Square/Rectangle to Round Transition Developer

How to use it: enter the base rectangle's width and depth, the round top's diameter, and the vertical height between the two planes. Leave the offset fields at 0 for a concentric (centered) transition, or set them for an eccentric transition where the round top sits off to one side. The diagram shows the flat pattern for all 4 side panels, laid out separately.

Method: triangulation. A square/rectangle-to-round transition is not a simple cone, so it can't be developed with the cone formula. Instead each side is divided into small flat triangular facets that approximate the curved surface above it - the standard sheet-metal "triangulation" or "radial line" layout method. Each side panel spans from one base corner to the next, fanning out to the corresponding quarter-arc of the round top. At each step, the calculator picks whichever of the two possible next triangles has the shorter diagonal, which keeps the developed pattern as close as possible to the true curved surface. Every triangle is then placed in 2D using its real (true) edge lengths, computed in 3D - not projected lengths - so the printed pattern folds up into the correct 3D shape.

Why 4 separate panels, not one continuous pattern. This surface is only approximately developable (unlike a true cone), so unrolling all 4 sides as one continuous strip back to the start accumulates a small closing error. Developing each side independently avoids that entirely and matches how many fabrication references present transition patterns - as 4 (or 2, using symmetry) separate face templates to cut and join at the seams.

The result above uses these exact values. This snapshot is included when the page is printed so the output can be checked against the original measurements.

Base width

300 mm

Base depth

200 mm

Round top diameter

200 mm

Vertical height

350 mm

Round top offset (X)

0 mm

Round top offset (Y)

0 mm

Development lines per side

4

Primary result: Base perimeter: 1000.0 mm.

• Measure from the datum or reference edge described by this tool, and do not mix inside, outside and centerline dimensions.
• Keep inputs in the displayed units and preserve more precision than the final cutting or purchasing tolerance requires.
• When the result is close to a limit, verify it with a test piece, field measurement, manufacturer drawing or qualified project professional.

This is a triangulated approximation of the true surface, not an exact analytical development; standard practice for square/rectangle-to-round transitions, since (unlike a cone) they are not exactly developable. More development lines per side reduce the approximation error.

The pattern is the bare developed geometry only - it does not add seam allowance, hem, or lap. Add those separately, on the outside of the printed outline, before cutting.

Height is the vertical (axial) distance between the base and round-top planes, not a slant length. Offsets must keep the round top reasonably within the base footprint; extreme offsets can produce a self-intersecting (unbuildable) transition that this tool does not detect.