. You get the pattern radius, the sector angle and a scale drawing to mark out on the sheet.

Get TrueflatRead the steps

Enter your measurements

Your dimensions are measured to the

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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685.6 mm430.2 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Pattern radius

430.2mm

Exact geometry

Sector angle
126.40°
Seam
860.5 mm
Arc length
949.2 mm
Sheet size
685.6 × 430.2 mm

How to lay it out

  1. Swing the arc

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

  2. Draw the first seam line

    Draw a straight line from the centre through the arc.

  3. Mark the sector angle

    Measure the sector angle from the first line with a protractor, or step the arc length off along the arc.

  4. Draw the second seam line and add the allowance

    Join the end of the arc to the centre. Add your lap or lock allowance outside both seam lines 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 122, pp. 249–250; Daugherty, Sheet-Metal Pattern Drafting (1922), Problem 43, p. 66

Method and formula

The side of a right cone unrolls into a circular sector. Every point keeps its distance from the apex, and the base circle keeps its length along the arc.

  • Slant length L = √(r² + H²), where r is half the base diameter.
  • Sector angle φ = 360° × r ÷ L.
  • Arc length = π × D, the circumference of the base.

With sheet thickness, the pattern is developed on the middle of the sheet (the neutral line). If your diameter is measured inside, the neutral radius is r + ½t ÷ cos β; the sector angle does not change, because it depends only on the cone's shape.

Worked example

D = 60 mm, H = 40 mm, thin sheet: r = 30, L = √(900 + 1600) = 50 mm, φ = 360° × 30 ÷ 50 = 216°. The arc is 2π × 30 = 188.5 mm long.

Questions

Why does the sector angle stay the same when I change the sheet thickness?

Thickness moves the pattern radius and the arc in proportion. The sector angle is 360° × sin of the half-apex angle, which depends only on the cone's shape.

What do inside, middle and outside mean?

They say which surface your diameter and height are measured to. The pattern is always developed on the middle of the sheet, so the formed part matches the surface you measured.

What are curve samples?

The number of straight segments the drawing uses along the arc. They affect the drawing and the cut length, not the pattern radius or the sector angle.

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