Rectangular Transition flat pattern

What it is

The pyramid frustum: the reducer between two rectangular openings, on the same axis. It is the only transition in this catalogue that is not triangulated, and does not need to be — each of the four faces has its bottom edge parallel to its top one, so the face is a flat trapezoid and its pattern is the face itself, with no approximation.

Where it is used

Reducers in exhaust and air-conditioning ductwork, hoppers and silo outlets, feed chutes, transitions between rectangular-section equipment.

Measurements the calculation needs

• X Measurement X
• Y Measurement Y
• X2 Top X
• Y2 Top Y
• H Height
• THK Thickness

Worked example

The values the form comes pre-filled with, run through the tool itself:

Measurement X	800 mm
Measurement Y	600 mm
Top X	400 mm
Top Y	300 mm
Height	500 mm
Thickness	3 mm
The flat pattern fits a plate of	1680 × 1509 mm

Frequently asked questions

Why is this part not triangulated like the rectangle-to-round?

Because all four faces are flat. Two parallel lines always lie in one plane, and here the bottom edge of each face is parallel to its top edge — so there is no curved surface to approximate with triangles. On the rectangle-to-round one opening is a circle, and then no face is flat at all.

Is the slant height the same on all four faces?

No, and that is exactly where marking out from memory goes wrong. The face with X at the bottom steps back (Y − Y2)/2 and the face with Y steps back (X − X2)/2, so each pair has its own slant height. They only coincide when the reduction is equal in both directions.

Can the top opening be larger than the bottom one?

Yes, and in one direction only if you like — widening in X while narrowing in Y is routine in ductwork. The calculation does not distinguish a reducer from an expander.

What if both openings are the same?

You get a straight rectangular tube, and the pattern is a plain rectangle of perimeter by height. That is a real part, not a degenerate case, and the calculation accepts it.