Pipe rolling offset calculator

What is a pipe rolling offset calculator?

A rolling offset is the piece of pipe that connects two parallel runs when the second run is displaced both vertically and horizontally from the first. A plain offset only steps up or down; a rolling offset also rolls to the side, so the connecting pipe leaves the plane of the wall and travels diagonally through space. This calculator takes the vertical displacement (the rise), the horizontal displacement (the roll), and the angle of the fittings you are using, and returns the three numbers a pipefitter needs to cut and place the piece: the true offset, the travel, and the run.

It is a bench calculation every fitter does when a line has to dodge a beam, a duct, or another pipe and pick the run back up somewhere off to the side. Get the travel wrong and the connecting pipe is cut long or short; get the run wrong and the second parallel run lands in the wrong place along the axis.

Rise, roll, offset, travel and run

The four measurements describe the same right-angled geometry:

• Rise — how far the second pipe sits above or below the first (vertical).
• Roll — how far it sits to one side of the first (horizontal).
• True offset — the straight-line distance between the two pipe centrelines, combining rise and roll. Because rise and roll are at right angles to each other, the true offset is the hypotenuse of that right triangle.
• Travel — the length of the connecting pipe itself, measured centre-to-centre between the two fittings.
• Run — how far the pipe advances along the direction of the original run while it makes the offset, i.e. the spacing of the two fittings measured along the pipe axis.

The travel and run depend on the fitting angle. A fitting is described by how far it bends the pipe away from a straight run: a 45° fitting turns the pipe through 45°, and it is by far the most common because it makes travel and run easy to reason about. Fitters also stock 22.5°, 60°, 30° and 11.25° fittings for shallower or steeper offsets.

How does the calculator work?

Enter the rise and the roll — each has its own unit selector, so you can measure in inches, centimeters, feet or millimeters — then choose the fitting angle. The calculator returns three results, each switchable between the same units:

• True offset — the diagonal distance between the two pipe centrelines.
• Travel — the length of connecting pipe to cut.
• Run — the advance along the original pipe axis.

The rise and roll are combined into the true offset first, and the fitting angle then turns that offset into the travel and the run.

Formulas

The true offset combines the rise and the roll. Because they are perpendicular, it is the Pythagorean hypotenuse of the rise-and-roll triangle. With rise $r$ and roll $R$:

$$O = \sqrt{r^2 + R^2}$$

The connecting pipe (the travel) is the hypotenuse of the triangle formed by the true offset and the fitting angle $\theta$, so:

$$T = \frac{O}{\sin\theta}$$

The run — the advance along the pipe axis — is the adjacent side of that same triangle:

$$N = \frac{O}{\tan\theta}$$

Because the fitting angle is one of a handful of stock values, the calculator uses precomputed multipliers rather than trigonometric functions. For each angle, the travel factor is $1/\sin\theta$ and the run factor is $1/\tan\theta$:

So a shorter way to write the travel and run is:

$$T = O \times f_{T}(\theta), \qquad N = O \times f_{N}(\theta)$$

Worked examples

Example 1: a 45° rolling offset

Two parallel pipes are separated by a rise of 3 in and a roll of 4 in, connected with 45° fittings. First combine the rise and roll into the true offset:

$$O = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \, \text{in}$$

Then apply the 45° factors:

$$T = 5 \times 1.41421356 = 7.071 \, \text{in}$$ $$N = 5 \times 1.00000000 = 5 \, \text{in}$$

So you cut a 7.071 in length of pipe (centre-to-centre between the fittings), and the second run picks up 5 in further along the axis. The 3-4-5 right triangle makes this a textbook case: the true offset is exactly 5 in, and at 45° the run equals the offset.

Example 2: the same offset with 22.5° fittings

Keep the same 3 in rise and 4 in roll, but use shallower 22.5° fittings. The true offset is unchanged at 5 in, but the shallower angle stretches both the travel and the run:

$$T = 5 \times 2.61312593 = 13.066 \, \text{in}$$ $$N = 5 \times 2.41421356 = 12.071 \, \text{in}$$

The connecting pipe is now 13.066 in and the run is 12.071 in — a shallower fitting reaches the same offset over a much longer, gentler diagonal, which is why it is chosen where a 45° elbow would be too abrupt for the flow.

Example 3: the same joint in metric

The identical joint measured in centimeters — a rise of 7.62 cm and a roll of 10.16 cm (which are 3 in and 4 in) — gives the same geometry:

$$O = \sqrt{7.62^2 + 10.16^2} = \sqrt{161.29} = 12.7 \, \text{cm}$$

That 12.7 cm true offset is exactly 5 in, confirming the result is the same whichever unit you enter. Switch any output to centimeters and it converts on the spot.

Practical notes

• Measure centre-to-centre. Rise, roll, travel and run are all pipe-centreline distances. The travel this calculator returns is the length between the centres of the two fittings, so when you cut the pipe you must subtract the fitting take-out (the length each fitting adds) at both ends to get the actual cut length.
• 45° is the default for a reason. At 45° the run equals the true offset and the travel is a tidy 1.414 times it, which makes the layout easy to check by eye. Reach for 22.5° or 11.25° only when a gentler bend is needed, and remember they eat up much more run.
• Rise and roll are interchangeable. The true offset uses rise² + roll², so it does not matter which you call rise and which you call roll — a 3-and-4 joint gives a 5 in offset either way. This is the same right-triangle relationship as the Pythagorean theorem calculator and the hypotenuse calculator.
• Both fittings share the angle. A rolling offset uses a matched pair of fittings of the same angle; the formulas assume both ends bend by the selected $\theta$. Once the run is fixed, the pipe volume calculator helps size the fluid the finished line carries.