Public evidence

engineering.tolerance.stackup

Machine-checked verification for calculation version 1.4.0 · tier internally_reviewed

Open calculator API Capability Download JSON CVP Manifest Reproduce MCP Review policy

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Basic RSS/WCA + Engineering dimensions[] + O3 mpmath tabulated RSS/WCA· O2 covers Basic tol[] / tol1…n and Engineering dimensions[] (symmetric, asymmetric, 1σ, 3σ, uniform). Geometric GD&T, 3-D loops, and Monte Carlo are not this calculator. · Protocol · Schema · Production report

Declared partition coverage: PASS · 8/8 declared partitions (basic-rss, basic-wca, engineering-symmetric, engineering-asymmetric, engineering-1sigma, engineering-3sigma, engineering-uniform, invalid-domain)
Versions: Calculation 1.4.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.o3-linear
Verification revision: 2026-09-16.o3-linear · 18/18 property · digest 9ae988cdc138

Verification

Legacy regression suite: 35/35 calculation tests · Production surface contract 8/8

Three distinct suites: educational examples on the calculator page, this legacy regression count (35/35 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.4.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-09-16.o3-linear. Calculation version 1.4.0. CVP 1.0.0-proposed. 10/10 golden · 11/11 CVP boundary · 5/5 invalid · 18/18 property · 10/10 O3 · 6/6 cross-interface · 8/8 CVP contract. digest 9ae988cdc138. ≤2 ULP vs O3 applies only to the published tabulated Basic RSS/WCA and Engineering dimensions[] vectors (symmetric, asymmetric, 1σ, 3σ, uniform). It is not a whole-domain stack guarantee and does not cover GD&T or 3-D loops.

Golden (oracle-backed) 10 / 10
CVP boundary 11 / 11
Invalid input 5 / 5
Property 18 / 18
O3 high-precision 10 / 10
Cross-interface 6 / 6
CVP contract 8 / 8
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Verified scope Basic RSS/WCA + Engineering dimensions[] + O3 mpmath tabulated RSS/WCA
Assurance Engineering
Deferred Geometric GD&T, 3-D assembly loops, and Monte Carlo remain out of this calculator (see Monte Carlo Tolerance). O3 does not cover GD&T.

contract page version PASS
contract capability version PASS
contract input schema version PASS
contract output schema version PASS
evidence version matches manifest PASS
schema valid input executes PASS
engine success output validates schema PASS
schema rejects incomplete input PASS

Fingerprint sha256:15f47c48aa2f91c65db3252e79e42892fb4b441ca9e5e5c73804cd220335f55b

Input schema sha256:036120d8f0e42fcc1ca177d0349b60957414b83b1e96effa9e22fa042525ed6a · Output schema sha256:1b287114a9eeb904ab9cc4dc18a33ccf7c997be16d2d695a3cc074445c7f2405 · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Build & scope

Engine identity and declared limitations.

Tool: tolerance-stackup
Engine: tolerance-stackup
Engine build: 2026-09-11
Evidence core: 2026-09-11T23:15:00.561Z
Rendered: 2026-09-16T22:03:43.725Z
Last reviewed: 2026-08-11

Assumptions

Linear 1-D stack
All contributors must use the same unit. CalculatorX performs no implicit unit conversion; mixed-unit input is unsupported
Basic mode: signs ignored via |tol|
Engineering: direction + adds / − subtracts; asymmetric ±tol supported
RSS assumes independent contributors
Default statistical_basis=magnitude → u=a with no coverage probability
1sigma → u=a; 3sigma → u=a/3; uniform → u=a/√3
Uniform asymmetric ±tol: statistical center uses interval midpoint; stack_nom stays drawing nominal
Legacy distribution=normal→1sigma, unknown→magnitude, uniform→uniform
stack_half_range ≠ stack_worst when +Tol/−Tol are asymmetric about nominal
When inputs are specification limits rather than σ-based values, prefer magnitude — RSS is an estimate and not a guaranteed assembly limit

Limitations

1-D linear stack only — not geometric GD&T or Monte Carlo
Basic inputs are treated as comparable tolerance magnitudes, not automatically as 1σ / 3σ / drawing limits
RSS is a statistical estimate under independence; it is not a guaranteed assembly limit
Engineering statistical_basis: magnitude (default, no coverage) and 1sigma use a; 3sigma uses a/3; uniform uses a/√3
Uniform asymmetric ±tol shifts statistical center to interval midpoint (NIST Type B rectangular); stack_nom stays drawing nominal
Legacy distribution=normal→1sigma, unknown→magnitude, uniform→uniform
stack_half_range is not a hard worst-case bound when +Tol/−Tol are asymmetric about nominal — use stack_worst_plus / stack_worst_minus

Sources

Standards and references supporting this tool specification. Methods are listed separately — they are algorithms, not bibliographic sources.

ASME Y14.5 — Dimensioning and Tolerancing — GD&T symbols, rules, and drawing requirements
Supports: Defines geometric dimensioning and tolerancing language used on engineering drawings; does not itself define the RSS stack-up formula
Mekid, S. — Metrology and Instrumentation (Wiley-ASME Press) — §6.5.4 Worst-Case Tolerance Stack-Up in Asymmetric Dimensional Tolerance; §6.6.2 Worst-Case vs RSS
Supports: 1-D worst-case stack for asymmetric ±tol and comparison of worst-case vs root-sum-square statistical analysis
SAE 2007-01-0407 — Tolerance Analysis of Mechanical Assemblies with Asymmetric Tolerances — Modified worst-case and RSS accumulation for asymmetric tolerances
Supports: Shows that asymmetric contributors produce asymmetric assembly limits; motivates reporting stack_worst_plus / stack_worst_minus separately
NIST Technical Note 1297 — 5. Combined standard uncertainty
Supports: Root-sum-square combination of independent uncertainty components estimated as standard deviations
NIST — Evaluating uncertainty components: Type B — Uniform (rectangular) distribution
Supports: For rectangular limits, best estimate is the interval midpoint (a++a−)/2 and u = a/√3 with a = (a+−a−)/2 — used when statistical_basis=uniform

Legacy published checks

Golden and boundary cases from the legacy Evidence JSON. CVP property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the Manifest — including SKIP when a suite has no vectors.

ID	Kind	Status	Detail
`rss`	golden	pass	Expected stack=0.24494897427831783 · stack_worst=0.4 · Actual n=3 · mode=rss · profile=basic · stack=0.24494897427831783 · stack_rss=0.24494897427831783 · stack_worst=0.4 · stack_worst_plus=0.4 · stack_worst_minus=0.4
`wca`	golden	pass	Expected stack=0.4 · Actual n=3 · mode=worst_case · profile=basic · stack=0.4 · stack_rss=0.24494897427831783 · stack_worst=0.4 · stack_worst_plus=0.4 · stack_worst_minus=0.4
`empty`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`bad-mode`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`tol-alias-tol3`	golden	pass	Expected n=3 · stack=0.24494897427831783 · Actual n=3 · mode=rss · profile=basic · stack=0.24494897427831783 · stack_rss=0.24494897427831783 · stack_worst=0.4 · stack_worst_plus=0.4 · stack_worst_minus=0.4
`eng-abc`	golden	pass	Expected stack_nom=8 · stack_min=7.6 · stack_max=8.4 · stack_worst=0.4 · stack_rss=0.24494897427831783 · Actual n=3 · mode=rss · profile=engineering · stack=0.24494897427831783 · stack_rss=0.24494897427831783 · stack_worst=0.4 · stack_worst_plus=0.4 · stack_worst_minus=0.4
`boundary-tol8`	boundary	pass	Expected n=8 · stack=0.282842712474619 · stack_worst=0.8 · Actual n=8 · mode=rss · profile=basic · stack=0.28284271247461906 · stack_rss=0.28284271247461906 · stack_worst=0.7999999999999999 · stack_worst_plus=0.7999999999999999 · stack_worst_minus=0.7999999999999999
`boundary-single`	boundary	pass	Expected stack=0.25 · stack_worst=0.25 · Actual n=1 · mode=rss · profile=basic · stack=0.25 · stack_rss=0.25 · stack_worst=0.25 · stack_worst_plus=0.25 · stack_worst_minus=0.25
`boundary-zero-pad`	boundary	pass	Expected stack=0.3 · stack_rss=0.22360679774997896 · Actual n=3 · mode=worst_case · profile=basic · stack=0.30000000000000004 · stack_rss=0.223606797749979 · stack_worst=0.30000000000000004 · stack_worst_plus=0.30000000000000004 · stack_worst_minus=0.30000000000000004
`boundary-invalid-mode`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`boundary-eng-abc`	boundary	pass	Expected stack_nom=8 · stack_min=7.6 · stack_max=8.4 · stack_worst=0.4 · stack_worst_plus=0.4 · stack_worst_minus=0.4 · stack_half_range=0.4 · stack_rss=0.2449489742783178 · Actual n=3 · mode=rss · profile=engineering · stack=0.24494897427831783 · stack_rss=0.24494897427831783 · stack_worst=0.4 · stack_worst_plus=0.4 · stack_worst_minus=0.4
`boundary-eng-asymm`	boundary	pass	Expected stack_nom=8 · stack_min=7.55 · stack_max=8.35 · stack_worst_plus=0.35 · stack_worst_minus=0.45 · stack_half_range=0.4 · stack_worst=0.45 · stack_range=0.8 · Actual n=3 · mode=worst_case · profile=engineering · stack=0.44999999999999996 · stack_rss=0.24494897427831783 · stack_worst=0.44999999999999996 · stack_worst_plus=0.35 · stack_worst_minus=0.44999999999999996
`boundary-eng-uniform`	boundary	pass	Expected stack_rss=0.17320508075688773 · stack_worst=0.3 · stack_half_range=0.3 · Actual n=1 · mode=rss · profile=engineering · stack=0.17320508075688773 · stack_rss=0.17320508075688773 · stack_worst=0.3 · stack_worst_plus=0.3 · stack_worst_minus=0.3
`boundary-eng-3sigma`	boundary	pass	Expected stack_rss=0.1 · stack_worst=0.3 · Actual n=1 · mode=rss · profile=engineering · stack=0.09999999999999999 · stack_rss=0.09999999999999999 · stack_worst=0.3 · stack_worst_plus=0.3 · stack_worst_minus=0.3
`boundary-eng-legacy-normal`	boundary	pass	Expected stack_rss=0.3 · stack_worst=0.3 · Actual n=1 · mode=rss · profile=engineering · stack=0.3 · stack_rss=0.3 · stack_worst=0.3 · stack_worst_plus=0.3 · stack_worst_minus=0.3
`boundary-eng-uniform-center`	boundary	pass	Expected stack_nom=8 · stack_stat_center=7.95 · stack_center_shift=-0.05 · stack_min=7.55 · stack_max=8.35 · Actual n=3 · mode=rss · profile=engineering · stack=0.14142135623730953 · stack_rss=0.14142135623730953 · stack_worst=0.44999999999999996 · stack_worst_plus=0.35 · stack_worst_minus=0.44999999999999996
`boundary-eng-empty`	boundary	pass	Expected MISSING_REQUIRED_INPUT · Actual MISSING_REQUIRED_INPUT
`property-rss`	property	pass	rss
`property-wca`	property	pass	wca
`property-permute`	property	pass	order-invariant
`property-zero`	property	pass	zero-pad
`property-single-eq`	property	pass	rss=wca
`property-scale`	property	pass	homogeneous
`property-rss-le-wca`	property	pass	rss≤wca
`property-tol-alias`	property	pass	tol[]≡tol1…n
`property-eng-nom`	property	pass	nom=8
`property-eng-matches-basic`	property	pass	eng≡basic-tol
`property-eng-asymm`	property	pass	asymm-wca
`property-eng-asymm-sides`	property	pass	plus/minus
`property-eng-half-ne-worst`	property	pass	half≠worst
`property-eng-range`	property	pass	range=plus+minus
`property-eng-3sigma`	property	pass	a/3
`property-eng-default-basis`	property	pass	default=magnitude
`property-eng-uniform-center`	property	pass	uniform-midpoint
`property-eng-mag-no-shift`	property	pass	mag-center=nom