Set-on vs set-in — which radius is used?

Set-on / miter intersect the header OD. Set-in intersects the header ID (through-hole). The calculator switches R_H accordingly.

Can branch NPS be larger than header NPS?

No for standard fitting practice. The UI blocks / warns when Branch NPS > Header NPS.

Does this calculate reinforcement pad size?

No. Use ASME B31.3 Paragraph 304.3 (or your project calc) for reinforcement. This tool only produces the cut layout template.

Pipe Coping & Branch Cut Layout — 2" on 2" Sch 40 · 60° | FieldEngineersKit

Parameter	Value
Header NPS	2"
Branch NPS	2"
Schedule	Sch 40
Intersection angle θ	60°

Engineering Reference & ASME Code Basis

1. Core Formula & Variable Definitions

ASME B31.3 (2022 Edition) · (Process Piping) — fabrication / branch connection practice · ASME B36.10M / B36.19M (Pipe OD & wall by NPS × schedule) · PIP fabrication practices (shop layout screening)

x = r_B·sin(φ) + e · y = r_B·cos(φ)

z_H = √(R_H² − x²) · z_cut = z_H / sin(θ) − y·cot(θ)

S = r_B·φ · Δz_max = max(z_cut) − min(z_cut)

ASME B31.3 fabrication screening · PIP shop layout practice

θ range 30°–90°Ordinates 16 / 32 ptsCuts Set-on · Set-in · MiterΔz_max Peak-to-valley

This calculator builds an unwrapped flat-pattern cut line for a branch pipe intersecting a header. Set-on / miter use the header OD envelope; set-in uses the header ID. Layout points (16 or 32) give shop marking distances S and relative cut offsets. Confirm bevel angle and branch reinforcement per ASME B31.3 Paragraph 304.3 — this is a fabrication aid, not a reinforcement design.

R_H (Header radius) — Header OD/2 for set-on/miter, or header ID/2 for set-in through-hole cuts.
r_B (Branch radius) — Branch outside radius (OD/2) used for the unwrapped circumference.
θ (Intersection angle) — Angle between branch axis and header axis (90° = orthogonal tee).
e (Eccentricity) — Lateral offset of the branch centerline. Max ≈ (OD_H − OD_B)/2 for concentric-to-eccentric range.
z_cut (Axial cut offset) — Distance along the branch axis from a reference plane to the header surface at angle φ.
Δz_max (Peak-to-valley depth) — max(z_cut) − min(z_cut) — primary wrap-template height.

2. Allowances, Tolerances & Standards

Use the ordinate table as a wrap-around marking guide. Bevel and reinforcement are separate code checks.

Bevel37.5° ± 2.5° typical

Apply weld bevel along z_cut after transferring the template (project WPS governs).

ReinforcementB31.3 §304.3

Verify pad / integrally reinforced branch / Weldolet requirements separately.

Branch ≤ headerNPS rule

Branch NPS must not exceed header NPS for standard set-on / set-in fittings.

Quick Reference Lookup Table

Example orthogonal set-on screening (illustrative)
Branch on header	Sch	θ	Focus metric
4" on 6"	40	90°	Δz_max + 16-pt table
3" on 6"	40	90°	Δz_max + 16-pt table
4" on 8"	40	45°	Angled branch template
6" on 8"	80	60°	Heavier wall envelope
2" on 4"	40	90°	Small-bore set-on

3. Material & Code Limitations

Screening tool for circular pipe-on-pipe intersections. Not for square headers, saddles with pad geometry, or CNC lofting replacement.

Material Group	Temperature Range	Allowable Stress / Limit	Engineering Notes
Carbon / alloy / stainless pipe	Geometry only (no T-limit in this tool)	N/A — not a stress calc	Uses B36 OD/ID. Actual mill OD/wall may differ slightly from catalog.
High-pressure process	Per project piping class	Verify separately (B31.3 §304.3)	Always verify branch reinforcement and WPS bevel requirements before hot work.

Code Applicability & Safety Boundaries

Fabrication layout aid only — does not size reinforcement pads, integrally reinforced branches, or Weldolets (ASME B31.3 §304.3).
Assumes circular pipe OD/ID envelopes from ASME B36 tables; do not use for square headers, structural tube, or cast fittings with non-circular hubs.
Bevel angle, root face, and WPS acceptance criteria are outside this tool — transfer the template, then prepare the joint per the approved procedure.
Eccentric / angled cases are geometric screening; always verify fit-up on the header before hot work when offset approaches (OD_H − OD_B)/2.

4. Step-by-Step Worked Example

Field VerificationShow

Step-by-Step Worked Example: 4" Sch 40 branch on 6" Sch 40 header @ 90°

Generate a set-on wrap template for an NPS 4 Sch 40 branch onto an NPS 6 Sch 40 header at θ = 90° (orthogonal tee), concentric (e = 0), using 16 layout points. OD values come from ASME B36.10M.

Header:NPS 6 Sch 40 · OD 168.28 mmBranch:NPS 4 Sch 40 · OD 114.30 mmAngle θ:90° (orthogonal)Offset e:0 mm (concentric)Cut type:Full-size set-on (header OD envelope)Ordinates:16 points

Resolve radii from B36 OD

R_{H} = O D_{H} /2, r_{B} = O D_{B} /2

R_H = 168.28 / 2 = 84.14 mm · r_B = 114.30 / 2 = 57.15 mm

Result:R_H = 84.14 mm, r_B = 57.15 mm

Set-on uses header OD radius. Set-in would use header ID/2 instead.

Evaluate surface depth at key φ

x = r_{B} sin ϕ + e, z_{H} = max (0, R_{H}^{2} - x^{2})

At φ = 0° (crotch): x = 0 → z_H = R_H = 84.14 mm. At φ = 90° (flank): x = 57.15 → z_H = √(84.14² − 57.15²) ≈ 61.72 mm.

Result:z_H(0°) ≈ 84.14 mm · z_H(90°) ≈ 61.72 mm

Convert to axial cut offset at θ = 90°

z_{cut} = \frac{z _{H}}{sin θ} - y cot θ

θ = 90° → sinθ = 1, cotθ = 0 → z_cut(φ) = z_H(φ). So crotch and flank offsets equal the surface depths above.

Result:z_cut(0°) ≈ 84.14 mm · z_cut(90°) ≈ 61.72 mm

Report peak-to-valley template height

Δ z_{m a x} = max z_{cut} - min z_{cut}

Δz_max ≈ 84.14 − 61.72 = 22.42 mm (wrap height from valley baseline). Mark S = r_B·φ along the branch OD, then transfer z_rel = z_cut − min(z_cut).

Result:Δz_max ≈ 22.4 mm for this 4" on 6" Sch 40 @ 90° case

Use the live ordinate table for all 16/32 shop marks. Confirm bevel and B31.3 §304.3 reinforcement separately.

Conclusion: The wrap template height is Δz_max ≈ 22.4 mm for a concentric 4"×6" Sch 40 orthogonal set-on. Open the matching spec URL (/4-on-6-sch-40-90deg), copy the ordinate table, mark the branch OD, cut, then bevel per the project WPS.

5. Frequently Asked Questions & Technical References

Show

Δz_max is the peak-to-valley height of the unwrapped cut curve — the amount of material you remove axially between the deepest and shallowest marks when wrapping the template.