What is a pipe saddle cut?

A saddle, fish-mouth, or coped cut is the curved profile on the end of a branch pipe so it sits flush against the round surface of a larger header pipe. The cut follows the intersection curve of the two cylinders so the joint mates with no gap.

How does the wrap-around template work?

The template lists a cut height at evenly spaced points around the branch circumference. You wrap a marked paper strip around the branch, transfer the heights, connect them into a smooth curve, and cut along it. Wrapping converts a flat layout into the correct 3D saddle profile.

Why does the intersection angle matter?

At 90 degrees the saddle is symmetric. As the angle drops toward a lateral, the cut becomes longer and more asymmetric on one side, with a deeper notch where the branch meets the header at an acute angle. The math accounts for the angle so the template stays accurate.

What if the branch and header are the same size?

Equal-diameter intersections produce the deepest saddle, because the branch wraps far around the header. The tool still computes it, but the cut is long and the fit is sensitive, so cut slightly proud and grind to fit for a tight root gap.

Does this give the bevel angle for welding too?

It gives the cut line for the saddle profile. The weld bevel angle is added on top by tilting the torch or grinder as you follow the line. Typical pipe welds use a 30 to 37.5 degree bevel per side; set that on your cutting tool while tracing the template.

Pipe Bevel & Saddle Layout Calculator

Fitting a branch pipe onto a round header means cutting a curved saddle so the branch sits flush with no gap. Laying that curve out by eye wastes pipe and leaves a poor root gap. This calculator computes the exact intersection of the two cylinders at any angle from 30 to 90 degrees and outputs a wrap-around template of cut heights you can print, wrap, and scribe.

How it works

The saddle is the curve where a branch cylinder of radius r intersects a header cylinder of radius R. Walking around the branch by angle theta, the lateral offset from the branch axis is r·sin(theta). That offset rides up the curved header surface, and the intersection angle tilts the whole profile:

x      = r × cos(theta)          (along the header axis component)
y      = r × sin(theta)          (across, rides on the header)
drop   = R − sqrt(R² − y²)       (how far the header surface curves up)
height = baseline − (x / tan(angle)) − drop

Sweeping theta from 0 to 360 degrees in small steps gives a height at each station around the branch. Connecting the heights produces the saddle cut line; wrapping the strip around the branch makes it three-dimensional.

Example and notes

A 2 in branch entering a 4 in header at 90 degrees produces a symmetric saddle whose deepest notch sits where the branch wraps furthest around the header. Drop the angle to 45 degrees and one side of the saddle lengthens noticeably while the other shortens, the classic lateral profile. Print the template at 100 percent scale, verify one known dimension with a rule before trusting it, and cut slightly outside the line so you can grind to a snug fit. Add your weld bevel by tilting the cutting tool as you trace the saddle.