Enter the run between angles, horizontal offset, and vertical offset into the calculator to determine the travel of the rolling offset.
Rolling Offset Formula
The calculator solves a rolling offset in two steps. First it finds the true offset from the rise and roll, then it divides by the sine of the elbow angle to get center-to-center travel.
True offset = sqrt(Rise^2 + Roll^2) Travel = True offset / sin(Angle) Cut length = Travel - 2 * Takeoff
- Rise: vertical distance between pipe centerlines (or absolute difference of start and end elevations)
- Roll: horizontal offset between the two pipe runs measured in plan view
- Angle: elbow angle used at both ends (45°, 22.5°, 30°, 60°, 90°, or custom)
- Travel: center-to-center length between the two elbows
- Takeoff: distance from the fitting centerline to the end of the socket or thread
- Cut length: pipe length to cut after subtracting two takeoffs
Both elbows are assumed to be the same angle. The travel sits along the slope of the offset, so the same multiplier works whether you call the vertical leg rise or drop. If you leave takeoff blank, the headline result is travel rather than cut length.
Fitting Multipliers and Common Values
The travel multiplier is 1 / sin(angle). Use the table below to sanity-check the calculator output.
| Elbow Angle | Travel Multiplier | Notes |
|---|---|---|
| 11.25° | 5.126 | Long travel, gentle bend |
| 22.5° | 2.613 | Common for shallow offsets |
| 30° | 2.000 | Clean 2x of true offset |
| 45° | 1.414 | Most common rolling offset |
| 60° | 1.155 | Tight, near-square turn |
| 90° | 1.000 | Travel equals true offset |
Typical fitting takeoffs vary by material and pressure rating. Confirm against the fitting manufacturer if you need exact numbers.
| Pipe Size | PVC 45° (in) | Copper 45° (in) | Steel 45° (in) |
|---|---|---|---|
| 1/2" | 0.50 | 0.38 | 0.62 |
| 3/4" | 0.62 | 0.44 | 0.75 |
| 1" | 0.75 | 0.50 | 0.88 |
| 1-1/2" | 1.00 | 0.69 | 1.12 |
| 2" | 1.25 | 0.81 | 1.38 |
| 3" | 1.75 | 1.12 | 1.88 |
Worked Example
You need to route around an obstacle. The pipe must drop 12 inches and shift 16 inches sideways, using two 45° elbows.
- True offset = sqrt(12² + 16²) = sqrt(144 + 256) = sqrt(400) = 20 in
- Travel = 20 / sin(45°) = 20 / 0.7071 = 28.28 in
- With a 1 in takeoff per fitting: cut length = 28.28 - 2(1) = 26.28 in
FAQ
Does it matter if the pipe rises or drops? No. The formula squares the vertical leg, so direction does not change the result.
Can I use different angles at each end? No. This calculator assumes matching elbows. Mixed-angle layouts need a different geometric approach.
Why is my cut length negative? Two takeoffs are longer than the calculated travel. Either the offset is too small for the elbow size you picked, or the takeoff value is wrong.
What is the difference between travel and true offset? True offset is the straight-line distance between the two pipe centerlines. Travel is the longer length measured along the diagonal pipe between the two elbow centers.
