FabLayout

Square to round transition calculator

For a square or rectangular duct going into a round one: enter the width, depth, round diameter and height. You get the seam, the cut length and a one-piece flat pattern by triangulation.

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Square to round

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1,337.3 mm758.9 mm
Flat pattern: cut on the bold outline, bend on the dashed blue lines, the thin lines are marking lines

Seam

301.0mm

Approximate, within ±3.2 mm

Cut length
3,111.7 mm
Top edge (chords)
1,103.3 mm
Sheet size
1,337.3 × 758.9 mm

How to lay it out

  1. Divide the round end

    Divide each quarter of the circle into the number of sections you chose, and number the points from the seam all the way round.

  2. Work out the true lengths

    For every point, measure in plan from the nearest corner of the rectangle and combine that distance with the height: true length = √(plan distance² + H²).

  3. Draw the seam and the first corner

    Draw the seam line, then swing half of side A from its lower end and the first corner line from its upper end; where the arcs cross is the first corner.

  4. Swing the corner fan

    From the corner, swing each true length in turn and step one chord of the circle along it, so the points of the round edge fan out from the corner.

  5. Add the flat side and repeat

    Draw the next flat triangle with the full side as its base and the last fan line as one side, then swing the next corner fan. Work round all four corners.

  6. Close at the second seam

    Finish with the second half side and the second seam line. Run a smooth curve through the round-edge points, keep the rectangle edges straight and add your seam allowance.

Good to know

  • This pattern is approximate; the result card shows how close it is.
  • Source: Kidder, Triangulation (1917), Chapter II "A Simple Transitional Fitting from Square to Round", Fig. 12, p. 13; Kittredge, The New Metal Worker Pattern Book (1917), Problems 176–177, Figs. 566–568, pp. 327–328

Method and formula

A square to round is four flat triangles, one on each side of the rectangle, and four corner pieces that are parts of oblique cones with their apex at the rectangle's corners. Each flat triangle reaches the circle at the point where the circle's tangent is parallel to that side. Both unroll without stretching, so the fitting comes out of one sheet, seamed up the middle of an A side.

  • Seam line = √(H² + (B/2 − D/2)²), from the middle of an A side to the circle.
  • Corner lines = √(x² + y² + H²) from a corner to each division point, where x and y are the plan distances.
  • Chords: each quarter of the circle is split into n equal parts and drawn as straight chords.

The pattern is a strip of triangles from one seam edge to the other, each built from three true lengths. The flat sides are exact. The cone corners are drawn with chords, so the round edge comes out slightly shorter than πD: in thin sheet by at most π³D ÷ (96 n²). More sections close the gap. The diameter may be larger than the width or depth.

With sheet thickness and inside or outside dimensions, each opening is moved by one amount to the middle of the sheet. This is approximate: the calculator shows how far the opening can be off, and asks for middle-of-sheet dimensions if that is more than 1 mm.

Worked example

A = B = 400 mm, D = 300 mm, H = 250 mm, thin sheet, one section per quarter. Seam line √(250² + 50²) = 254.95 mm. Corner line from a corner to the tangent point in the middle of its side √(200² + 50² + 250²) = 324.04 mm. Each chord on the circle is 150√2 = 212.13 mm. The rectangle edge totals 1600 mm and the round edge 848.53 mm, so the cut length is 2448.53 mm.

One section per quarter is coarse on purpose: the round edge is 93.95 mm short of πD, inside the 96.89 mm bound. The default is six.

Questions

Does it work for rectangle to round?

Yes. Enter a different width and depth; a square is just A = B. The round end can also be larger than the width or depth. The sizes have to stay within 20:1 of each other, and the height must be at least a tenth of the largest size, which keeps the walls steeper than about 11°.

How is this different from round to square?

It is the same part turned upside down, and the flat pattern is identical. Use square to round when the rectangle is the bottom end you measure from, for example a hood or plenum outlet going up into a round pipe. Use round to square when the round duct is below and the rectangle on top. Only the order of the inputs and the 3D preview change.

Is the pattern exact?

The flat sides are exact. The cone corners are drawn with n straight chords per quarter, so the round edge is a little shorter than πD: in thin sheet by at most π³D ÷ (96 n²). Inside or outside dimensions with thickness are converted approximately, and the page shows by how much the opening can be off.

What does the Seam result show?

The total length of both seam edges. Each edge runs from the middle of an A side straight up to the circle and is √(H² + (B/2 − D/2)²) long. Both edges are the same length, so the pattern closes.

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