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Tee and branch pipe flat pattern
Enter both diameters, the branch height from the main pipe axis, the main pipe length and the angle between the axes.
The branch of a pipe tee is cut to the curve where it meets the main pipe, and the main pipe gets a matching hole. For a 200 mm main pipe and a 100 mm branch at 90°, with the open end 250 mm from the main pipe axis, the branch blank is 314.2 mm wide and 150.0 to 163.4 mm tall, and the 400 mm main pipe blank is 400 x 628.3 mm with the hole in its middle.
| Piece | Qty | Flat size, mm | Area, mm² | Cut length, mm |
|---|---|---|---|---|
| Branch pipe | 1 | 314.2 × 163.4 | 49,190.6 | 933.9 |
| Main pipe with hole | 1 | 400 × 628.3 | 243,207.2 | 2,376.3 |
Patterns are developed at mid-thickness. An inside dimension is increased by the thickness, an outside dimension is reduced by it.
CutMeter is software. Check every result before you cut or bend. The person who approves the part is responsible for its dimensions.
Formula
For the point at angle φ round the branch, the distance along the branch axis from the main pipe axis to the intersection is s(φ) = (sqrt(R² - r² sin² φ) - r cos φ cos β) / sin β. The branch blank is 2 x pi x r wide, and the cut line lies g(φ) = H - s(φ) above the open end. In the main pipe the hole point lies s cos β - r cos φ sin β along the pipe from the branch axis and R x atan2(r sin φ, s sin β + r cos φ cos β) round it from the top line.
R = main pipe diameter / 2; r = branch diameter / 2 (r ≤ R); β = angle between the axes, 30° to 90°; H = height of the open branch end above the main pipe axis, along the branch axis. The main pipe seam is at its bottom.
Both pipes are developed at mid-thickness. No bevel or wall correction for set-on or set-in branches is applied, and the axes must intersect. H must be more than (R + r |cos β|) / sin β.
Worked example
Main pipe 200 mm, branch 100 mm, branch height 250 mm, main pipe length 400 mm, angle 90°, thickness 2 mm, mid-thickness dimensions.
At φ = 0° the branch meets the main pipe at s = 100 mm, so g = 250 - 100 = 150.0 mm. At φ = 90°, s = sqrt(100² - 50²) = 86.6 mm, so g = 163.4 mm.
Branch: 314.2 x 163.4 mm, area 49,190.6 mm², cut length 933.9 mm. Main pipe with hole: 400.0 x 628.3 mm, area 243,207.2 mm², cut length 2,376.3 mm including the hole.
Branch cut line every 30°
| Angle round the branch, ° | Distance along the blank, mm | Cut line height, mm |
|---|---|---|
| 0 | 0 | 150 |
| 30 | 26.18 | 153.175 |
| 60 | 52.36 | 159.861 |
| 90 | 78.54 | 163.397 |
| 120 | 104.72 | 159.861 |
| 150 | 130.9 | 153.175 |
| 180 | 157.08 | 150 |
| 210 | 183.26 | 153.175 |
| 240 | 209.44 | 159.861 |
| 270 | 235.62 | 163.397 |
| 300 | 261.8 | 159.861 |
| 330 | 287.98 | 153.175 |
| 360 | 314.16 | 150 |
Questions about tee flat patterns
How do I make a pipe tee template?
Enter both diameters, the branch height from the main pipe axis, the main pipe length and the angle. You get the branch blank with its curved cut line and the main pipe blank with the hole, as one DXF.
Can the branch be at an angle?
Yes, from 30° to 90° between the axes. At 45°, with the example sizes, the branch blank is 314.2 x 158.6 mm.
Does it work for an equal tee?
Yes. The branch may be as wide as the main pipe but not wider. For two 200 mm pipes the branch cut line runs from 150 to 250 mm above the open end.
Is the wall thickness taken into account?
Both pipes are developed at mid-thickness, so inside or outside diameters are converted by the thickness. Bevels and set-on or set-in corrections are not applied.
What is in the DXF?
The branch blank and the main pipe blank side by side, 20 mm apart, on layer CUT.