What this template calculates
The branch is treated as a perfect circular cylinder whose outside surface intersects a perfect circular parent cylinder. The curve is sampled around the full branch circumference, then unwrapped horizontally by arc distance. The long point becomes depth zero, so every station tells you how far to cut back from one straight reference around the tube.
The entered angle is the acute included angle between finished tube centerlines. A 90° centered joint creates a symmetric saddle. Lower angles stretch the profile and move its extrema. Signed offset shifts the parent axis across the branch: positive is toward +90° on the printed clock marks. For a complete wrap, every point around the branch must reach the parent surface, requiring parent radius to be at least branch radius plus the offset magnitude.
Diameter, thickness, and real fit-up
Use measured outside diameters, not nominal pipe names. This is an outside contact line, so wall thickness does not alter the theoretical curve. It matters to bevel preparation, remaining edge thickness, weld procedure, and structural design—all outside this calculator. Oval, bent, seamed, coated, or deformed tube will depart from the ideal profile.
The line includes no saw kerf, abrasive-wheel radius, hole-saw geometry, coping-machine setup, root opening, bevel, shrinkage, or grinding allowance. A practical workflow is to cut conservatively outside the line and finish to a verified fit. The template is a layout aid, not a machine setup angle or engineering approval.
Printing and wrapping accurately
Print sheets use physical millimeter dimensions and CSS paged media, with 10 mm drawing overlap and registration crosses. The standalone SVG also declares its canvas in millimeters. Browser, PDF viewer, and printer settings can still rescale either output. Select the matching A4/Letter size and orientation, use Actual size / 100%, and measure the 100 mm check line before using the curve.
Cut or fold the paper at its two seam edges, wrap it squarely to the branch axis, and make the seam edges meet without a gap or overlap. Tape away from the cut line. Confirm the clock orientation and offset direction before marking metal. If the wrap width does not equal the measured circumference, stop and correct the diameter or print scale.
Cutting and hot-work safety
Cutting, grinding, and welding can expose people to sparks, fragments, noise, fumes, ultraviolet radiation, fire, and kickback. Secure the work; use guarded equipment within its ratings; isolate fuel and ignition sources; provide ventilation and fire protection; and select eye, face, hearing, hand, clothing, and respiratory protection through a proper hazard assessment. OSHA’s hot-work guidance describes these hazards and controls.
Do not cut pressurized, contaminated, structural, roll-cage, fuel-system, or safety-critical tube from this template alone. Follow applicable drawings, material specifications, welding procedures, codes, permits, and competent-person review.
Frequently asked questions
Is the angle a saw or hole-saw setting?
No. It is the smaller included angle between the finished branch and parent centerlines: 90° is perpendicular. Tool setup depends on the machine’s angle convention and geometry.
Why is a smaller parent tube rejected?
A full paper wrap assumes every point around the branch reaches the parent’s outside cylinder. When the parent radius is smaller than the branch radius plus offset magnitude, that complete intersection does not exist. A partial intersection or other joint needs different geometry.
Which edge is the seam?
The left −180° and right +180° edges are the same longitudinal line on the branch. Join them around the tube. The −90°, 0°, and +90° marks establish orientation; offset sign uses that printed convention.
Does wall thickness change the curve?
Not for an ideal outside-surface contact template. Thickness matters to bevels, root gaps, weld design, and strength, which this tool deliberately does not calculate.
How do I know the print is truly full size?
Choose the matching paper and orientation, print at Actual size / 100%, and measure the 100 mm check line. Also compare the printed seam-to-seam width with π times the branch OD.
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