How to use the pipe elbow miter cut layout calculator
Building a mitered elbow from straight pipe starts with the cut angle. If a total bend of θ is made from p pieces there are p − 1 joints, each joint turns the axis by θ/(p − 1), and each cut face is inclined to the pipe cross section by half of that, θ/(2(p − 1)). For a three-piece 90 degree elbow that is a 45 degree turn at each joint and a 22.5 degree cut on each face.
Piece lengths come from the centerline radius and the pipe radius. An end piece, cut on one side only, measures tan α × (R + OD/2) on the heel and tan α × (R − OD/2) on the throat; a middle piece, cut on both ends, is twice those values. The difference between heel and throat is the maximum offset of the cut line, equal to OD × tan α, and the total centerline length of the assembly is 2R·tan α·(p − 1).
The table gives wrap-around layout coordinates. Divide the outside circumference into the chosen number of stations, mark a line at each, set the throat as zero, step up by the tabulated offset at each station, and connect the marks in a smooth curve to get the cut line. On the shop floor, measuring the actual circumference beats calculating it, and root gap for welding plus torch kerf has to be added separately. Pressure piping codes limit where mitered bends are allowed, so check the governing design code first.
Frequently Asked Questions
More joints means a smaller turn at each one, so the bend follows the ideal curve more closely and flow resistance drops. Three pieces is common for a 90 degree elbow, while high velocity lines use four or five. The trade-off is more weld length and more fit-up time.
Set the throat, the short side, as zero and measure along the pipe surface at each station, marking the offset from the table. Station 1 is the throat and the last station is the heel, where the offset reaches its maximum of OD times tan of the cut angle.