Calculate travel length for rolling offsets in pipe fitting with various elbow angles.
Rolling offset is the calculation that produces a single bent pipe to connect two parallel non-coplanar pipes, common in industrial piping where multiple lines change elevation and direction simultaneously. This calculator solves true-length, run, and travel angles from the X (horizontal offset), Y (vertical rise), and Z (roll) dimensions, plus the fitting angle (45°, 60°, 22.5°). The result is the cut length and the projected angles for isometric layout.
Rolling offset has three orthogonal components: horizontal X, vertical Y, and roll Z (lateral displacement). True offset (the hypotenuse of the offset triangle) is H = √(Y² + Z²), and run length = H × cot(θ) where θ is the fitting angle (typically 45°). Travel (the cut pipe segment) = H / sin(θ). The roll angle in the projected isometric view is α = arctan(Z / Y); the fitter rotates the spool by α around the run axis. For 45° fittings, travel = 1.414 × H and run = H. The calculator returns cut length, projected travel, run, and rotation angle for all four fitting standards used in the field (45°, 60°, 22.5°, 11.25°).
A piping fitter routing a 4-inch line over a structural beam: X = 1,200 mm horizontal, Y = 600 mm vertical, Z = 400 mm lateral, with 45° elbows. Calculator returns H = 721 mm, travel = 1,020 mm, run = 721 mm, rotation 33.7°.
A sprinkler installer connecting two parallel mains separated by 800 mm offset using 60° fittings picks a 60° rolling offset, gets travel = 924 mm cut length, and uses the rotation angle to align the connection without field welding.
An HVAC contractor sizing a chilled-water cross-over computes the cut piece between two parallel returns; the rotation angle drives the field gauge that orients the swivel-clamp during assembly.
Simple offset is two-dimensional (offset in one plane only). Rolling offset is three-dimensional, adding a roll (lateral) component — required when the receiving pipe is not directly above or below the source.
45° is the most common because it minimizes pressure drop and is widely stocked. 60° gives shorter travel for a given offset but slightly higher loss. 22.5° is used for very shallow grades.
Project the offset triangle onto each of the three principal planes (X-Y, X-Z, Y-Z); the rotation angle from the Y-axis equals arctan(Z/Y) and tells the fitter how to roll the spool before tacking the second elbow.