How to calculate a pipe offset

1. Offset, travel and run

A pipe offset is what you build when a straight run has to step sideways to clear something — a beam, a duct, another pipe — and then carry on in the same direction. You make it with two fittings of the same angle: the first turns the pipe off the line, a diagonal length crosses the gap, and the second turns it back parallel to where it started. Three measurements describe that shape. The offset (also called the set or spread) is the perpendicular distance the pipe shifts. The travel is the length of the diagonal pipe between the two fittings, measured centre-to-centre. The run (or advance) is how far the pipe moves along its original direction while it is making the shift.

Those three form a right triangle: the offset and the run are the two legs, and the travel is the hypotenuse joining them. That is the whole secret to offset maths — once you see it as a right triangle, the fitting angle is simply the angle the diagonal makes with the run, and ordinary trigonometry gives you every length you need. Because the travel is the hypotenuse, it is always the longest of the three, which is why cutting a diagonal a touch short is the classic offset mistake.

2. The formula

Call the fitting angle θ — the number of degrees each fitting bends the pipe, measured from the straight run. In the offset triangle the offset is the side opposite θ and the run is the side next to it, so from the definitions of sine and tangent:

travel = offset ÷ sin θ  and  run = offset ÷ tan θ.

You do not have to work the sine and tangent out every time. For any given fitting angle, 1 ÷ sin θ and 1 ÷ tan θ are fixed numbers — the multipliers in the table below. Multiply the offset by the travel multiplier to get the diagonal, and by the run multiplier to get the advance. For 45° fittings the travel multiplier is 1 ÷ sin 45° = 1.414 (the square root of 2) and the run multiplier is 1 ÷ tan 45° = 1.000, which is why a 45° offset has a run exactly equal to its offset. These are exact trigonometric identities, not code values or rules of thumb — they are the same in every country and for every pipe material.

3. Fitting-angle multiplier table

Plumbing and DWV fittings come in a handful of standard bends, named as fractions of a circle: a 1⁄8 bend is 45°, a 1⁄16 bend is 22½°, a 1⁄6 bend is 60°, and so on. Here are the travel and run multipliers for the common angles:

Read the pattern: the shallower the fitting (11¼°, 22½°), the bigger both multipliers, because a gentle bend needs a long diagonal and eats a lot of forward run to make even a small sideways move. The steeper the fitting (60°, 72°), the closer the travel gets to the offset itself and the shorter the run. The 45° row sits in the middle and is the one most jobs use — enough angle to keep the run compact, shallow enough to be easy to fit and to flow well on a drain.

4. Worked examples

A 45° offset around a beam. The pipe must step over 10 inches to clear a joist, and you are using two 45° fittings. Travel = 10 × 1.414 = 14.14 inches, and the run = 10 × 1.000 = 10 inches. So you cut a 14.14-inch diagonal (centre-to-centre), and the whole offset uses up 10 inches of forward run. In metric the same shape with a 250 mm offset gives a travel of 250 × 1.414 = 353.6 mm and a 250 mm run.

A shallow 22½° offset. Sometimes you need to hug a wall and only shift a little. A 6-inch offset with 22½° fittings gives travel = 6 × 2.613 = 15.68 inches and run = 6 × 2.414 = 14.49 inches. Notice how much longer both are than the 45° case for the same 6-inch shift: the gentle angle buys you a smooth, low-turbulence path at the cost of a long diagonal and nearly 14½ inches of run — which is exactly why you would choose it on a drain where flow matters, and avoid it where space along the run is tight.

A rolling offset. Suppose the pipe has to move 8 inches across and 6 inches up at the same time to reach its new position. First find the true offset with Pythagoras: √(8² + 6²) = √(64 + 36) = √100 = 10 inches. Now it is just a 10-inch offset: with 45° fittings the travel is 10 × 1.414 = 14.14 inches. The only extra step for a rolling offset is that first diagonal; everything after it is the ordinary offset maths.

5. Rolling offsets in detail

A plain offset shifts the pipe in one plane — left, right, up or down. A rolling offset shifts it in two at once: the new run is both to the side and at a different height, so the diagonal rolls around the pipe rather than lying flat. It looks intimidating on the job, but the calculation splits cleanly into two steps. Step one is the true offset — the straight diagonal distance between the old centreline and the new one — which is the hypotenuse of the horizontal roll and the vertical rise: offset = √(roll² + rise²). Step two is identical to a normal offset: feed that true offset into travel = offset ÷ sin θ and run = offset ÷ tan θ.

The reason the two-step method works is that the roll and the rise are at right angles to each other, so together they define a single flat plane that the diagonal lies in — and within that plane the geometry is the ordinary offset triangle again. Set the calculator to rolling mode, type the roll and the rise, and it does the Pythagoras for you before applying the fitting-angle multiplier, so you never have to hold two triangles in your head at once. The one thing to measure carefully is the roll and rise themselves: take them between the two pipe centrelines, not the outsides, or the true offset — and therefore the travel — will be off.

6. From travel to the pipe you cut

The travel the formula gives you is a centre-to-centre length — the distance between the imaginary centre points of the two fittings. The pipe you physically cut is shorter than that, because each fitting swallows some pipe. The amount a fitting swallows is its take-off(also called the make-up or fitting allowance): the distance from the fitting's centreline to the point where the pipe stops inside it — the socket shoulder on a solvent-weld or push-fit, or the thread engagement on a threaded fitting. To get the cut length, subtract the take-off of each fitting from the travel: cut length = travel − take-off₁ − take-off₂.

Take-offs are not universal numbers — they depend on the fitting pattern, the pipe size and the material — so this guide will not hand you one to plug in blindly; that is exactly the kind of figure it would be wrong to invent. Get them from the fitting manufacturer's data, or measure them once by dry-fitting a fitting on a marked pipe and reading where the stop lands. Keep the offset, travel and run figures the calculator gives you as your framing numbers, then apply your own verified take-offs at the bench. The same measure-first discipline runs through the rest of the flow and layout tools on the plumbing hub — for instance the pipe velocity calculator for checking a run flows well, or the pipe friction loss calculator for what those extra fittings cost you in pressure.

Common questions

How do you calculate a pipe offset?

Measure the offset — how far the pipe has to shift sideways — then divide by the sine of the fitting angle for the travel (the diagonal pipe between the fittings) and by the tangent of the angle for the run (how far it advances). For the common 45° offset that is travel = offset × 1.414 and run = offset. So a 10-inch offset with 45° fittings needs 14.14 inches of travel.

What is the multiplier for a 45 degree offset?

For 45° fittings the travel multiplier is 1.414 (1 ÷ sin 45°, the square root of 2) and the run multiplier is 1.000 (1 ÷ tan 45°). A 10-inch offset gives 10 × 1.414 = 14.14 inches of travel and a 10-inch run. The 1.414 constant is the number pipefitters memorise for the 45° offset.

What are travel and run on a pipe offset?

Offset is the sideways distance the pipe moves; travel is the diagonal pipe length between the two fittings, measured centre-to-centre; run is how far the offset advances in the original direction. Offset and run are the two legs of a right triangle and travel is the hypotenuse, so travel is always the longest of the three.

How do you calculate a rolling offset?

A rolling offset shifts the pipe across and up at once. First find the true offset with Pythagoras: offset = √(roll² + rise²) — an 8-inch roll and 6-inch rise give √(64 + 36) = 10 inches. Then treat it as an ordinary offset: travel = offset × 1.414 for 45° fittings. The calculator's rolling mode works the true offset out for you.

How do I turn travel into the pipe cut length?

Travel is the centre-to-centre distance between the two fittings. To get the pipe to actually cut, subtract each fitting's take-off — the make-up from the fitting centreline to where the pipe seats. The take-offs depend on the specific fittings and pipe, so read them off the fittings or lay one out, then take them off the travel.