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Equipment Nozzle Load Check Calculator (API 610 / NEMA SM-23)

Returns the per-component unity ratios |applied|/allowable at an equipment nozzle, the governing component, and the resultants F_R and M_R. Allowables come from the governing standard — API 610 §5.4, NEMA SM 23 §8.4, API 650 Annex P — and stay user inputs; none are embedded.

Compares the six applied load components at an equipment nozzle — F_x, F_y, F_z, M_x, M_y, M_z from your flexibility analysis — against the allowables for that nozzle size, and reports the unity ratio of each, the governing component, and the resultants F_R and M_R. The allowable-load tables in API 610, API 560, API 660, API 661, API 650, API 620 and NEMA SM 23 are copyrighted and are not embedded: you enter the allowables for your nozzle size from the governing standard or the vendor datasheet, and the standard you pick is a report label only. This page, its method and its worked example are free to read; opening the live calculator on the Equipment line requires a Pro subscription — see pricing.

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Method

The check is a per-component unity ratio. Every component is tested independently against its own allowable, and the largest ratio governs the result:

r_i = |applied_i| / allowable_i for i = F_x, F_y, F_z, M_x, M_y, M_z

r_max = max(r_i) governing = the i that produced r_max

F_R = √(F_x² + F_y² + F_z²) M_R = √(M_x² + M_y² + M_z²)

status = PASS if r_max ≤ 1, otherwise FAIL

where applied_i is the load component transmitted by the piping to the nozzle, taken from the flexibility model in the axis system the equipment standard defines, and allowable_i is the limit for that component at that nozzle size, read from the governing standard's table or the vendor datasheet. The absolute value is taken, so a sign convention error in the model will not be caught here. F_R and M_R are the vector resultants of the applied loads, reported for the record — they are not compared against any allowable, because most standards limit components (and combinations), not the bare resultant. Ratios are reported to five decimals, resultants to two. A zero or negative allowable is rejected rather than silently divided by.

Inputs
standard	Governing standard label for the report (API 610, 560, 660, 661, 650, 620, NEMA SM-23, or vendor datasheet) — selects nothing in the arithmetic	—
NPS	Nozzle nominal size — tells you which row of the allowable table to read; it does not enter the calculation	in
F_x, F_y, F_z	Applied nozzle forces from the piping flexibility analysis	lbf
M_x, M_y, M_z	Applied nozzle moments from the piping flexibility analysis	ft·lb
F_x,all, F_y,all, F_z,all	Allowable forces for that nozzle size — user-supplied from the governing standard or datasheet	lbf
M_x,all, M_y,all, M_z,all	Allowable moments for that nozzle size — user-supplied from the governing standard or datasheet	ft·lb
Outputs
F_R	Resultant applied force, √(F_x² + F_y² + F_z²) — reported, not checked	lbf
M_R	Resultant applied moment, √(M_x² + M_y² + M_z²) — reported, not checked	ft·lb
ratios	The six per-component unity ratios \|applied\|/allowable	—
maxRatio	Largest of the six component ratios	—
governing	Component that produced maxRatio	—
status	PASS when every component ratio is ≤ 1, otherwise FAIL	—

Limitations — what this calculator is not

Component check only — it does not evaluate the combined criteria that most standards layer on top: NEMA SM 23's combined-resultant / 3F + M index and API 617 rotating-equipment limits are handled by the NEMA SM-23 / API 617 Combined Index calculator on the same Equipment line, and API 610 Annex F resolution of all nozzle loads to the pump centreline is a separate check. A PASS here is necessary, not sufficient.
No allowable-load table is embedded for any standard. The standard field is a report label; you supply the allowables for your nozzle size from the governing edition or the vendor datasheet, and selecting the correct table row (size, rating, material, temperature, anchored vs. unanchored) is the engineer's responsibility.
No local shell or nozzle-junction stress is computed — nothing here tells you the stress in the vessel wall at the nozzle. Use the Shell Nozzle Loads calculator (WRC 107/297, BPVC Section VIII Div 2 Part 5) for that, or PiperFEA for a finite element nozzle/shell model.
Ratios use absolute values, so the tool cannot detect a mismatch between your pipe-stress model's axis system and the axis system the equipment standard defines. Align the axes before entering loads.
It does not produce the applied loads — they come from your flexibility analysis (ASME B31.3 ¶319.4.4). Nozzle flexibility, equipment thermal growth, settlement, cold spring and bolt-up effects must already be in that model.
No flange leakage, gasket seating or bolt-stress check at the nozzle joint — use the Section VIII Appendix 2 bolted flange calculator on the Auxiliary line.

Worked example — fixture-verified

NPS 6 discharge nozzle on an API 610 centrifugal pump. The flexibility model delivers Fx 100, Fy 200, Fz 200 lbf and Mx 300, My 400, Mz 0 ft·lb. The allowables read from the governing standard's table for that nozzle size are 400 lbf on each force component and 600 ft·lb on each moment component.

Given
Governing standard	API 610	—
Applied Fx	100	lbf
Applied Fy	200	lbf
Applied Fz	200	lbf
Applied Mx	300	ft·lb
Applied My	400	ft·lb
Applied Mz	0	ft·lb
Allowable force, each component	400	lbf
Allowable moment, each component	600	ft·lb

Step by step

Resultant force: F_R = √(100² + 200² + 200²) = √(10,000 + 40,000 + 40,000) = √90,000 = 300 lbf.
Resultant moment: M_R = √(300² + 400² + 0²) = √(90,000 + 160,000 + 0) = √250,000 = 500 ft·lb.
Force ratios: F_x 100/400 = 0.25; F_y 200/400 = 0.50; F_z 200/400 = 0.50.
Moment ratios: M_x 300/600 = 0.50; M_y 400/600 = 0.66667; M_z 0/600 = 0.
Largest of the six: 0.66667 at M_y. Since r_max ≤ 1, every component is inside its allowable and the check returns PASS.
Note what was not compared: F_R = 300 lbf and M_R = 500 ft·lb are reported for the record only — no resultant allowable is applied, and the API 610 combined criteria are a separate check.

Result PASS
Resultant force FR	300	lbf
Resultant moment MR	500	ft·lb
Max unity ratio	0.66667	—
Governing component	My	—

My carries the least margin at 0.66667 — it is the component to watch if the routing, the support scheme or the operating temperature changes. Push any component past 1.0 and the status flips to FAIL and names that component instead.

Why you can trust these numbers: this exact case is fixture nozzle-load-check.json — case “API 610 style, all components within allowables -> pass” (tolerance 0.00001) — in the calc-core release gate. It re-runs on every commit; a red fixture blocks deployment. See the validation methodology.

Additional verified cases in this fixture

NEMA SM23 style, Fz over allowable -> fail FAIL

input:  {"standard":"NEMA SM23","applied":{"Fx":100,"Fy":200,"Fz":500,"Mx":300,"My":400,"Mz":0},"allowable":{"Fx":400,"Fy":400,"Fz":400,"Mx":600,"My":600,"Mz":600}}
expect: {"maxRatio":1.25,"governing":"Fz"}
tol:    0.00001

Sources & citations

API 610 / ISO 13709, Centrifugal Pumps for Petroleum, Petrochemical and Natural Gas Industries — §5.4 nozzle loadings and Annex F allowable-load criteria; table values user-supplied, not embedded.
NEMA SM 23, Steam Turbines for Mechanical Drive Service — §8.4 nozzle load limits, including the combined-resultant criterion evaluated by the separate combined-index calculator.
API 650, Welded Tanks for Oil Storage — Annex P, loads on shell openings; API 620 for low-pressure storage tanks.
API 560 (fired heaters), API 660 (shell-and-tube heat exchangers) and API 661 (air-cooled heat exchangers) — nozzle loading clauses; allowables per the standard or the purchased datasheet.
ASME B31.3, Process Piping — ¶319.4.4, flexibility analysis. Reactions on connected equipment are judged against the equipment standard's limits, not against B31.3 stress allowables.

Per the source & citation policy, allowable-stress and factor table values are user-supplied — this page and the app cite paragraph numbers and never reproduce ASME table data.

FAQ

Which standard's allowable loads does this calculator use?

None — it holds no allowable-load tables at all. You enter the six allowables for your nozzle size from API 610, 560, 660, 661, 650, 620, NEMA SM 23 or the vendor datasheet, and the standard you select is written into the report as a label. That is deliberate: those tables are copyrighted, and embedding a snapshot of them would silently go stale the moment a new edition is issued.

If every component passes, will the equipment vendor accept the loads?

Not necessarily. Most standards apply combined criteria on top of the component limits — NEMA SM 23's combined-resultant / 3F + M index, and API 610 Annex F, which permits components above table values only if the loads resolved to the pump centreline satisfy further conditions. Run the NEMA SM-23 / API 617 Combined Index calculator as well, and confirm against the datasheet.

Why is there an NPS selector if the nozzle size does not enter the arithmetic?

Because the allowable is a function of nozzle size in every one of these standards. The selector records which table row you read and prints it on the report, so a reviewer can check that the allowables entered belong to the nozzle actually being assessed. It changes nothing in the unity-ratio maths.

Is the nozzle load check free to use?

The method, the equations and the worked example on this page are free to read and always will be. The live calculator sits on the Equipment line, which is included with Pro — see pricing. The ASME B31 pressure-design and stress calculators remain free with no account.

Related calculators

Flange Equivalent Pressure Calculator (Kellogg Method) — The flanged joint at the same nozzle carries these loads
Displacement Stress Range Check (ASME B31.3 ¶319.4.4) — Source of the moments and forces checked here
Expansion Loop / Leg Sizing Calculator (Guided Cantilever) — Add flexibility when nozzle loads exceed allowables

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