Practical tools for measured work
Segmented (Lobster-Back) Elbow Pattern Developer
Lay out a gored/lobster-back elbow's miter angles and per-piece flat pattern from diameter, bend radius, angle and piece count.
Calculate the layout, check the diagram, then print the result for the shop or jobsite.
Includes both end pieces. More pieces = a smoother bend and a smaller cut angle per joint.
Cut 2 end pieces (mirror images of each other) and 2 identical middle pieces - every middle piece and every end piece shares the same pattern.
How it works
How to use it: enter the pipe or duct diameter, the centerline radius of the overall bend you want, the total elbow angle (90° for a standard elbow), and how many straight pieces to build it from. More pieces give a smoother-looking bend and less flow resistance, at the cost of more cutting and welding/seaming.
Method: tangent-line construction. The bend's centerline arc is approximated by straight pieces tangent to it, changing direction at each joint. This gives the standard result: cut angle per joint = total angle ÷ (2 × (pieces − 1)) - the same angle at every joint. End pieces get one angled cut (mating to straight pipe on the square end); every middle piece gets two opposing cuts.
Flat pattern. A cylinder sliced by a plane tilted at the joint angle unrolls into a cosine curve - long on the outside of the bend, short on the inside, with amplitude = pipe radius × tan(joint angle). All middle pieces are geometrically identical, as are both end pieces, so the diagram shows one of each: cut the quantities noted below it.
Current-input example
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.
- Pipe/duct diameter
- 200 mm
- Bend centerline radius
- 400 mm
- Total elbow angle
- 90 deg
- Number of pieces
- 4
Primary result: Miter (cut) angle per joint: 15.00 deg.
Before using the result
- 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.
Limitations
If the short (inside) length of a piece would come out at zero or below, the combination of diameter, bend radius, angle and piece count is not physically buildable - the calculator returns no result in that case. Increase the bend radius, reduce the angle, or add more pieces.
The pattern is the bare developed geometry only - add seam allowance for a welded or lock-seamed joint separately, on the outside of the printed outline.
Frequently asked questions
Why do I only see two panels, not one per piece?
Every middle piece uses the identical cut angle and pipe diameter, so they all share one pattern; likewise both end pieces (mirror images of each other). Trace the shown pattern the stated number of times rather than re-deriving it per piece.
How is bend radius different from pipe diameter?
Bend radius is the radius of the overall curve the elbow follows (centerline to centerline) - a gentle, wide sweep uses a large radius, while a tight elbow uses a small one. It is independent of the pipe's own diameter, though very small radii relative to diameter can produce an invalid (pinched) piece; see Limitations.
Related tools
Pipe Notch Template
Generate a full-size fishmouth or saddle template for the theoretical intersection between two tubes.
Reducer Layout
Develop the flat-pattern template for a pipe reducer, concentric or eccentric, including the fully flush case.
Duct Rolled Offset
Calculate rolled-offset travel, advance and roll angle, with a printable mitered-elbow cut template.
Bend Allowance Calculator
Calculate bend allowance, bend deduction and setback for a sheet metal bend, with a diagram.