FabLayout

Rectangular pyramid hopper flat pattern calculator

A rectangular hopper or pyramid, pointed or cut off. Enter the base width and depth, the height and the top ratio; you get the four faces laid out as one piece.

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Enter your measurements

Your dimensions are measured to the

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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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686.4 mm538.3 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

531.5mm

Exact geometry

Edge length
In the app
Cut length
In the app
Sheet size
In the app

Every result is in Trueflat

The free web version shows the main result and the drawing. Trueflat gives you every mark and measurement, and exports a cut sheet. It is free to download.

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How to lay it out

  1. Find the true face heights

    Work out the slant height of the width faces, √(H² + (b − bk)²), and of the depth faces, √(H² + (a − ak)²), using half sizes a and b and the top ratio k.

  2. Draw the first face

    Draw a trapezoid with the full base width at the bottom, the top width k times that at the top, and the width-face slant height between them.

  3. Add the next face

    On the shared corner line, draw the depth face: base depth at the bottom, k times that at the top, depth-face slant height. Check the corner line against the edge length.

  4. Complete the four faces

    Repeat for the second width face and the second depth face. The last corner line is the seam.

  5. Mark the bends

    Mark the three inner corner lines as bend lines and add your seam allowance.

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 115, Figs. 433–434, and Problem 114, Figs. 430–432, p. 242

Method and formula

All four faces are flat, so the pattern is exact. It is laid out as one chain of faces joined along three bend lines, with the seam on the fourth corner.

  • Width faces (base A): slant height √(H² + (b(1 − k))²), with b = B ÷ 2.
  • Depth faces (base B): slant height √(H² + (a(1 − k))²), with a = A ÷ 2.
  • Corner edge √(H² + (a(1 − k))² + (b(1 − k))²).
  • Pointed pyramid (k = 0): a fan around the apex with radius √(H² + a² + b²).

With thickness, each face is moved to the middle of the sheet. The edge length and slant heights stay the same; the face widths change. A cut-off hopper can be measured inside, middle or outside; a pointed pyramid only to the middle of the sheet.

Worked example

Base 36 × 20 mm, height 12 mm, top ratio 0.5, thin sheet: width faces have a slant height of 13 mm, depth faces 15 mm, and the corner edge is √250 = 15.81 mm. Width faces run 36 to 18 mm, depth faces 20 to 10 mm. Total area 2 × (27 × 13 + 15 × 15) = 1152 mm². Measured inside with 2 mm sheet, the width faces become 38.5 mm at the bottom and 20.5 mm at the top.

Questions

What does the top / bottom ratio mean?

It is the size of the top opening as a fraction of the base. At 0.5 the top is half the base width and half the base depth. At 0 the pyramid comes to a point.

How is this different from the polygon pyramid?

Here the base is a rectangle, so the width and depth faces have different shapes and slant heights. The polygon pyramid has 3 to 16 identical faces. For a square base both pages give the same pattern.

Can the top be off-centre?

Not on this page: the top opening is centred over the base. An offset hopper needs a triangulated transition.

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