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The diameter across the wider of the two open ends.
Measure across the widest point of the open end, through the centre. Whether that measurement is taken over the outside of the sheet, inside it, or at mid-thickness is asked separately, because for thin material it barely matters and for thick material it is the difference between a seam that closes and one that does not.
The diameter across the narrower open end. Zero for a full cone with a point.
A full cone is a frustum whose small end has closed to nothing, so entering zero here is valid and gives a complete sector rather than a ring. The closer the two diameters get to each other, the flatter the taper and the larger the pattern radii become — at equal diameters the shape is a cylinder and no longer develops as a sector at all.
The straight-up height between the two ends — not the sloping face.
This is the axial height, measured along the centreline, not the distance up the sloping side. The sloping distance is the slant height and the calculator works it out; entering it here instead is the commonest way to get a pattern that is slightly too small.
The thickness of the sheet being rolled.
Used only to find the neutral surface when the diameters are given over the outside or inside of the sheet. It moves the pattern RADII and leaves the included angle alone, because shifting both ends by the same amount does not change the taper between them. Enter zero to develop on the diameters exactly as given, which is what a drawing dimensioned to the mean already does.
Which surface the two diameters were taken over.
A rolled cone develops on its neutral surface, which for practical purposes is mid-thickness. Diameters taken over the outside are therefore reduced by one thickness before developing, and inside diameters increased by one, so that the pattern rolls up to the size actually wanted.
Pattern included angle
128.7 °
Right cone assumed: the axis is square to both ends and the two ends are parallel. The pattern is exact for that case.
- Outer radius
- 33.5 in
- Inner radius
- 16.37 in
- Slant height
- 17.13 in
- Arc length, large end
- 75.25 in
- Blank width needed
- 67 in
They open the calculator with your figures already in it
Cone and Frustum Flat Pattern Development Calculator: 129 ° — shown in imperial, US market. The link sets both, so the result they see is the one on your screen.
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How this was calculated
Formula source(s)
- Slant height of the frustum = √(h² + ((D − d)/2)²), where h is the vertical height between the two ends
- Pattern included angle = 180 × (D − d) / L degrees; outer radius = D × L / (D − d); inner radius = outer radius − L
- The pattern develops on the neutral surface — the mean diameter at mid-thickness — because that is the fibre that neither stretches nor compresses as the sheet is rolled
Inputs used
- Large End Diameter
- 24 in
- Small End Diameter
- 11.75 in
- Vertical Height
- 16 in
- Material Thickness
- 0.05 in
- Diameters Measured
- Over the outside of the sheet
Intermediate steps
- Outer radius
- 33.5 in
- Inner radius
- 16.37 in
- Slant height
- 17.13 in
- Arc length, large end
- 75.25 in
- Blank width needed
- 67 in
Confidence note: Right cone assumed: the axis is square to both ends and the two ends are parallel. The pattern is exact for that case.
What this calculation does not cover
- A development assumes the sheet bends without stretching, and rolling stretches the outer fibre while compressing the inner one. Developing on the neutral surface is what keeps that from accumulating, which is why the thickness and the surface the diameters were taken over are asked for at all — on thin sheet the difference is smaller than the marking out, and on heavy plate it is the difference between a seam that closes and one that has to be cut and re-rolled.
- No seam, lap, lock or edge allowance is in any of these figures. They are the developed shape and nothing else, so whatever the joint needs — a grooved seam, a riveted lap, a welded butt with a root gap — is added to the pattern afterwards, and it is added in the direction the joint runs rather than all round.
- This is a RIGHT cone: the axis stands square to both ends and the two ends are parallel to each other. An oblique cone, or a frustum cut at an angle to make a transition, does not develop to a simple sector and cannot be marked out from one radius and one angle — those are set out point by point from a true-length diagram.
Computed in your browser — nothing you enter is uploaded. Presented in US customary units and US trade terminology. Where a formula follows a published standard, that standard and its edition are cited beside it on this page; where none governs, the page says so. Local amendments override model codes — verify against the code in force where you build.
Sources checked 2026-09-24 · v1.0.0
Regulatory standards & verification citations3
- Slant height of the frustum = √(h² + ((D − d)/2)²), where h is the vertical height between the two ends
- Pattern included angle = 180 × (D − d) / L degrees; outer radius = D × L / (D − d); inner radius = outer radius − L
- The pattern develops on the neutral surface — the mean diameter at mid-thickness — because that is the fibre that neither stretches nor compresses as the sheet is rolled
Cite this page
Your workspace
Most jobs need more than one number. Add the calculators you need next and they open right here, underneath this one — your figures stay on screen and nothing is lost to a page change.
Full-size cone pattern
Print the pattern to cut round, the whole of it or one of two halves: both arcs, the lap for the seam and the rolling lines, with the corner-to-corner checks that stand in for an apex no trammel can reach, and a calibration square on every sheet.