Square to Round Transition Calculator

Inputs

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Width of the rectangular or square opening.
in
Height of the rectangular or square opening.
in
Finished round opening diameter.
in
Straight distance between the rectangular and round planes.
in
Horizontal offset of the round center from the rectangular center. Positive X moves toward the right side.
in
Vertical offset of the round center from the rectangular center. Positive Y moves toward the top side.
in
Number of equal stations around the round end and rectangular perimeter.
stations
Perimeter station zero starts at this side midpoint.
Simple extra strip width added to the average true length for blank area.
in
Sheet thickness used for shell mass only.
in
Material density for shell mass estimate.
lb/ft³

Results

Default result
Edit inputs
Blank area with seam(Ablank)
733.1in²
Pass

Developed station-strip area plus simple seam allowance.

Also computed

Max true length(Lmax)Pass13.297in

Longest station line from rectangle perimeter to round end.

Average true length(Lavg)12.534in

Min true length(Lmin)12.166in

Max station skew angle(alpha)Pass25.52°

atan(max plan offset / transition height).

Perimeter mismatch(DeltaP/P)Caution−38.9%

Positive means the round circumference is larger than the rectangular perimeter.

Rectangle perimeter(Prect)72in

True length vs StationTrue length from each rectangular perimeter station to the matching round station.True length vs Station0510150102030StationTrue length (in)
True length from each rectangular perimeter station to the matching round station.
Square to round transition triangulation previewSquare-to-round transition previewPlan stations map the rectangular perimeter to equal stations around the round end.Rectangle perimeter72.00 inRound circumference43.98 inStations24Max true length13.30 inBlank area with seam733.1 in2Developed true-length strip previewUse the station list as a layout worksheet; verify production patterns with shop practice or CAD.
Method notes 3 notes
  • Rectangle stations are spaced equally along the rectangular perimeter; round stations are spaced equally by angle around the round circumference.
  • Each true length is sqrt(transition height^2 + plan offset^2). Pattern area is a station-strip approximation using the average rectangle/round station pitch.
  • This is a triangulation worksheet for layout and takeoff. Thickness compensation, seams, locks, hems, stretch, notching, fitting losses and shop-specific fabrication allowances are not included.

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