Square to round transition calculator

How to use it

1. Choose millimetres or inches. Enter the base width (left to right) and length (front to back), the round's diameter and the height.
2. If the round is not centred over the base, enter its offset: X to the right, Y to the back. The Flat buttons line the round up with one side of the base (a flat-bottom or flat-back transition); press two for a corner.
3. Say whether your sizes are to the inside, outside or centre of the metal, and enter the thickness.
4. Pick 1, 2 or 4 pieces and where the seams go (the middle of a side, or a corner), and add seam allowances, end allowances or fastener holes.
5. Check the plan and the preview. Corner letters A to D on the pattern match the plan. Then download the PDF and print it at 100% / Actual size (measure the rulers first), or the DXF or SVG.
6. Every setting is in the page address, so you can bookmark a transition or send the link to someone.

How the pattern is calculated

A square-to-round is made of four flat triangles, one on each side of the base, and four cone-shaped corner fans. Each triangle's point touches the round where the round's edge runs parallel to that side: its front-most point for the front side, and so on. That point does not depend on where the round sits, which is why the same method works for centred, offset, double-offset and flat-side transitions, and for a round wider than the base, where the hand method's arcs overshoot. Each corner fan joins a base corner to the quarter of the round between two of those points.

The flat pattern is built by laying the triangles and fan slices down one after another with their true lengths (the 3D distance between their ends), the same triangulation a sheet metal worker does with dividers. The calculator slices each fan finely, so the template's curved edge matches the round's circumference to within a few millionths. The number of divisions you choose only sets the bend lines and the rows of the mark-out table.

Worked example: a 400 × 300 mm base to a 250 mm round, 300 mm high, centred. The front and back triangles have a slant height of 301.0 mm (√(300² + (150 − 125)²)), the left and right ones 309.2 mm. From corner B, the true lengths to the six divisions of its quarter of the round run from 361.4 mm to 343.7 mm. The template's bottom edge is the whole 1,400 mm perimeter, and its curved edge is π × 250 = 785.4 mm long. The surface area is 0.3375 m².

The geometry is checked by automated tests against independent calculations: true lengths written out by hand, a separate 3D triangulation of the surface, and a check that the template shows the outside face rather than its mirror image.

For the hand method behind these numbers, with a worked square to round and its full true-length table, see how to lay out a square to round transition.

Offset, flat-side and round-bigger-than-base transitions

Offsets move the centre of the round relative to the centre of the base. A flat side, where one face of the transition is square to the base, has an offset of half the difference: for a flat right side, X = (W − D) ÷ 2. When the round is wider than a side of the base, that face leans outwards like a hood, and the pattern is still exact. Offset pieces are all different, so every piece is drawn and numbered.

Try some real cases people have asked about in comments on layout videos:

• 1600 × 650 base to a 1068 round, 1000 high (the round is wider than the 650 side)
• 100 × 100 square to a 200 round
• 16 × 12 in to a 10 in round, 18 in high
• 130 × 40 to a 90 fan outlet, flat on one side

Rectangle to rectangle (hoppers)

Choose Rectangle (hopper) for a top that is also a rectangle: a hopper, chute, plenum reducer or pyramid-frustum hood. Each side is then a flat trapezoid, developed exactly, and the offsets work the same way. The table gives each face's height and where its top edge starts.

Inside, outside or centre of the metal?

Metal keeps its length at mid-thickness when it bends, so the pattern is developed on the mean sizes: inside size + thickness, or outside size − thickness, for the base and the round alike. Offsets are between centres and do not change. For thick plate, make a trial piece: bends move the neutral axis a little.

Printing the full-size template

• The PDF tiles the pattern across as many pages as needed, with a map of the pages and 100 mm and 4 in calibration rulers on the first page.
• Print at 100%, "Actual size" or "No scaling", never "Fit to page", and measure the rulers before cutting.
• Trim each page along the grey border where it overlaps a neighbour, line up the circled cross marks, and tape.
• The template shows the outside face of the part. Blue dotted lines are bend lines; give each a light bend on the brake.

DXF, SVG and the mark-out table

• DXF (AutoCAD R12) in millimetres or inches, with layers CUT (outline), SEAM (seam lines when there is an allowance), MARK (bend lines, and finished edges when you add end allowances) and HOLES (fastener holes as true circles). Straight edges are single lines; the curved edge is a chain of short lines within 0.002 mm of the true curve.
• SVG at full size, with the same layers as groups, for Inkscape, Illustrator, laser and vinyl cutters.
• CSV: the true-length table, for marking out by hand or checking a layout.

Limitations

• The base and top are parallel. Pitched or inclined tops, rounded-corner rectangles and oval ends are not supported yet.
• The pattern is geometric: it does not add weld gaps, kerf or lock seams. Add those with the seam and end allowances, or in your CAD program.
• It is a layout aid, not a strength or pressure calculation. Check the first piece with a paper or thin-sheet test fit before cutting plate.

Frequently asked questions

What if the round is bigger than the square?

Enter it as it is. The triangles then lean outwards and the fans turn the other way round the corner, and the pattern stays exact.

Where should the seam go?

Usually up the middle of the shortest or flattest side, which keeps the seam straight and square to the base. Corner seams sit on a bend line. With 4 pieces there is a seam on every side (or corner).

Why are my offset pieces all different?

Moving the round changes every triangle and fan, so each piece has its own shape. All pieces are drawn and numbered.

Can I make an eccentric reducer here?

An eccentric (offset) cone between two rounds is in the cone flat pattern calculator: open "Eccentric (offset) cone".

Is anything I enter sent to a server?

The calculation, preview and files are all made in your browser. Your settings are kept in the page address so you can share them; see privacy for what the host and analytics receive.