These are the 3 basic trigonometry functions, based on a right triangle:
cos(angle) = adjacent / hypotenuse
tan(angle) = opposite / adjacent
Mnemonic: SOH-CAH-TOA
- Sin = Opposite / Hypotenuse
- Cos = Adjacent / Hypotenuse
- Tan = Opposite / Adjacent
In pipe fitting: Used to calculate heights, lengths, and cut angles.
If you know two sides of a right triangle, you can find the angle with inverse functions:
angle = arcsin(opposite / hypotenuse)
angle = arccos(adjacent / hypotenuse)
Concrete example:
Simple offset with H = 100 mm and Run = 150 mm:
angle = arctan(0.667)
angle = 33.7°
Two ways to measure angles:
- Degrees: full circle = 360°
- Radians: full circle = 2π ≈ 6.28
Conversion:
degrees = radians × 180 / π
In practice:
- In the field → degrees (more intuitive)
- In formulas/code → often radians
Common angles: 90° = π/2 | 45° = π/4 | 30° = π/6
A generator line is a vertical line on the pipe surface used as a reference for layout.
- We divide the circumference into equal parts (often 12)
- Each division = a numbered generator (0, 1, 2... 11)
- We calculate the cut height at each generator
- We connect the points = cutting curve
More generators = more precise layout.
A flat pattern is the pipe "unrolled" flat. It gives you a cutting template.
- The circumference becomes a straight line
- X = position on circumference = R × θ
- Y = cut height at that point
Usage:
- Print the development at 1:1 scale
- Wrap around the pipe
- Trace the curve
- Cut!
A branch = a small pipe entering a larger one. The cut curve looks like a saddle (fish mouth).
Formula (90° perpendicular branch):
Where:
- R₁ = radius of the header pipe
- R₂ = radius of the branch pipe
- θ = generator angle (0° to 360°)
Steps:
- Calculate z for each generator
- Mark the heights on the pipe
- Connect the points
- Cut!
A Rolled Offset is a 3D offset with:
- H = vertical height
- DEP = lateral offset
Using 45° elbows, the assembly can be done flat on the workbench — that's the main advantage!
Our calculator gives you the sleeve length and the rotation angle to apply.
Simple Offset (2D):
- Offset in one plane
- 2 elbows, 1 sleeve
- To shift a line by a few inches
S-Offset (beam clearance):
- Double offset to clear an obstacle
- 4 elbows, 3 sleeves
- Goes up, across, and back down
Yes. The formulas are based on:
- Triouleyre methods (reference in pipe layout)
- ASME and EN standards
- 25 years of field experience
Results have been verified on real production cases.
Yes, 100% free.
- No registration
- No usage limits
- No "premium" version
Personal use, professional use, or training — everything is free.
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