15.2 Pipe Offsets

15.2 Pipe Offsets

Quick Answer: For a 45° offset, travel = offset × 1.414 and run = offset. 22.5° constants are travel 2.613 and run 2.414. 60° constants are travel 1.155 and run 0.577. A rolling offset: true offset = √(offset² + roll²), then apply those constants to the true offset. Travel is center-to-center; cut length subtracts takeoffs from the fittings you have, not from a memorized manufacturer chart. These five Part II math items share the 160-minute, closed-book, 70 percent session with the rest of the 40-item practical.

Offset math moves a pipe around a duct, a beam, or another pipe and brings it back parallel to the original centerline. Offset is the perpendicular distance between those two parallel centerlines. Travel is the center-to-center length of the diagonal piece. Run is the distance along the original pipe axis between the two fitting centers. PSI will give two of those three, or give offset plus angle, and ask for travel or run. Independent OpenExamPrep teaching here is the arithmetic. It is not a Board takeoff booklet.

248 CMR 10.05(3) lists eighth, sixteenth, and sixth bends among legal drainage changes of direction. Those names are the angles: an eighth bend is 45°, a sixteenth bend is 22.5°, a sixth bend is 60°. Memorize the constants; a non-programmable calculator may have square root for rolling offsets but you should not plan to rebuild 1/sin(θ) under the clock unless the machine actually has trig keys and you still know which ratio is travel.

Constants you can defend

Travel = offset ÷ sin(θ). Run = offset ÷ tan(θ). The shop numbers are those ratios, rounded the way trade books print them:

Checks (not the exam procedure, the reason the numbers are not folklore): sin 45° = 0.7071, 1/0.7071 = 1.414; tan 45° = 1, so run constant 1. sin 22.5° = 0.3827, 1/0.3827 = 2.613; tan 22.5° = 0.4142, 1/0.4142 = 2.414. sin 60° = 0.8660, 1/0.8660 = 1.155; tan 60° = 1.732, 1/1.732 = 0.577.

On a 45° offset the triangle is 45-45-90: the two legs are equal, so run = offset, and the hypotenuse is offset × √2. If someone answers travel = offset on a 45° problem, they reported the run. If they answer travel = 2 × offset, they treated it as a 30-60-90 long side.

60° is the opposite personality: run shrinks to about 0.58 × offset. A 10-inch 60° offset does not eat 10 inches of wall length; it eats about 5.8 inches of run and about 11.6 inches of travel.

These constants are for pipe offsets (two fittings of the same angle, pipe returning parallel). They are not 248 CMR 10.15(7) stack-offset sizing. That rule is load: an offset 45° or less from vertical may size as a straight stack; more than 45° sizes from Table 2. Chapter 11.3 owns that. Do not multiply a DFU total by 1.414.

Worked example 1 — 45° around a Worcester beam

A water line must throw 14 inches of offset with two 45° ells.

Travel = 14 × 1.414 = 19.796 inches → 19.80 inches (19-13/16 in. if you still think in sixteenths: 0.796 × 16 ≈ 12.7, so about 19-13/16).

Run = 14 inches.

That 19.80 inches is center of ell to center of ell. It is not the length you cut until you remove takeoffs.

Fitting allowance (method only). Cut length = travel − T₁ − T₂, where T is the end-to-center (takeoff) of that fitting for that size and angle. A 1/2-inch copper 45 and a 2-inch threaded 45 do not share T. Read T from the fitting you hold, the carton, or a given number in the stem. This guide will not print a fake brand chart. If the item asks for travel, stop at 19.80 inches. If it gives T = 1-1/4 inches each (a number the problem invented for you), cut length = 19.80 − 1.25 − 1.25 = 17.30 inches. If it does not give T, do not invent 2-5/8 inches because a catalog you once saw used that for one size of one material.

Worked example 2 — 22.5° and 60° on the same 8-inch offset

Same 8-inch offset, two different fitting pairs.

22.5° pair

• Travel = 8 × 2.613 = 20.904 inches → 20.90 inches
• Run = 8 × 2.414 = 19.312 inches → 19.31 inches

60° pair

• Travel = 8 × 1.155 = 9.240 inches → 9.24 inches
• Run = 8 × 0.577 = 4.616 inches → 4.62 inches

The 22.5° travel is more than double the 60° travel for the same offset. That is why a sixteenth-bend offset needs a long clear diagonal, and why a sixth-bend offset tucks into a short bay. Using 1.414 on a 22.5° stem (8 × 1.414 = 11.31 inches) is the 45° constant on the wrong angle — a likely distractor.

A 10-inch 60° offset, because the quiz will use it: run = 10 × 0.577 = 5.77 inches, travel = 10 × 1.155 = 11.55 inches. Reporting 10 inches as travel is the 45° run/offset mix-up. Reporting 11.55 inches when the question asked for run is the travel/run swap.

Worked example 3 — rolling offset, Lawrence water line

The pipe must move 10 inches over and 24 inches up (or any two perpendicular offsets — shop language is offset and roll). Fittings are 45°.

True offset = √(10² + 24²) = √(100 + 576) = √676 = 26 inches.

That 26 inches is the single offset the two 45° fittings actually “see.” Then:

Travel = 26 × 1.414 = 36.764 inches → 36.76 inches.

Run = 26 × 1.000 = 26 inches (45° run constant is 1).

If you skip the square root and take 10 × 1.414 = 14.14 inches, you ignored the roll. If you take 24 × 1.414 = 33.94 inches, you ignored the side offset. If you add first — (10 + 24) × 1.414 = 48.08 inches — you treated the two legs as if they were already the true offset.

Rolling at 22.5° uses the same true offset, then the 22.5° constants. True offset still 26 inches; travel = 26 × 2.613 = 67.94 inches; run = 26 × 2.414 = 62.76 inches. Rolling does not change the angle constants; it changes the offset you feed them.

Calculator note. √676 is a perfect square so you can catch a keystroke error. When the true offset is not pretty — √(7² + 10²) = √149 ≈ 12.21 inches — compute the root, then multiply by 1.414. 12.21 × 1.414 ≈ 17.26 inches of 45° travel. Round the way the options are printed; do not carry eight decimals into a four-choice item.

Takeoff still comes last. 36.76 inches remains center-to-center. Subtract two end-to-center dimensions only after the stem gives them or you measure the fittings. Threaded, grooved, solder, and fused 45s of the same nominal size do not share a takeoff. 248 CMR 10.05 tells you which bend geometries are legal on drainage; it does not publish inches of takeoff.

Pacing. Five calculation items share the clock with 20 isometric-analysis items. If an offset stem is clean — 45°, offset given, ask travel — it should be one multiply. Spend the saved seconds on the isometric, not on inventing a cut length the question never asked.

Official resources

• PSI Massachusetts plumbing Candidate Information Bulletin — Part II General Trade Calculations 5; calculator limits
• 248 CMR 10.05(3) (Cornell) — eighth, sixteenth, and sixth bends as legal drainage fittings
• 248 CMR 10.15 (Cornell) — stack offsets of 45° or less versus more than 45° (sizing, not travel constants)