FabLayout

Round to square transition calculator

For a round duct below a square or rectangular one: enter the round diameter first, then the width, depth and height. Same flat pattern as square to round, measured from the round end.

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Round to square

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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 circle

    Split each quarter of the round end into the chosen number of sections, starting at the point that lines up with the middle of an A side.

  2. Take the true lengths

    For each division point, measure in plan to the nearest rectangle corner and combine that run with the height H to get the true length.

  3. Start at the seam

    Draw the seam line from the circle to the middle of an A side, then swing half of A and the first corner line to fix the first corner.

  4. Fan out from each corner

    Swing the true lengths from the corner and step the chords of the circle along them, then add the flat triangle that has the full side as its base.

  5. Close the pattern

    After the fourth corner, add the last half side and the second seam line, run a smooth curve through the round-end points and add your allowances.

Good to know

  • This pattern is approximate; the result card shows how close it is.
  • Source: Kidder, Triangulation (1917), Chapter II, Fig. 12, p. 13; Kittredge, The New Metal Worker Pattern Book (1917), Problems 176–177, pp. 327–328. Both books show the square to round direction; round to square is the same surface turned over

Method and formula

Round to square is the square to round fitting turned over: the round end is at the bottom and the rectangle on top. Turning a part over changes no true length, so the flat pattern is exactly the one a square to round with the same D, A, B and H gives. Four flat triangles stand on the sides of the rectangle, and four oblique cone pieces fan out from its corners to the circle.

  • Seam line = √(H² + (B/2 − D/2)²), from the circle to the middle of an A side.
  • Corner lines = √(x² + y² + H²) from each corner to each division point, x and y measured in plan.
  • The circle is drawn as n chords per quarter, so its edge in the pattern is shorter than πD by at most π³D ÷ (96 n²) in thin sheet.

With sheet thickness, inside means the face toward the inside of the duct at both ends, the same as on square to round. The conversion to the middle of the sheet is approximate; the page shows the deviation at the openings and asks for middle-of-sheet dimensions above 1 mm.

Worked example

D = 400 mm, A = B = 300 mm, H = 200 mm, thin sheet, two sections per quarter. The circle is larger than the square, which this fitting allows. Seam line √(200² + 50²) = 206.16 mm. The line from a corner to the tangent point in the middle of its side is √(150² + 50² + 200²) = 254.95 mm. The round edge in chords totals 1224.59 mm and the rectangle edge 1200 mm, so the cut length is 2424.59 mm.

Questions

What is the difference between round to square and square to round?

Only which end is at the bottom and which you enter first. Here the round end is below, for example a round fan outlet or round duct feeding a rectangular duct above it. The flat pattern is the same as a square to round with the same sizes, so if you already have one, you have the other. Pick the page that matches how the part sits and how you measured it.

Can the round end be bigger than the rectangle?

Yes. The worked example has a 400 mm circle under a 300 mm square. The sizes must stay within 20:1 of each other and the height must be at least a tenth of the largest size.

How accurate is the pattern?

The flat sides are exact. The cone corners are drawn with n chords per quarter, so the round edge is short of πD by at most π³D ÷ (96 n²) in thin sheet. Thickness conversion for inside or outside dimensions is approximate and the deviation is shown.

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