What is a miter bend or mitered elbow?

A miter bend (also called mitered elbow, segmented elbow or lobster back bend) is a pipe fitting fabricated by cutting straight pipe at an angle and welding the segments together to form a curve. It replaces standard wrought elbows for large diameters (typically DN 350 / 14" and above), low-pressure services, or when standard fittings are not available. Per ASME B31.3 §304.2.3, a 90° miter bend usually requires between 2 and 5 cuts (3 to 6 segments) depending on pipe diameter and design pressure.

How many cuts are needed for a 90° mitered elbow?

The number of cuts (n) for a 90° miter bend is determined by design pressure and pipe size. A common rule on the shop floor: 2 cuts (3 segments) for low pressure and small diameters, 3 to 5 cuts (4 to 6 segments) for larger pipes or higher allowable stresses. The cut angle θ = 90° / (2 × n). With more cuts the bend is smoother and the allowable pressure higher, but fabrication cost and the number of weld joints increase.

How do I calculate the cutback for a miter bend?

The cutback is the offset between the cut line and the reference line on the pipe surface. For a miter bend with n cuts forming a total angle β, the cut angle of each face is θ = β / (2n). The cutback at the outermost generator equals (D/2) × tan(θ), where D is the pipe outside diameter. Our calculator computes this automatically for every generator (12, 24, 48 or more development lines) and exports a 1:1 paper template you can wrap directly around the pipe in the workshop.

Is this miter bend calculator really free?

Yes — 100% free, no registration, no watermark, no time limit. All calculations run in your browser (no data sent to any server). You can print 1:1 templates and export DXF files (AutoCAD TrueView 2022 compatible) without paying anything. The tool is built and maintained by a working pipefitter (25 years of field experience) to help colleagues in the trade. If you'd like to support, share it with a friend who fabricates pipework.

Can I export the miter bend layout to AutoCAD or DXF?

Yes. The Export DXF button produces a DXF file with the 3D mesh of the elbow (high resolution, 96 generators), the flat pattern development of each segment, dimensions, generator lines and reference circles — all organized in named layers (ELBOW_3D, DEV_CONTOUR, DEV_GENERATRICES, DEV_COTES, DEV_SOUDURE, etc.). The format is compatible with Autodesk TrueView 2022, AutoCAD, DraftSight and BricsCAD. You can then send it directly to a CNC plasma cutter or a fabrication shop.

Free Miter Bend Calculator — Mitered Elbow Flat Pattern & 3D Layout

Free Miter Bend & Mitered Elbow Calculator — Flat Pattern Layout for Pipe Fabrication

This free online miter bend calculator generates the complete flat pattern layout of mitered elbows (also called segmented elbows, lobster back bends or fabricated elbows) for pipe fabrication in workshops and on site. It computes the cut angle, the cutback on each generator, the developed length of every segment and the total raw pipe length required — for any pipe diameter from DN 15 to DN 1200 and any elbow angle from 15° to 360°.

Unlike a textbook formula sheet, this tool gives you an interactive 3D preview of the elbow as you change parameters, a 1:1 printable template that wraps directly around the pipe in the workshop, and a DXF export (AutoCAD TrueView 2022 compatible) ready to send to a CNC plasma cutter or a fabrication shop.

👷 Built by a working pipefitter — 25 years of hands-on field experience in refineries, chemical plants and shop fabrication. Every formula here has been tested with a tape measure and a grinder before being coded.

What is a mitered elbow (miter bend)?

A mitered elbow is a curved fitting fabricated by cutting straight pipe segments at an angle and welding them together. It replaces a standard wrought elbow when:

Pipe diameter is too large for off-the-shelf elbows (typically DN 350 / 14" and above)
Standard fittings are not available or too expensive
The service is low-pressure (utility, vent, drain, ducting)
A non-standard angle is required (37°, 53°, 67.5°, etc.)

In trade language you'll also hear: segmented elbow, lobster back bend, gore bend, cut bend or fabricated bend — all describing the same thing.

The miter bend formula (ASME B31.3 §304.2.3)

For an elbow of total angle β made of n cuts (n + 1 segments), the cut half-angle θ of each face is:

θ = β / (2 × n)

The cutback (offset of the cut line from the reference line, measured on the pipe surface) at the outer generator equals:

cutback_max = (D / 2) × tan(θ)

where D is the pipe outside diameter. For each intermediate generator at angle φ around the pipe axis, the cutback becomes:

cutback(φ) = (D / 2) × tan(θ) × cos(φ)

The total pipe length needed is the sum of all segment lengths plus the cutting allowance (typically 3–5 mm per cut depending on the cutting method).

How many cuts do I need?

The minimum number of cuts depends on the design pressure (per ASME B31.3 §304.2.3) and on the smoothness you want. A practical shop rule:

2 cuts (3 segments): low-pressure utility, small diameter, fast fabrication
3 cuts (4 segments): standard 90° elbow on medium pressure lines
4–5 cuts (5–6 segments): high pressure, larger diameter, smoother bend
8 cuts and above: insulation, ducting, lobster back style for sheet metal

The more cuts you use, the smoother the bend and the higher the allowable pressure — but fabrication cost and the number of weld joints grow linearly.

How to use the layout calculator

Enter the pipe outside diameter (DE) — pick from the DN list or type a custom value
Set the elbow angle (typically 30°, 45°, 60° or 90°; can go up to 360° for a full torus)
Choose the number of sectors (2 to 40)
Set the mean radius Rm of the bend (e.g. 1.5 × D for short radius, 3 × D for long radius)
Pick the number of development lines (12, 24 or 48 — more lines = more accurate template, longer marking time)
Rotate the 3D view to verify the geometry, then click Print 1:1 or Export DXF

Frequently asked questions

What's the difference between a mitered elbow and a segmented elbow?

In practice, none. Both terms describe a pipe elbow fabricated from multiple straight segments welded together. "Mitered elbow" is the term used in piping engineering and ASME standards; "segmented elbow" and "lobster back bend" are more common in sheet metal, ducting and insulation trades. This calculator handles all of them.

Can I use this for ducting and HVAC, not just pipe?

Yes. The flat pattern math is identical whether you're fabricating in heavy carbon-steel pipe, in thin stainless duct or in aluminum insulation. Just enter the outside diameter and the angle — the developed pattern is the same.

How accurate is the 1:1 printable template?

The template is rendered at true scale (96 DPI assumed; verify with the printed ruler on the page). For pipes up to DN 400 / 16", one A3 sheet usually fits the full development. For larger pipes the template is split across multiple A3/A4 pages with alignment marks — wrap each strip around the pipe, line up the marks, and trace.

Does the DXF export work with AutoCAD and CNC plasma cutters?

Yes. The DXF is written in AC1009 format (AutoCAD Release 12+, compatible with all modern CAD/CAM software including AutoCAD, DraftSight, BricsCAD, LibreCAD, and most CNC plasma controllers). It includes the 3D mesh, the flat pattern of every segment, generator lines, dimensions and reference circles — all on named layers so you can isolate what you need before cutting.

Can I fabricate a full torus (360° elbow / ring)?

Yes — this calculator supports angles from 15° all the way to 360°. A 360° "elbow" is actually a torus (donut shape), useful for compensation loops, air rings and certain custom applications.

Is the math validated against ASME B31.3?

The geometric flat pattern follows the classical method described in J. Triouleyre, "Traçage en Chaudronnerie et Tuyauterie" (Éditions Delagrave) — the French reference for layout fabrication. The pressure-design rules for miter bends are covered in ASME B31.3 §304.2.3 but are not included in this layout calculator (which is a geometry tool, not a stress analyzer). For pressure design, see our DESP/PED Calculator below.

Related tools on PipeCalculators

If you're fabricating piping by hand, you might also need:

References: ASME B31.3 §304.2.3 (Pressure Design of Miter Bends) · EN 13480-3 (Industrial Metallic Piping) · J. Triouleyre, Traçage en Chaudronnerie et Tuyauterie, Éditions Delagrave (classical layout method)