Piping
45 degree parallel pipe offset formula
In short
To offset parallel pipes and keep their spacing e, each line starts its elbows d = e × tan(α / 2) further on than the previous one. Every line then has the same travel T = H / sin α and the same cut length L = T − 2E − 2j.
Calculation
Example calculated with the tool’s default values.
Inputs
- Pipe
- DN50 · 60.3 × 2.9 mm
- Number of lines
- 3
- Line spacing (centre to centre)
- 150 mm
- Offset (axis to axis)
- 300 mm
- Elbow angle
- 45°
- Elbow radius
- Bought long-radius elbow (EN 10253-2 3D or ASME B16.9 LR per pipe)
- Root gap
- 0 mm
Results
- Start shift between two lines
- 62.1 mm
Worked example
Every value in this section belongs to the example, calculated with the tool’s default values.
Other results of the example
- Cut length (every line)
- 361.3 mm
- Travel
- 424.3 mm
- Run
- 300.0 mm
- Spread of sloped lines, along the run
- 212.1 mm
- Start shift line 1 → last
- 124.3 mm
- Radius used
- 76.0 mmEN 10253-2 3D elbow
- Line 1 = inside line of the first elbow (on the side the offset goes): the others start further on.
Step-by-step calculation
Start shift
d = e × tan(α / 2)
150.0 × tan 22.50° = 62.1 mm
Spread along the run
e′ = e / sin α
150.0 / sin 45.00° = 212.1 mm
Travel
T = H / sin α
300.0 / sin 45.00° = 424.3 mm
Elbow take-out
E = R × tan(α / 2)
76.0 × tan 22.50° = 31.5 mm
Cut length
L = T − 2E − 2j
424.3 − 63.0 − 0.0 = 361.3 mm
Elbow start per line (from line 1)
| Line | Start shift (mm) | Travel (mm) | Cut length (mm) |
|---|---|---|---|
| 1 | 0.0 | 424.3 | 361.3 |
| 2 | 62.1 | 424.3 | 361.3 |
| 3 | 124.3 | 424.3 | 361.3 |
How to use it
- Pick the pipe: outside diameter and wall thickness.
- Enter the number of lines (2 to 20), their spacing measured square to the pipes in the offset plane, and the axis-to-axis offset.
- Enter the elbow angle, the elbow radius and the root gap.
- Read the start shift between two lines.
Frequently asked questions
What is the 45 degree parallel offset formula?
With a 150 mm spacing and 45° elbows: d = 150 × tan 22.5° = 62.1 mm between two neighbouring lines. Along the run, the spread of the sloped pipes is e′ = e / sin α = 150 / sin 45° = 212.1 mm.
How does a parallel pipe offset work?
The elbow vertices line up on the bisector of the angle. Each line therefore starts its elbows d = e × tan(α / 2) further on than the previous one, starting from line 1, the inside line of the first elbow (on the side the offset goes). The spacing e stays the same in the sloped part.
What is the equal offset pipe formula for the cut length?
Every line has the same cut length. Example for three 60.3 × 2.9 pipes, a 300 mm offset and long radius 45° elbows: travel 300 / sin 45° = 424.3 mm, elbow take-out 90.4 × tan 22.5° = 37.5 mm, cut length 424.3 − 74.9 = 349.3 mm for each line, with no root gap.
What spacing should the pipes have?
The spacing must be larger than the outside diameter, otherwise the pipes touch and the calculation is refused. When the gap between pipes (spacing − OD) is under 50 mm, the calculation asks you to check room for welding and insulation.
Limits
Indicative results. The lines lie in the same offset plane, at a constant spacing, with identical elbows. Outside 45° and 90°, each elbow is cut from a 90° elbow and its take-out is taken as R × tan(α / 2); the 1.5 D and 1 D radii are approximated on the outside diameter.
Sources
- Géométrie du dévoiement : Trigonométrie du triangle rectangle (T = S / sin α, A = S / tan α, E = R × tan(α / 2))
- Lignes parallèles au même dévoiement : Géométrie : sommets des coudes alignés sur la bissectrice, décalage e × tan(α / 2) entre lignes voisines
- EN 10253-2:2021+A1:2026 (raccords à souder bout à bout) : Coudes 2D/3D (rayon R), tés égaux (F), réductions (L) ; tableaux Zickwolff, consultés le 08/11/2026 (link)