When a pipe has to jog around an obstruction, the plumber sets two fittings and runs a diagonal between them. This calculator solves that offset triangle for any standard fitting angle, giving the travel (diagonal cut length), the run, and the net pipe length after subtracting fitting take-out.
How it works
The offset, travel and run form a right triangle where the fitting angle is measured from the original pipe line:
travel = offset / sin(angle) = offset × cosecant(angle)
run = offset / tan(angle) = offset × cotangent(angle)
cut = travel − 2 × fitting take-out
The classic memorized constants fall straight out of this: cosecant of 45° is 1.414, of 22.5° is 2.613, of 60° is 1.155, and of 30° is 2.000. Multiply your offset by the constant to get travel without trigonometry on the job.
Example and notes
To clear a 10-inch obstruction with 45° fittings, travel is 10 × 1.414 = 14.14
inches center to center, and the run is also 10 inches. If each fitting has a
1-inch take-out, the actual pipe cut is 14.14 − 2 = 12.14 inches. Smaller
angles like 22.5° give a longer, gentler diagonal that drains better and adds
less turbulence, while 60° fittings make a tight, abrupt offset in confined
spaces. For a rolling offset, combine the horizontal and vertical shifts into one
true offset first, then apply the constant.