Engineering calculator

Gauge R&R Calculator

Compose AIAG Gauge R&R from EV, AV, and PV: GRR, TV, %GRR, and ndc. Optional range-method EV = R̄/d2. Runs locally. Not a full ANOVA study.

Instant result

Result

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Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · AIAG Gauge R&R compose GRR/TV/%GRR/ndc from EV/AV/PV, optional range EV=R̄/d2 + O3 mpmath tabulated GRR.

Input interpretation: Enter values to calculate.
Result: —
Verified scope: AIAG Gauge R&R compose GRR/TV/%GRR/ndc from EV/AV/PV, optional range EV=R̄/d2 + O3 mpmath tabulated GRR.
Assurance: Engineering
Declared partition coverage: PASS · 6/6 declared partitions (stated-ev, range-ev, custom-d2, alias, pv-zero, invalid-domain) · Matrix
Deferred: Not a full ANOVA Gauge R&R, not nested study tables, not %tolerance vs spec, not Cg/Cgk, and not X̄/R constants beyond d2 for n=2.
Numerical scope: O2: AIAG GRR/TV/%GRR/ndc and range EV=R̄/d2 vs separate-module identities (≤2 ULP). Not full ANOVA, not %tolerance vs spec, not Cg. ≤2 ULP vs O3 applies only to the published tabulated GRR vectors (stated EV, range EV, custom d2, AV=0, PV=0, aliases, scale). It is not a whole-domain guarantee and does not cover full ANOVA or %tolerance vs spec.
Known limitations: Core CVP does not include live graph, viewport, or pointer interaction.
Model: AIAG Gauge R&R compose from EV/AV/PV, with optional range-method EV.
Scope: AIAG compose: GRR=√(EV²+AV²), TV=√(GRR²+PV²), %GRR=100·GRR/TV, ndc=1.41·PV/GRR
Verification: Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · AIAG Gauge R&R compose GRR/TV/%GRR/ndc from EV/AV/PV, optional range EV=R̄/d2 + O3 mpmath tabulated GRR.· View Manifest · CVP overview · Specification
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.o2-o3
Verification revision: 2026-09-16.o2-o3 · 3/3 property · digest 91696d47fa7d
Legacy regression: 8/8 tests · Production surface contract 4/4
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 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: 5/5 golden · 4/4 CVP boundary · 7/7 invalid · 3/3 property · 2/2 metamorphic · 8/8 O3 · 4/4 cross-interface · 4/4 CVP contract · Manifest
Sources: AIAG Measurement Systems Analysis (MSA) — Gauge R&R — %GRR and ndc
NIST Engineering Statistics Handbook — Repeatability — 2.4.5 Repeatability and reproducibility
Sources
Evidence: 1 legacy golden · 4 legacy boundary · legacy regression suite · 5/5 oracle-backed golden · 7/7 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.

Repeatability EVEV = R̄ / d2

GRRGRR = √(EV² + AV²)

TVTV = √(GRR² + PV²)

%GRR%GRR = 100 · GRR / TV

ndcndc = 1.41 · PV / GRR

iAIAG compose of stated components. Range-method EV uses d2=1.128 for n=2. Not a full ANOVA Gauge R&R.

How to use

Enter EV or average range R̄

Either equipment variation EV, or R̄ (then EV = R̄/d2). Do not send both.

Enter AV and PV

Appraiser variation and part variation. All ≥ 0. GRR must be > 0 for ndc.

Read %GRR, then GRR, TV, and ndc

This is MSA compose, not process Cp/Cpk and not Monte Carlo.

Example calculations

Common configurations with formula and result.

3-4-12

EV=3 · AV=4 · PV=12

GRR=5; TV=13

GRR=5 · %GRR=500/13 · ndc=3.384

Range EV

R̄=1.128 · AV=4 · PV=12

EV=R̄/1.128=1

EV=1 · GRR=√17

Gauge R&R calculator specification

Version 1.0.0 · Engine tested

Calculation status

Engine tested 8/8 tests · Production surface contract 4/4
Named expert review Not performed
Calculation version 1.0.0

Review policy · Evidence

Definition: GRR = √(EV² + AV²). TV = √(GRR² + PV²). %GRR = 100·GRR/TV. ndc = 1.41·PV/GRR. Optional EV = R̄/d2 with d2 default 1.128.
What it calculates: AIAG Gauge R&R compose from EV/AV/PV, with optional range-method EV.
Inputs: ev
rbar
d2
av
pv
Outputs: EV
AV
PV
GRR
TV
pct_grr
ndc
Formula: GRR=√(EV²+AV²); TV=√(GRR²+PV²); %GRR=100·GRR/TV; ndc=1.41·PV/GRR
Assumptions: AIAG compose: GRR=√(EV²+AV²), TV=√(GRR²+PV²), %GRR=100·GRR/TV, ndc=1.41·PV/GRR
Range-method EV = R̄/d2 (d2 defaults to 1.128 for n=2). Not a full ANOVA Gauge R&R.
Provide ev or rbar, not both
Units: same as EV / AV / PV
Boundary conditions: missing ev and rbar → MISSING_REQUIRED_INPUT
both ev and rbar → INVALID_INPUT
GRR=0 → VALUE_MUST_BE_POSITIVE (ndc)
negative EV/AV/PV → VALUE_OUT_OF_RANGE
Example: ev=3 av=4 pv=12 → GRR=5 TV=13 pct_grr=500/13 ndc=3.384
Validation cases: 2 published on this page · 8/8 tests · Production surface contract 4/4 · View evidence
ev=3 av=4 pv=12 → GRR=5 TV=13 pct_grr=500/13 ndc=3.384
ev=0 av=0 pv=12 → VALUE_MUST_BE_POSITIVE
Sources: AIAG Measurement Systems Analysis (MSA) — Gauge R&R — %GRR and ndc
Supports: GRR=√(EV²+AV²); %GRR=100·GRR/TV; ndc≈1.41·PV/GRR
NIST Engineering Statistics Handbook — Repeatability — 2.4.5 Repeatability and reproducibility
Supports: Range-method equipment variation EV = R̄/d2; d2 for n=2
Calculation version: 1.0.0

Background

Interpretation and common distinctions.

Compose AIAG Gauge R&R from equipment, appraiser, and part variation.

Supported and not supported

Supported — EV (or R̄/d2) · AV · PV · GRR · TV · %GRR · ndc · API engineering.msa.gauge_rr

Not supported — full ANOVA Gauge R&R, nested study tables, %tolerance vs spec, X̄ and R control-chart constants beyond d2 for n=2

Agent / API notes

Capability id: engineering.msa.gauge_rr · tool id: gauge-rr · pin 1.0.0.

{ "ev": 3, "av": 4, "pv": 12 }

Range-method EV: { "rbar": 1.128, "av": 4, "pv": 12 }. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, INVALID_INPUT, VALUE_OUT_OF_RANGE, VALUE_MUST_BE_POSITIVE.

Calculator URL stays /calc/engineering/gauge-repeatability-reproducibility. There is no /calc/metrology.

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Frequently asked questions

Key distinctions behind the calculation.

Is this a full ANOVA Gauge R&R?

No. This page composes AIAG GRR/TV/%GRR/ndc from EV, AV, and PV. Optional EV comes from the range method R̄/d2. It does not run an ANOVA table from a nested study.

Why is ndc 1.41·PV/GRR?

That is the AIAG number-of-distinct-categories factor used in the metrology overlay (ndc_factor=1.41). GRR must be greater than zero.

Where does this run?

Locally in the browser by default. REST and MCP call the same metrology-engine gauge_rr ops.