FabLayout

Offset rectangular transition calculator

For a rectangular transition whose top is moved off centre: enter both rectangles, the height and the x and y offset of the top. You get an exact one-piece pattern with the seam on a corner.

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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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1,043.9 mm771.4 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

519.6mm

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.

App StoreGoogle Play

How to lay it out

  1. Place the top in plan

    Draw the bottom rectangle, then the top rectangle with its centre moved by X along the width and Y along the depth.

  2. Work out each corner line

    For each corner, take the plan offsets dx and dy between the bottom corner and the top corner above it: true length = √(dx² + dy² + H²).

  3. Lay out side by side

    Start from the seam corner and build each side as two triangles across a diagonal, using its edges and the true lengths.

  4. Close and mark the bends

    End on the seam corner line again, 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

The top rectangle stays parallel to the bottom one, but its centre is moved by X and Y. Each side is still a flat trapezoid. The four sides now lean by different amounts, so each corner line has its own true length. A side may also lean outward past the bottom edge; the layout does not change.

  • Runs: (A1 − A2)/2 − X and (A1 − A2)/2 + X for the two B sides, (B1 − B2)/2 − Y and (B1 − B2)/2 + Y for the two A sides.
  • Slant height of a side = √(H² + run²).
  • Corner line = √(dx² + dy² + H²) from the plan offsets between a bottom corner and the top corner above it.

The pattern is exact. With inside or outside dimensions, each side moves along its own plane by ½t × slant height ÷ H. Because the sides lean differently, the converted openings also move slightly sideways; the calculator handles this for you.

Worked example

Bottom 600 × 400 mm, top 300 × 200 mm, H = 250 mm, X = 100 mm, Y = −50 mm. The top corner over the seam corner is at (250, −150) against the bottom corner at (300, −200), so dx = 50 and dy = 50 mm. The seam line is √(50² + 50² + 250²) = 259.81 mm and both seam edges total 519.62 mm. The cut length stays 2(600 + 400) + 2(300 + 200) = 3000 mm.

Questions

How is this different from the rectangle to rectangle calculator?

With X = Y = 0 it gives the same pattern. Use this page when the top has to sit off centre, for example to line up with a duct that does not share the centre line of the bottom opening.

Which way do X and Y go?

X moves the top centre along the width (A) and Y along the depth (B), measured from the bottom centre. Negative values move it the other way. No side may run more than 10 × H horizontally.

Is the pattern exact?

Yes. The sides are flat trapezoids and every line is a true length. The conversion of inside or outside dimensions to the middle of the sheet is exact as well.

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