Cone Development Calculator

Develop a cone or frustum into a flat cutting outline. Enter neutral-surface diameters and height, then download a dimensioned 1:1 SVG for your drawing workflow.

Neutral-surface inputs

Inputs are editable examples. Replace them with your job measurements and shop records.

Use zero for a full cone, or match the large diameter for a cylinder.

Diameters must refer to the neutral surface selected for your material and forming process. No seam, weld gap, thickness, or kerf allowance is added.

Developed pattern

Frustum annular sector

Slant length
6.3246 in
Developed area
119.2151 in²
Outer pattern radius
12.6491 in
Inner pattern radius
6.3246 in
Sector angle
113.842°
Pattern bounding size
21.1979 × 9.1972 in
Scaled neutral-surface flat pattern preview; join the two radial edges when forming a cone or frustum

Preview is scaled to fit. The downloaded SVG uses 1:1 physical millimeter dimensions. Join the two radial edges for a cone or frustum; for a cylinder, join the edges separated by the circumference. Add your own fabrication allowances.

  • Geometry is developed on the entered neutral surface. No sheet thickness, bend allowance, seam, kerf or forming correction is included.

Method

Use diameters at the neutral surface of the material, not automatically the finished inside or outside diameters. A small diameter of zero creates a full cone. Equal diameters create a cylinder and a rectangular pattern. For a frustum, the generator extends the sloping sides to an imaginary apex and develops the surface as an annular sector. Review the outline before importing it into CAD or CAM.

R = large diameter ÷ 2; r = small diameter ÷ 2; s = √[height² + (R − r)²]. For R > r: outer pattern radius = s × R ÷ (R − r); inner pattern radius = s × r ÷ (R − r). Sector angle (radians) = 2π × (R − r) ÷ s; developed area = π × (R + r) × s. For R = r: rectangular pattern width = π × diameter; height = entered height.

Worked example

For neutral-surface diameters of 8 in and 4 in and a height of 6 in, the slant length is about 6.3246 in. The flat pattern has outer radius 12.6491 in, inner radius 6.3246 in, and sector angle 113.8420°. Its developed surface area is about 119.2151 in². A full cone uses a zero small diameter; a cylinder uses equal diameters.

Limits

This tool develops centered, right circular cones and frustums only. It does not calculate square-to-round transitions, eccentric reducers, seam overlaps, weld gaps, flanges, thickness compensation, springback, or laser kerf. The SVG describes the entered neutral surface. Its physical dimensions are expressed in millimeters at 1:1 scale, but CAD import settings and printer scaling must still be checked.