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The longer side of the rectangle at the wide end.
Both ends are treated as rectangles centred on the same axis. If your transition is square, enter the same figure for both sides of that end — a square is a rectangle and the arithmetic does not change.
The shorter side of the rectangle at the wide end.
Measured across the same end as the long side, at right angles to it. The two sides taper independently, which is why the finished pattern has two different face heights rather than one.
The longer side of the rectangle at the narrow end.
Entering zero for both top sides gives a full pyramid closing to a point, which is a valid shape and develops to four triangles rather than four trapezoids.
The shorter side of the rectangle at the narrow end.
The narrow end does not have to keep the wide end's proportions. A transition from a wide flat duct to a nearly square one is ordinary, and it simply gives the two pairs of faces very different heights.
The straight-up height between the two ends, not the sloping face.
Measured along the axis, square to both ends. The sloping distances are what this page works out — entering one of them here instead produces a pattern that is short on every face at once.
Corner edge true length
21.32 in
Right truncated pyramid assumed: both ends rectangular, parallel to each other, and centred on a common axis. The pattern is exact for that case.
- Face height, long sides
- 20.42 in
- Face height, short sides
- 20.92 in
- Blank length along the base
- 80 in
- Top perimeter
- 39 in
They open the calculator with your figures already in it
Truncated Pyramid Flat Pattern Calculator: 21.32 in — 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)
- Corner edge true length = √(h² + ((A − a)/2)² + ((B − b)/2)²) for a right truncated pyramid centred on its axis
- Face true height = √(h² + (half the taper measured ACROSS that face)²); the two pairs of faces therefore have different heights whenever the two tapers differ
- Blank length along the base = the bottom perimeter, 2 × (A + B), the four trapezoids laid edge to edge
Inputs used
- Bottom, Long Side
- 24 in
- Bottom, Short Side
- 16 in
- Top, Long Side
- 11.75 in
- Top, Short Side
- 7.75 in
- Vertical Height
- 20 in
Intermediate steps
- Face height, long sides
- 20.42 in
- Face height, short sides
- 20.92 in
- Blank length along the base
- 80 in
- Top perimeter
- 39 in
Confidence note: Right truncated pyramid assumed: both ends rectangular, parallel to each other, and centred on a common axis. The pattern is exact for that case.
What this calculation does not cover
- No bend allowance is in any of these figures, and a folded transition needs one at every corner. Metal does not fold on a line — it wraps a radius, and the material taken up by that wrap has to come off the flat pattern or the finished piece comes out oversize by four deductions at once. That allowance depends on the thickness, the radius and the tooling, which is a property of the press rather than of the shape, so it is applied to this pattern rather than computed in it.
- No seam or lock is included either. These four trapezoids are the developed faces and nothing else, so whatever closes the last corner — a grooved seam, a riveted lap, a welded butt — is added afterwards, along the edge the joint runs down rather than all the way round.
- This is a RIGHT transition, centred on its axis. An offset one, where the narrow end sits to one side, has four DIFFERENT corner edges and four different face heights, and none of them can be read from a single figure. Those are set out point by point from a true-length diagram, and using this pattern for one produces a piece that will not close.
Add the equipment this sizes
This result is a specification — 21.32 in — not a quantity. Put the thing it sizes into your project: how many, what you call it, and your supplier’s price.
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
- Corner edge true length = √(h² + ((A − a)/2)² + ((B − b)/2)²) for a right truncated pyramid centred on its axis
- Face true height = √(h² + (half the taper measured ACROSS that face)²); the two pairs of faces therefore have different heights whenever the two tapers differ
- Blank length along the base = the bottom perimeter, 2 × (A + B), the four trapezoids laid edge to edge
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