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Worst-Case Tolerance Analysis Calculator

1-D linear dimensional tolerance stack: worst-case Σ|tol| with RSS comparison. Deterministic bound under declared limits — pairs with Tolerance Stack-up and Monte Carlo.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · 1-D linear magnitude stack Σ|Tᵢ| with RSS comparison; canonical tolerances[] ≥ 0; REST signed-magnitude compatibility warning; O3 mpmath tabulated sum/RSS
Input interpretation
Enter values to calculate.
Result
—
Verified scope
1-D linear magnitude stack Σ|Tᵢ| with RSS comparison; canonical tolerances[] ≥ 0; REST signed-magnitude compatibility warning; O3 mpmath tabulated sum/RSS
Assurance
Engineering
Declared partition coverage
PASS · 13/13 declared partitions (single-term, multi-term, all-zero, mixed-magnitude, signed-input-policy, large-N, scale-small, scale-large, canonical-array, legacy-fields, invalid-missing, invalid-numeric, xcal) · Matrix
Deferred
Nominal chains, asymmetric ±Tol, GD&T, geometric stacks, Monte Carlo, and general sensitivity |cᵢ|≠1 are out of this calculator
Numerical scope
≤2 ULP vs O3 applies only to the published tabulated 1-D magnitude vectors (fields, array, signed REST, single, zeros, small, large, 3-4-5). Long equal-term sums such as n=100×0.01 remain Evidence/property and are not an O3 2-ULP claim. It is not a whole-domain guarantee and does not cover GD&T or nominal chains.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
1-D linear worst-case tolerance magnitude stack (Σ|t|, |cᵢ|=1) with RSS comparison.
Scope
Linear 1-D magnitude stack only
Verification
Engine tested · Source checked · v1.3.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · 1-D linear magnitude stack Σ|Tᵢ| with RSS comparison; canonical tolerances[] ≥ 0; REST signed-magnitude compatibility warning; O3 mpmath tabulated sum/RSS· View Manifest · CVP overview · Specification
Versions
Calculation 1.3.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.o3-rss
Verification revision
2026-09-16.o3-rss · 10/10 property · digest 9146ee258d55
Legacy regression
27/27 tests · Production surface contract 8/8
Trust layers
Verification VERIFIED · Production CURRENT · overall VERIFIED
Reference
O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 2/2 (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.
Supplemental domain review
Internal · Pass · tolerance-engineer
  • Model / formula · 2026-08-12 · still current
  • Interface / input semantics · 2026-09-12
Named expert review
Not performed
CVP suite
4/4 golden · 11/11 CVP boundary · 9/9 invalid · 10/10 property · 3/3 metamorphic · 8/8 O3 · 5/5 cross-interface · 4/4 cross-calculator · 8/8 CVP contract · Manifest
Sources
Sources
Evidence
7 legacy golden · 7 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 9/9 invalid · Artifact integrity PASS · CalculatorX tolerance / mechanical engineering review
This calculator CURRENT · Public schema 1.3.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

Worst caseT_WC = Σ |T_i|
Unit sensitivityT_Y = Σ |c_i| T_i (|c_i|=1)
RSS (compare)T_RSS = √Σ T_i²
iThis calculator assumes unit sensitivity magnitude |cᵢ|=1. For general sensitivity coefficients, use Uncertainty Propagation. For nominal / direction / asymmetric ±Tol, use Tolerance Stack-up. 1-D linear stack of tolerance magnitudes only — not a full nominal min/max dimensional chain.

How to use

1

Enter each tolerance magnitude

List every non-negative ± magnitude in the same unit. Use + Add tolerance for extra contributors; REST aliases remain tol1…tol8.

2

Confirm all terms are included

Worst-case adds absolute magnitudes: T_WC = Σ|T_i|. A negative value is not a dimensional direction.

3

Read the bound, then go deeper if needed

Use RSS only when statistical bases match. Next: Tolerance Stack-up for a dimensional chain, then Monte Carlo for distributions, yield, and sensitivity.

Example calculations

Common configurations with formula and result.

ϟ

0.1+0.2+0.1

three tols

Σ|t|
±0.4 mm

Worst-Case Tolerance Analysis calculator specification

Version 1.3.0 · Engine tested · Supplemental domain review · Internal · 2026-09-12

Calculation status

Review policy · Evidence · Reviewed by CalculatorX tolerance / mechanical engineering review (tolerance-engineer)

Definition
1-D linear dimensional tolerance stack. Worst-case = Σ|tol_i| (deterministic magnitude bound, |c_i|=1). RSS √Σtol² is shown for comparison when tolerances share a consistent statistical basis.
What it calculates
1-D linear worst-case tolerance magnitude stack (Σ|t|, |cᵢ|=1) with RSS comparison.
Inputs
  • tolerances[] ≥ 0 (canonical)
  • tol[] or tol1…tol8 (REST, signed-magnitude compatibility)
  • unit (optional shared label)
Outputs
  • stack
  • stack_worst
  • stack_rss
  • wc_over_rss
  • warnings
Formula
Σ|t|
Assumptions
  • Linear 1-D magnitude stack only
  • Unit sensitivity |cᵢ|=1
  • Worst-case assumes every included contributor can reach its declared limit
  • RSS comparison assumes consistent statistical basis and independence
  • Canonical/UI magnitudes are non-negative; REST signed values ignore sign
Units
  • same as tol / unit
Boundary conditions
  • No tol → MISSING_REQUIRED_INPUT
  • Canonical negative → NEGATIVE_TOLERANCE_MAGNITUDE
  • binary64 overflow → RESULT_OVERFLOW
Example
0.1,0.2,0.1 → total worst-case tolerance ±0.4 · RSS ≈ 0.244949
Validation cases

2 published on this page · 27/27 tests · Production surface contract 8/8 · View evidence

  • tol1=0.1 tol2=0.2 tol3=0.1 → stack=0.4
  • tolerances=[0.1,0.2,0.1] → stack=0.4
Sources
Last reviewed
2026-09-12
  • Model / formula · 2026-08-12 · still current
  • Interface / input semantics · 2026-09-12
Reviewed by
CalculatorX tolerance / mechanical engineering review (tolerance-engineer)
Calculation version
1.3.0

Background

Interpretation and common distinctions.

Compute a 1-D linear worst-case tolerance magnitude stack — the deterministic upper bound under declared contributor limits.

v1.3.0 makes tolerance magnitudes an explicit non-negative quantity on UI and canonical Agent/MCP input (NEGATIVE_TOLERANCE_MAGNITUDE). REST tol[] / tol1… still accept a negative for compatibility and return SIGN_IGNORED_FOR_TOLERANCE_MAGNITUDE instead of silently looking like dimensional direction. Overflow of Σ|T| or RSS is RESULT_OVERFLOW.

Product position

Tolerance & Uncertainty Analysis
├── Worst-case Analysis     → fastest deterministic magnitude bound (this page)
├── Tolerance Stack-up     → dimensional chain (nominal, direction, +Tol/−Tol)
├── Monte Carlo            → distributions / yield / sensitivity
└── Uncertainty Propagation → GUM linear combination / general |cᵢ|

Supported and not supported

Supported — Worst-case Σ|tol| with RSS comparison · API engineering.tolerance.worst_case

Not supported — Nominal chains, asymmetric +Tol/−Tol, GD&T, geometric stacks, Monte Carlo, general sensitivity |cᵢ|≠1

Agent / API notes

Capability id: engineering.tolerance.worst_case · tool id: worst-case-analysis · pin 1.3.0.

Canonical agent input:

{ "tolerances": [0.1, 0.2, 0.1], "unit": "mm" }

REST still accepts tol[] or tol1…tol8. Unit is a shared label; all contributors must already use the same unit.

Errors: MISSING_REQUIRED_INPUT, INVALID_INPUT, INVALID_NUMBER, NEGATIVE_TOLERANCE_MAGNITUDE, RESULT_OVERFLOW.

Other calculators in this family: Tolerance / Uncertainty Workspace, Tolerance stack-up, Monte Carlo tolerance, Uncertainty propagate .

WS Tolerance / Uncertainty Workspace › ±Σ Tolerance stack-up › MC Monte Carlo tolerance › ± Uncertainty propagate ›
}

Frequently asked questions

Key distinctions behind the calculation.

When use worst-case vs RSS?

Worst-case bounds the declared 1-D linear stack when every included contributor remains within its specified limits. RSS comparison assumes tolerance magnitudes have a consistent statistical basis and contributions are independent. For distribution-aware analysis, use Monte Carlo Tolerance Analysis.

Is this a full dimensional chain?

No. This calculator reports total worst-case tolerance magnitude (Σ|t|) with unit sensitivity |cᵢ|=1. It does not compute nominal gap, min/max limits, asymmetric +Tol/−Tol, or GD&T. Use Tolerance Stack-up for a dimensional chain, or the Monte Carlo Tolerance Workspace for distributions and yield.

What does a negative tolerance mean here?

A tolerance magnitude must be ≥ 0 in the UI and canonical Agent/MCP input. REST tol[] / tol1… still accept a negative for compatibility, but the sign is ignored and the response includes SIGN_IGNORED_FOR_TOLERANCE_MAGNITUDE. For +/− dimensional direction, use Tolerance Stack-up Engineering mode.

What does the RSS number mean here?

RSS = √Σt² of the same tolerance magnitudes. The comparison is most meaningful when every limit shares the same statistical interpretation (e.g. all ±3σ). Mixed bases (3σ vs 6σ vs uniform half-width) make the RSS figure less interpretable.