Pipe offset math explained: set, run, travel and the 1.414 rule

An offset is a change in a pipe's line to get around something — a beam, a duct, another pipe — before carrying on parallel to where it started. Working out how long the angled piece must be is one of the first bits of math a pipefitter or plumber uses every day, and it is a natural kind of problem for an aptitude test's math section to borrow.

Set, run and travel

• Set (also called the offset): how far the pipe moves sideways, measured square to the pipe's line.
• Run: how far the pipe moves along its line while it makes that move.
• Travel: the length of the angled piece, measured center to center of the fittings.

The three make a right-angled triangle, with the travel as the long side. Once you know the set and the angle of the fittings, everything else follows.

The multipliers

For a given fitting angle, the travel is always the same multiple of the set. That multiple is 1 ÷ sin(angle), and the run multiple is 1 ÷ tan(angle). Fitters keep them on a card:

Fitting angle	Travel = set ×	Run = set ×
60°	1.155	0.577
45°	1.414	1.000
30°	2.000	1.732
22½°	2.613	2.414
11¼°	5.126	5.027

The 45° row is the one to know by heart. At 45° the set and the run are equal, and the travel is the diagonal of a square: √2, or 1.414, times the side. So a 45° offset with a 10-inch set needs 10 × 1.414 = 14.14 inches of travel.

Working it backwards

If you know the travel and need the set, divide instead of multiplying. A 45° travel of 21.21 inches gives a set of 21.21 ÷ 1.414 = 15 inches.

Rolling offsets

A rolling offset moves the pipe both sideways and up or down at once. Measure the two moves — usually called the roll and the set — and combine them with Pythagoras to get the true offset: √(roll² + set²). Then treat the true offset like an ordinary set and multiply by the constant for your fittings.

Example: a roll of 8 inches and a set of 6 inches. 8² + 6² = 64 + 36 = 100, so the true offset is √100 = 10 inches. With 45° fittings, travel = 10 × 1.414 = 14.14 inches.

From travel to a cut length

The travel is measured center to center. The pipe you actually cut is shorter, because each fitting takes up part of that length. Subtract the allowance for the fitting at each end — the figure depends on the fitting and the joint, so it comes from the fitting's dimensions, not from a rule. And convert the decimal to the nearest sixteenth before you mark the pipe: 14.14 inches is 14 and 0.14 × 16 = 2.24 sixteenths, so 14 1/8 inches.

Try some

On the test

UA locals do not publish their tests, and an aptitude test is not a trade exam, so do not expect offset questions on every paper. What the math sections locals describe do test — multiplying decimals by hand, converting decimals to fractions, rearranging a simple formula, and Pythagoras — is exactly what offset math uses. Our UA math practice includes offsets alongside the rest.