How to Use the Pipe Notch Cut Profile Calculator
When one round pipe is welded onto another as a tee or a lateral, the end of the branch pipe has to be cut into a saddle shape that wraps the outside of the run pipe. That curve is called a notch or fishmouth cut, and its shape is fixed completely by three numbers: run pipe OD, branch pipe OD and the intersection angle.
With branch radius r, run radius R and intersection angle θ, the cut position measured along the branch axis is s(φ) = (√(R² − r²·sin²φ) − r·cosφ·cosθ) ÷ sinθ, where φ sweeps around the branch circumference. The table reports cut depth relative to the longest surviving point at φ = 180°, the heel on the obtuse side, so every number is material you still have to remove.
On the shop floor, wrap the branch pipe and divide the circumference into the number of equal parts you selected, then step down from the end by the listed cut depth at each point and connect the marks with a smooth curve. The layout distance starts at the toe on the acute side, at φ = 0°. Add weld root gap and bevel allowance separately, and measure the real outside diameters instead of trusting nominal pipe sizes, because OD tolerance alone can shift the saddle by several thousandths of an inch.
Frequently Asked Questions
No. The layout assumes a normal saddle joint where the branch OD is equal to or smaller than the run OD. A larger branch becomes a reverse saddle cut into the run pipe, which uses a different development formula.
Twelve divisions are enough for branch pipes up to about 4 in OD. For larger pipe or shallow angles of 45 degrees or less, step up to 16 divisions so the marked curve stays smooth.