Calculate cope angles and templates for saddle joints and pipe tee connections.
Saddle bend is the cut profile required to fit one pipe (the branch) against the curved outer surface of another (the run), like a saddle. This calculator solves the cut depth and the cope outline from the branch OD, the run OD, the intersection angle, and the wall thickness, producing a flat developable pattern that can be wrapped onto the branch for marking.
When a branch of diameter D_b meets a run of diameter D_r at angle θ, the cope-out profile follows a curve generated by projecting circle intersections onto the branch surface. The maximum cope depth on the centerline is D_b/2 − √((D_r/2)² − (D_b/2 × sin θ)²) for branch perpendicular to run. The calculator approximates the development by dividing the circumference into 12 stations and computing the radial cut at each — adequate for hand-marking. For equal-diameter or near-equal lateral cuts the depth approaches D_r/2 and the profile becomes an ellipse. The branch end is cut along this profile, then ground for a flush butt-weld fit-up.
A pipe fitter making a 50 mm branch onto a 200 mm header at 90° computes a saddle depth of 13 mm, marks 12 stations along the branch circumference with the developed cope, and cuts with an oxy-fuel torch for a 1.5 mm fit-up gap.
A welder fabricating a 45° lateral on a 100 mm process line uses the calculator to develop the elliptical cope, gets a longer cope on one side, and prints a paper template that wraps the branch for marking.
A maintenance technician fitting an emergency repair patch wraps the dimensions into the calculator, gets the cope outline for the saddle-clamp's inner curve, and trims the clamp on a band saw for a leak-proof seat.
90° (right-angle tee) is most common. 45° laterals are used for branching with reduced pressure drop and easier flow distribution. Other angles (60°, 30°) appear in specialized geometry.
For branch/run ratio under 0.6, the 12-station development is within 1-2 mm of the exact cope. For larger ratios, 24 stations or CAD development is recommended.
Yes for full-penetration welds. The cope marked on the OD must be offset inward by the wall thickness to leave a flush root face. Add 1-1.5 mm extra cope depth per 3 mm wall.