Engineering calculator

Test Uncertainty Ratio Calculator

Compute the two-sided test uncertainty ratio TUR from an already-expanded U and a specification interval. Runs locally. Not a pass/fail, not a guard band, and not combined RSS.

Instant result

Result

—

Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · ANSI/NCSL Z540.3 two-sided TUR = (USL−LSL)/(2U) for an already-expanded U, plus span T and half-width tol, + O3 mpmath tabulated TUR.

Input interpretation: Enter values to calculate.
Result: —
Verified scope: ANSI/NCSL Z540.3 two-sided TUR = (USL−LSL)/(2U) for an already-expanded U, plus span T and half-width tol, + O3 mpmath tabulated TUR.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (limits, span, half-width, alias, invalid-domain) · Matrix
Deferred: Not a TUR≥4 pass/fail, not a guard band, and not U = k·u_c.
Numerical scope: O2: ANSI/NCSL Z540.3 two-sided TUR = span/(2U) vs a separate-module identity (≤2 ULP). Not a TUR≥4 verdict, not a guard band, and not U = k·u_c. ≤2 ULP vs O3 applies only to the published tabulated Z540.3 vectors (limits, span, half-width, aliases, and one awkward span). It is not a whole-domain guarantee and does not cover a TUR≥4 verdict, a guard band, or U = k·u_c.
Known limitations: Core CVP does not include live graph, viewport, or pointer interaction.
Model: Two-sided test uncertainty ratio TUR from expanded U and a specification interval.
Scope: ANSI/NCSL Z540.3 two-sided TUR = (USL−LSL)/(2U)
Verification: Engine tested · Source checked · v1.0.1 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · ANSI/NCSL Z540.3 two-sided TUR = (USL−LSL)/(2U) for an already-expanded U, plus span T and half-width tol, + O3 mpmath tabulated TUR.· View Manifest · CVP overview · Specification
Versions: Calculation 1.0.1 · CVP protocol 1.0.0-proposed · Evidence 2026-09-23.o2-o3
Verification revision: 2026-09-23.o2-o3 · 1/1 property · digest 883bc95d518c
Legacy regression: 12/12 tests · Production surface contract 6/6
Trust layers: Verification VERIFIED · Production CURRENT · Overall CVP state: VERIFIED under CVP 1.0.0-proposed
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 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.
Supplemental domain review: Not performed
Named expert review: Not performed
CVP suite: 4/4 golden · 7/7 CVP boundary · 8/8 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 4/4 cross-interface · 6/6 CVP contract · Manifest
Sources: ANSI/NCSL Z540.3 — Requirements for the Calibration of Measuring and Test Equipment — Test uncertainty ratio (two-sided TUR = specification span / 2U)
ILAC G8:09/2019 — Guidelines on Decision Rules and Statements of Conformity — Decision rules are a different contract from TUR
Sources
Evidence: 1 legacy golden · 7 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 8/8 invalid · Artifact integrity PASS
Semantic contract: PASS

Full verification

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

Formulas

Core equations used by this calculator.

Two-sided TURTUR = (USL − LSL) / (2U)

From spanTUR = T / (2U)

iU is an already-expanded uncertainty. This page does not compute U = k·u_c, does not combine u_i, and does not issue a TUR≥4 pass/fail.

How to use

Enter expanded U

U > 0. Compute k on Coverage factor and U = k·u_c on Uncertainty propagate if you still need to expand.

Enter the specification

LSL and USL with USL > LSL, or the full span T, or a half-width tol.

Read TUR

A common lab rule of thumb is TUR ≥ 4. This page reports the ratio only — not a verdict.

Example calculations

Common configurations with formula and result.

Limits

U=0.5 · LSL=0 · USL=4

TUR=(4−0)/(2·0.5)

TUR=4

Span

U=0.5 · T=4

TUR=4/(2·0.5)

TUR=4

Test Uncertainty Ratio calculator specification

Version 1.0.1 · Engine tested

Calculation status

Engine tested 12/12 tests · Production surface contract 6/6
Named expert review Not performed
Calculation version 1.0.1

Review policy · Evidence

Definition: For a two-sided specification, TUR = (USL − LSL) / (2U), where U is already expanded. You may give the span T instead of limits, or a half-width tol (span = 2·tol).
What it calculates: Two-sided test uncertainty ratio TUR from expanded U and a specification interval.
Inputs: U
lsl
usl
T
tol
Outputs: TUR
T
U
Formula: TUR = (USL−LSL)/(2U)
Assumptions: ANSI/NCSL Z540.3 two-sided TUR = (USL−LSL)/(2U)
U is already expanded; this page does not compute U = k·u_c
tol is a half-width (span = 2·tol)
Not a pass/fail, not a guard band, and not combined RSS
Units: dimensionless TUR
Boundary conditions: missing U or missing spec → MISSING_REQUIRED_INPUT
U ≤ 0 or T ≤ 0 or tol ≤ 0 → VALUE_MUST_BE_POSITIVE
usl ≤ lsl or more than one spec form → INVALID_INPUT
Example: U=0.5 lsl=0 usl=4 → TUR=4
Validation cases: 3 published on this page · 12/12 tests · Production surface contract 6/6 · View evidence
U=1 lsl=0 usl=5 → TUR=2.5, T=5
U=0.5 lsl=0 usl=4 → TUR=4
U=0 lsl=0 usl=4 → VALUE_MUST_BE_POSITIVE
Sources: ANSI/NCSL Z540.3 — Requirements for the Calibration of Measuring and Test Equipment — Test uncertainty ratio (two-sided TUR = specification span / 2U)
Supports: TUR = (USL−LSL)/(2U) for a two-sided specification and an already-expanded U
ILAC G8:09/2019 — Guidelines on Decision Rules and Statements of Conformity — Decision rules are a different contract from TUR
Supports: This page does not implement ILAC G8 guarded acceptance or a pass/fail
Calculation version: 1.0.1

Background

Interpretation and common distinctions.

Compute the two-sided test uncertainty ratio TUR.

Supported and not supported

Supported — TUR from expanded U and lsl+usl, T, or half-width tol · API engineering.uncertainty.tur

Not supported — RSS of u_i, U = k·u_c as a product, guard band, Cp/Cpk, ILAC G8 pass/fail, TUR≥4 verdict boolean

Agent / API notes

Capability id: engineering.uncertainty.tur · tool id: tur · pin 1.0.1.

{ "U": 0.5, "lsl": 0, "usl": 4 }

Exactly one specification form: lsl+usl, or T/span, or tol (half-width). Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, INVALID_INPUT.

Calculator URL stays /calc/engineering/test-uncertainty-ratio. There is no /calc/metrology.

Other calculators in this family: Guard band, Conformity decision, Normalized error En, Coverage factor k, Process capability (Cp/Cpk), Uncertainty propagate, Type B uncertainty, Tolerance / Uncertainty Workspace .

Frequently asked questions

Key distinctions behind the calculation.

Is TUR≥4 a pass?

No. Some labs use TUR ≥ 4 as a rule of thumb for calibration or test equipment. This page only reports TUR. It does not apply ILAC G8, JCGM 106, or a guarded-acceptance decision.

Is this the same as a guard band?

No. Guard band computes GB = k·u and optional acceptance limits. TUR is the ratio of the specification span to 2U. They answer different questions.

Where does this run?

Locally in the browser by default. REST and MCP call the same metrology-engine tur op.