HomeCalculatorsEngineeringGauge Capability Calculator (Cg / Cgk)
Engineering calculator

Gauge Capability Calculator (Cg / Cgk)

Compute Type-1 Cg and Cgk from repeats on a master, a reference xm, and the characteristic tolerance. frac defaults to 0.2. Runs locally. Not AIAG GRR and not process Cp/Cpk.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Cg = (frac T)/(6s) and Cgk = (frac T/2 − |x̄−xm|)/(3s), + O3 mpmath tabulated Cg.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
Cg = (frac T)/(6s) and Cgk = (frac T/2 − |x̄−xm|)/(3s), + O3 mpmath tabulated Cg.
Assurance
Engineering
Declared partition coverage
PASS · 7/7 declared partitions (alias, awkward, frac, limits, bias, centered, invalid-domain) · Matrix
Deferred
Not Gauge R&R and not a capability verdict.
Numerical scope
O2: Cg and Cgk vs a separate-module sample identity (≤2 ULP). Not Gauge R&R. ≤2 ULP vs O3 applies only to the published tabulated Cg vectors. Not Gauge R&R.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Type-1 Cg and Cgk from repeats on a master, xm, and a characteristic tolerance.
Scope
Type-1 Cg = (frac·T)/(6s), Cgk = (frac·T/2 − |x̄−xm|)/(3s). frac defaults to 0.2 (Bosch / VDA 5).
Verification
Engine tested · Source checked · v1.0.1 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Cg = (frac T)/(6s) and Cgk = (frac T/2 − |x̄−xm|)/(3s), + O3 mpmath tabulated Cg.· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.1 · CVP protocol 1.0.0-proposed · Evidence 2026-09-25.o2-o3
Verification revision
2026-09-25.o2-o3 · 1/1 property · digest 48f057c8d64f
Legacy regression
11/11 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 · 5/5 CVP boundary · 6/6 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 6/6 CVP contract · Manifest
Sources
  • VDA Volume 5 — Capability of Measurement Processes — Type-1 study Cg, Cgk (20% of characteristic tolerance)
  • ISO 22514-7 — Capability of measurement processes — Cg and Cgk from a Type-1 study on a reference
Sources
Evidence
1 legacy golden · 5 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 6/6 invalid · Artifact integrity PASS
This calculator CURRENT · Public schema 1.0.1 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.

CgCg = (frac · T) / (6s)
CgkCgk = (frac · T / 2 − |x̄ − xm|) / (3s)
ifrac is a tolerance fraction (default 0.2), not coverage factor k. T is the characteristic tolerance span. This is not AIAG GRR and not process Cp/Cpk.

How to use

1

Enter repeats on a master

Comma, space, or semicolon separated. JSON arrays also work. Sample s needs at least two values when ddof=1.

2

Enter the master value and tolerance

xm is the reference. Give T, or LSL+USL, or a half-width tol. Do not send more than one spec form.

3

Read Cgk, then Cg

Cgk includes bias |x̄−xm|. This page reports the indices only — not a Cg≥1.33 verdict. Use Gauge R&R for EV/AV/PV compose.

Example calculations

Common configurations with formula and result.

ϟ

Centered

values=7, 8, 9 · xm=8 · T=30

s=1; Cg=(0.2·30)/(6·1)
Cg=1 · Cgk=1
ϟ

With bias

values=6, 7, 8 · xm=8 · T=30

s=1; Cgk=(3−|7−8|)/3
Cg=1 · Cgk=2/3

Gauge Capability Calculator (Cg / Cgk) specification

Version 1.0.1 · Engine tested

Calculation status

Review policy · Evidence

Definition
From n repeats on a master, s is the overall sample standard deviation (ddof=1) and x̄ is the sample mean. Cg = (frac · T) / (6s). Cgk = (frac · T / 2 − |x̄ − xm|) / (3s). frac defaults to 0.2 (Bosch / VDA 5).
What it calculates
Type-1 Cg and Cgk from repeats on a master, xm, and a characteristic tolerance.
Inputs
  • values
  • xm
  • T
  • lsl
  • usl
  • tol
  • frac
  • ddof
Outputs
  • Cg
  • Cgk
  • s
  • xbar
  • xm
  • bias
  • T
  • frac
  • n
Formula
Cg=(frac·T)/(6s); Cgk=(frac·T/2−|x̄−xm|)/(3s)
Assumptions
  • Type-1 Cg = (frac·T)/(6s), Cgk = (frac·T/2 − |x̄−xm|)/(3s). frac defaults to 0.2 (Bosch / VDA 5).
  • s is overall sample s of repeats on a master. Not AIAG GRR, not Cp/Cpk, and not a Cg≥1.33 verdict.
  • Exactly one spec form: lsl+usl, T/span, or half-width tol
  • frac is a tolerance fraction (0 < frac ≤ 1), not coverage factor k
Units
  • same as values / xm / T
Boundary conditions
  • missing values, xm, or spec → MISSING_REQUIRED_INPUT
  • n < 2 when ddof=1 → VALUE_OUT_OF_RANGE
  • s = 0 → VALUE_MUST_BE_POSITIVE
  • frac > 1 or more than one spec form → INVALID_INPUT
Example
values=7,8,9 xm=8 T=30 → Cg=1 Cgk=1
Validation cases

2 published on this page · 11/11 tests · Production surface contract 6/6 · View evidence

  • values=7,8,9 xm=8 T=30 → Cg=1 Cgk=1
  • values=1 xm=8 T=30 → VALUE_OUT_OF_RANGE
Sources
  • VDA Volume 5 — Capability of Measurement Processes — Type-1 study Cg, Cgk (20% of characteristic tolerance)
    Supports: Cg = 0.2·T / (6s); Cgk includes bias against the master
  • ISO 22514-7 — Capability of measurement processes — Cg and Cgk from a Type-1 study on a reference
    Supports: Gauge capability indices from repeats on a master versus a tolerance fraction
Calculation version
1.0.1

Background

Interpretation and common distinctions.

Compute Type-1 gauge capability from repeats on a master.

Supported and not supported

Supported — Cg, Cgk from values · xm · T (or lsl+usl or tol) · optional frac · API engineering.msa.gauge_capability

Not supported — AIAG GRR compose, process Cp/Cpk or Pp/Ppk, Cg≥1.33 verdict, coverage factor k as frac

Agent / API notes

Capability id: engineering.msa.gauge_capability · tool id: gauge-capability · pin 1.0.1.

{ "values": [7, 8, 9], "xm": 8, "T": 30 }

Aliases: sample for values; xref / ref / x_m for xm; span for T; k_tol for frac. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, INVALID_INPUT, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE.

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

Other calculators in this family: Gauge R&R, Measurement bias (trueness), MSA linearity, MSA hysteresis, Process capability (Cp/Cpk), Process performance (Pp/Ppk), Type A uncertainty, Guard band, Tolerance / Uncertainty Workspace .

GRR Gauge R&R › δ Measurement bias (trueness) › lin MSA linearity › H MSA hysteresis › Cp Process capability (Cp/Cpk) › Pp Process performance (Pp/Ppk) › uA Type A uncertainty › GB Guard band › WS Tolerance / Uncertainty Workspace ›

Frequently asked questions

Key distinctions behind the calculation.

Is this the same as Gauge R&R?

No. Gauge R&R composes AIAG GRR/TV/%GRR/ndc from EV, AV, and PV. This page is a Type-1 study: repeats on one master, then Cg and Cgk against a tolerance fraction of T.

Is frac the coverage factor k?

No. frac is the fraction of the characteristic tolerance used in the Type-1 formulas (Bosch / VDA 5 default 0.2). Coverage factor k is a different page.

Does Cg≥1.33 mean pass?

This page does not issue that verdict. It reports Cg and Cgk only.

Where does this run?

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