FabLayout

Rectangle to rectangle transition calculator

For a centred rectangular reducer or hopper with flat sides: enter the bottom and top rectangles and the height. You get an exact one-piece pattern of four trapezoids, seam on a corner.

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Enter your measurements

Your dimensions are measured to the

Export from the Trueflat app

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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1,224.4 mm746.5 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

616.4mm

Exact geometry

Cut length
In the app
Top edge (chords)
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. Work out the corner line

    Find the true length of a corner line: √(((A1 − A2)/2)² + ((B1 − B2)/2)² + H²).

  2. Draw the first side

    Draw the corner line as the seam, then lay out the first side as two triangles across a diagonal, using its bottom edge, top edge and true lengths.

  3. Add the other sides

    Add the next three sides the same way, each one sharing a corner line with the side before it.

  4. Close and mark the bends

    The last corner line is the second seam edge. 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: No published source checked for this shape. Method: each side is a plane trapezoid between the two openings, laid out exactly from true lengths; checked against a separate reference implementation in Trueflat.

Method and formula

When both rectangles are centred and parallel, every side of the transition is a flat trapezoid with its top edge parallel to its bottom edge. The four trapezoids unfold into one exact pattern with the seam on a corner. Nothing is drawn with chords, so there is no approximation.

  • Slant height of a side = √(H² + run²). The run is (B1 − B2)/2 for the A sides and (A1 − A2)/2 for the B sides.
  • Corner line = √(((A1 − A2)/2)² + ((B1 − B2)/2)² + H²).
  • Cut length = 2(A1 + B1) + 2(A2 + B2).

With inside or outside dimensions, each side is moved along its own plane by half the sheet thickness. That converts the sizes to the middle of the sheet exactly: each face moves by ½t × slant height ÷ H, outward for inside dimensions and inward for outside ones.

Worked example

Bottom 400 × 400 mm, top 200 × 200 mm, H = 300 mm. Every side is a trapezoid with slant height √(300² + 100²) = 316.23 mm, so the area is 4 × 300 × 316.23 = 379 473 mm². The corner line is √(100² + 100² + 300²) = 331.66 mm, the two seam edges total 663.32 mm and the cut length is 2400 mm.

With thickness: inside 600 × 400 and 300 × 200 mm, H = 250 mm, t = 4 mm become 604.66 × 404.31 and 304.66 × 204.31 mm at the middle of the sheet.

Questions

When do I need the offset or twisted version?

Use this page when the top rectangle sits centred over the bottom one with its sides parallel. If the top is moved sideways, use the offset rectangular transition. If the top is turned relative to the bottom, use the twisted transition.

Is the pattern exact?

Yes. All four sides are flat, every line in the pattern is a true length and nothing is drawn with chords. The conversion of inside or outside dimensions to the middle of the sheet is exact too.

Can the top be larger than the bottom?

Yes. The two rectangles just have to stay within 20:1 of each other, and the height must be at least a tenth of the largest size.

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