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 Engine tested · Source checked · 11/11 tests · Production surface contract 4/4 · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
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 · 11/11 tests · Production surface contract 4/4 · Source checked · v1.0.0
Named expert review: Optional · Not performed
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: 6 boundary · 5 property · Production surface contract 4/4 · Artifact integrity PASS
Production: Embedded snapshot: STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status PASS (0 stale; 164 CURRENT) @ 2026-09-16T06:44:24.909Z
Semantic contract: PASS

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

Enter repeats on a master

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

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.

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.

Centered

values=7, 8, 9 · xm=8 · T=30

s=1; Cg=(0.2·30)/(6·1)

Cg=1 · Cgk=1

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 1.0.0 · Engine tested

Calculation status

Engine tested 11/11 tests · Production surface contract 4/4
Named expert review Not performed
Calculation version 1.0.0

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 4/4 · 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: 1.0.0

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 1.0.0.

{ "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 .

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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.