45° rolling offset

From rise and roll to travel

A rolling offset moves a pipe both vertically and sideways. For two equal 45° bends connecting parallel pipe axes, combine those two movements first. Do not multiply the rise alone by 1.414.

True offset = √(rise² + roll²)
Travel = true offset ÷ sin(45°)

With 180 mm rise and 240 mm roll, the true offset is 300 mm and travel is 424.3 mm, rounded to 0.1 mm. Travel is the diagonal centreline distance between bend centres, not automatically the straight pipe cut length.

1. Combine rise and roll

Measure centreline-to-centreline rise and sideways displacement in the plane perpendicular to the starting pipe axis. Here, both are positive distances. Use one unit throughout.

√(180² + 240²) = √90,000 = 300 mm

2. Calculate travel and run

The bend angle is measured between the diagonal connector axis and the starting pipe axis. In this triangle, sine is opposite divided by hypotenuse, so travel = true offset ÷ sin(angle).

Travel = 300 ÷ sin(45°) = 424.264… mm
Run = 300 ÷ tan(45°) = 300 mm

Run is the advance along the starting pipe axis. At 45°, run equals true offset. That shortcut does not apply at other bend angles.

Same 180 mm rise and 240 mm roll, different equal bend angles:

• 30°: travel 600.0 mm; run 519.6 mm.

• 45°: travel 424.3 mm; run 300.0 mm.

• 60°: travel 346.4 mm; run 173.2 mm.

The familiar 1.414 multiplier is a rounded 45° shortcut. Use the full calculation until the final displayed result.

3. Keep travel separate from cut length

For a straight connector between fittings, subtract the takeout at each end and any required end gaps, all measured along that connector. Obtain those deductions for the actual fittings and joint preparation; this example supplies no fitting dimensions.

For arithmetic practice only, suppose each takeout is 25 mm and each gap is 2 mm:

Cut length = travel − 25 − 25 − 2 − 2
= 424.264… − 54 = 370.264… mm
Displayed to 0.1 mm: 370.3 mm

Do not use the example deductions on a real fitting. A zero or negative result means the entered deductions leave no positive straight connector. Check the measurements and layout rather than cutting from that result.

Geometry only. Verify inputs, fitting deductions, and field dimensions before cutting. This guide does not check bend-radius development, interference, tolerances, pressure requirements or installation rules.

Check the example in OffsetKit

1. In Settings, choose Metric and 0.1 mm display precision.

2. Select Rolling offset. Enter rise 180, side (roll) 240 and bend angle 45°.

3. Check true offset 300.0 mm, travel 424.3 mm and run 300.0 mm.

4. Open Connector deductions. Enter 25 for both takeouts and 2 for both gaps. The straight cut length should display 370.3 mm.

You can work through the formulas above with a scientific calculator. For repeated layouts, OffsetKit for Android keeps the geometry and entered deductions together.

Math background: OpenStax, Precalculus 2e, 5.4: Right Triangle Trigonometry, for sine, cosine and tangent relationships. The worked dimensions and diagrams here are original examples, not manufacturer data.