Coping one tube to fit another
When a round tube meets another round tube — a roll cage node, a handrail, a chassis gusset — the end of the joining tube has to be cut in a saddle, or fishmouth, so it wraps the surface it lands on. This calculator works out how deep that notch is from the two tube diameters and the joint angle, so you can set up a hole-saw notcher or mark the cut by hand.
The geometry
The cut line is where the branch tube cylinder intersects the surface of the main tube. For a square tee of equal tubes the saddle is exactly one radius deep; as the branch gets smaller than the main tube the notch gets shallower, and as the joint angle leans away from 90 degrees one side of the saddle deepens while the other shortens.
Reading the result
Notch depth is the difference between the deepest and shallowest points of the saddle — the amplitude of the fishmouth. The heel is the long side that reaches furthest down the main tube; the toe is the short side. The profile line below lists how far to cut back at stations around the tube, measured from the longest point.
Related fabrication tools
For straight cut lengths in a piping run, use the pipe cut length calculator; for the area of tube to coat, the pipe surface area calculator.
Worked example
Two 1.5 in tubes meeting at 90 degrees: the branch radius is 0.75 in, and the saddle is one radius deep, so the notch depth is 0.75 in. Cut the sides back 0.75 in relative to the front and back tips and the tube drops onto the main with no gap.
FAQ
What if the branch is bigger than the main tube?
Then there is no clean saddle — the larger tube cannot wrap the smaller one, and the joint needs a different treatment such as a flat-on coped end or a gusset. The calculator flags this case.
How do I mark the cut without a notcher?
Print or draw a wraparound template using the station depths, wrap it around the branch tube, and scribe along the edge. A tube notcher with a hole saw of the main tube diameter does the same cut mechanically.