FitUp

Guide · Offsets

Rolling offset formula: true offset, travel, and run

Short answer

True offset = √(rise² + roll²). Then travel = true offset ÷ sin(angle) and run = true offset ÷ tan(angle). With 45s, the travel is the true offset × 1.414 and the run equals the true offset. An 8 inch rise and a 16 inch roll give a true offset of 17.889, a 45 degree travel of 25.298, and a run of 17.889. Take off two take-outs and two gaps for the cut.

A rolling offset moves the line in two directions at once, up and over. The trick is that the pipe still makes an ordinary offset; it just makes it on a diagonal. Find that diagonal, the true offset, and the rest is the simple offset formula.

A rolling offset drawn as a box: rise 8, roll 16, true offset 17.889 across the end of the box, run 17.889 at 45 degrees, travel 25.298 corner to corner rise 8 roll 16 true offset 17.889 run 17.889 travel 25.298
The pipe runs corner to corner through a box. The true offset (solid diagonal on the end of the box) comes from rise and roll. At 45 degrees the run equals the true offset.

How the box works

Picture the offset inside a box. The rise is the height of the box, the roll is its width, and the run is its length along the line. Looking down the pipe, the true offset is the diagonal across the end of the box, which is why it comes from rise and roll by Pythagoras. The travel runs from one corner of the box to the opposite corner.

That gives a check you can do in your head: travel² = rise² + roll² + run². For the example above, 8² + 16² + 17.889² = 64 + 256 + 320 = 640, and √640 = 25.298.

Fitters name the two sides differently: rise and roll, set and rise, vertical and horizontal offset. The formula does not care which is which, only that the two are measured square to each other.

Measuring the rise and the roll

  • Rise: the vertical distance between the two centerlines, measured plumb with a level or a plumb bob.
  • Roll: the horizontal distance between the same centerlines, measured level and square to the run.
  • Measure both to centerlines. On same-size pipe, the same side of both pipes works too.

Steps

  1. Square and add

    Rise² + roll².

  2. Take the square root

    That is the true offset.

  3. Travel from the angle

    True offset × the travel multiplier: 1.414 for 45s, 2.613 for 22.5s, 2.000 for 30s, 1.155 for 60s.

  4. Run from the angle

    True offset × the run multiplier, to place the second fitting along the line.

  5. Cut length

    Travel minus two take-outs and, for butt welds, two gaps. Round once.

Worked examples

8 inch rise, 16 inch roll, 45s on 2 inch pipe

True offset = √(64 + 256) = 17.8885 Travel = 17.8885 × 1.4142 = 25.2982 Run = 17.8885 Cut = 25.2982 − 2 × 1.375 − 2 × 0.125 = 22.2982, marked 22 5/16

12 inch rise, 9 inch roll, center to center

True offset = √(144 + 81) = 15 Travel = 15 × 1.4142 = 21.2132, marked 21 3/16 Run = 15

A 3-4-5 shape in disguise: 9, 12, 15. When the rise and roll fall into those ratios the true offset comes out even.

When the run is fixed: the setback method

If a wall or a valve decides how much run you have, work backward. The travel is the corner-to-corner diagonal of a box whose length is the setback:

Travel = √(true offset² + setback²) Fitting angle = atan(true offset ÷ setback)

A 3 inch rise and a 4 inch roll give a 5 inch true offset. In a 12 inch setback, the travel is √(25 + 144) = 13 and the fittings must be cut to atan(5 ÷ 12) = 22.6 degrees. A factory 45 would not fit here; a 90 cut down to 22.6 degrees would. The cut-down elbow guide gives its take-out.

How far to roll the fittings

The two fittings are turned off plumb so the travel points along the true offset. That roll angle is atan(roll ÷ rise) measured from plumb. For an 8 inch rise and a 16 inch roll it is atan(2) = 63.4 degrees off plumb, or 26.6 degrees off level. The two fittings and the travel all lie in one tilted plane, so both fittings are rolled the same amount off plumb and the two runs stay parallel.

Common mistakes

  • Using the rise or the roll as the offset. The pipe crosses the diagonal, so only the true offset gives the right travel.
  • Adding rise and roll. 8 + 16 is 24; the true offset is 17.889. Adding overshoots by more than 6 inches here.
  • Measuring the roll on an angle. The roll has to be square to the run, or the box is not a box.
  • Using the 45 run at another angle. The run equals the true offset only with 45s.
  • Cutting the travel. The travel is center to center; take off the fittings and the gaps.

Related questions

Run one now

The rolling offset calculator does the box, the travel, the run, and the cut, with a setback option. In the FitUp app, ten rolling offsets at 45 degrees a month are free, saved to a cut list.

Verify measurements before cutting.