Perpendicular pipe saddle coordinates
Mistake: Cutting by contour drop instead of square-end cutback.
Fix: Use the cutback column for the stated square-end baseline; the two columns use opposite reference planes.
Calculators · Free
Perpendicular pipe saddle coordinates
Calculate a round branch pipe’s outside contact contour on a larger round header.
01Enter your values
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02Perpendicular pipe saddle coordinates
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How it works
Calculate a round branch pipe’s outside contact contour on a larger round header.
h(θ) = R − √(R² − r²sin²θ); c(θ) = hmax − h(θ)
Centered perpendicular circular pipes only; branch outside diameter cannot exceed header outside diameter. The table models outside-surface contact, not wall thickness, bevel, weld gap or structural fitness. Cutback and contour drop have opposite references: remove material from the square end by the cutback value. Print scaling is not provided. Works offline after loading. Zero angle lies in the plane containing both pipe axes; the 90° station is transverse to the header axis.
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Inputs are processed on this page and are never sent to a server.
About this tool
Use tool ↑Calculate a round branch pipe’s outside contact contour on a larger round header.
For header radius R, branch radius r and circumferential angle θ, contour drop h=R−sqrt(R²−r² sin²θ). Maximum drop is R−sqrt(R²−r²). Cutback from a square end at the lowest contact plane is maximum drop minus h. Arc distance around the branch is r×θ.
How to use it
- Enter your values
Header outside diameter · Branch outside diameter · Circumference intervals
- Calculate / generate
Calculate a round branch pipe’s outside contact contour on a larger round header.
- Result
Maximum contour drop: 10 mm Branch circumference: 188.49556 mm
Calculation method
- For header radius R, branch radius r and circumferential angle θ, contour drop h=R−sqrt(R²−r² sin²θ).
- Maximum drop is R−sqrt(R²−r²).
- Cutback from a square end at the lowest contact plane is maximum drop minus h.
- Arc distance around the branch is r×θ.
h(θ) = R − √(R² − r²sin²θ); c(θ) = hmax − h(θ)
Perpendicular pipe saddle coordinates
- Header outside diameter
- 100 mm
- Branch outside diameter
- 60 mm
- Circumference intervals
- 12
Result
Maximum contour drop: 10 mm Branch circumference: 188.49556 mm
Frequently asked questions
What does this result assume?
Centered perpendicular circular pipes only; branch outside diameter cannot exceed header outside diameter. The table models outside-surface contact, not wall thickness, bevel, weld gap or structural fitness. Cutback and contour drop have opposite references: remove material from the square end by the cutback value. Print scaling is not provided. Works offline after loading. Zero angle lies in the plane containing both pipe axes; the 90° station is transverse to the header axis.
Where does my data go?
Calculations run on your device. Form inputs are not sent to a server.
Terms and definitions
Enter your values
- Measurement system
The initial choice follows your browser region. Your choice is remembered on this device. Gallons are US gallons. Switching units keeps your numbers unchanged and interprets them in the new unit.
Numbers stay unchanged. Check the new unit and enter the intended measurement, or select an example for that system.
- Header outside diameter
Outside diameter of the main pipe.
Enter a numerical value for this quantity. Use the unit shown beside this field. mm / in
Minimum: 1e-9 · Maximum: 1000000000000 mm
- Branch outside diameter
Outside diameter of the perpendicular branch pipe.
Enter a numerical value for this quantity. Use the unit shown beside this field. mm / in
Minimum: 1e-9 · Maximum: 1000000000000 mm
- Circumference intervals
Number of equal intervals around the branch; at least four. The closing row repeats the starting position.
Enter a whole number; fractional counts are not valid.
Minimum: 4 · Maximum: 10000
Result
- Result
For header radius R, branch radius r and circumferential angle θ, contour drop h=R−sqrt(R²−r² sin²θ). Maximum drop is R−sqrt(R²−r²). Cutback from a square end at the lowest contact plane is maximum drop minus h. Arc distance around the branch is r×θ.
Calculated from your entries using the method below.
- Maximum contour drop
Difference between highest and lowest contact planes.
Calculated from your entries using the method below.
- Branch circumference
Outside circumference used for the unwrapped coordinate table.
Calculated from your entries using the method below.
- Station number
Sequential position around the pipe.
Calculated from your entries using the method below.
- Distance around branch · mm
Unwrapped arc distance from the chosen zero-angle generator.
Calculated from your entries using the method below.
- Contour drop · mm
Distance below the highest contact plane.
Calculated from your entries using the method below.
- Cutback from square end · mm
Material cut back from the lowest-contact square-end reference; not contour drop.
Calculated from your entries using the method below.
Common mistakes and quick fixes
Limits and key assumptions
- Centered perpendicular circular pipes only; branch outside diameter cannot exceed header outside diameter. The table models outside-surface contact, not wall thickness, bevel, weld gap or structural fitness. Cutback and contour drop have opposite references: remove material from the square end by the cutback value. Print scaling is not provided. Works offline after loading. Zero angle lies in the plane containing both pipe axes; the 90° station is transverse to the header axis.
- Displayed results may be rounded; rounding does not add measurement precision.