Engineering calculator

Process Capability Cpm Calculator

Compute Taguchi Cpm from μ, σ, LSL, USL, and a target. Runs locally. Not Cp/Cpk, not Pp/Ppk, and not a 1.33 verdict.

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 · Design-stage Taguchi Cpm from stated μ, σ, LSL, USL, and a target, + O3 mpmath tabulated Cpm.

Input interpretation: Enter values to calculate.
Result: —
Verified scope: Design-stage Taguchi Cpm from stated μ, σ, LSL, USL, and a target, + O3 mpmath tabulated Cpm.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (on-target, off-target, alias, awkward, invalid-domain) · Matrix
Deferred: Not Cp/Cpk, not Pp/Ppk from a sample, and not a Cpm≥1.33 verdict.
Numerical scope: O2: design-stage Taguchi Cpm vs a separate-module identity (≤2 ULP). Not Cp/Cpk, not Pp/Ppk, and not a Cpm≥1.33 verdict. ≤2 ULP vs O3 applies only to the published tabulated Cpm vectors (on target, off target, below target, an alias, a wider σ, a target away from the midpoint, one awkward sample, and a tiny offset). It is not a whole-domain guarantee and does not cover Cp/Cpk, Pp/Ppk, or a Cpm≥1.33 verdict.
Known limitations: Core CVP does not include live graph, viewport, or pointer interaction.
Model: Taguchi Cpm from stated μ, σ, LSL, USL, and a target.
Scope: Taguchi Cpm = (USL−LSL)/(6√(σ²+(μ−target)²)) from stated μ, σ, LSL, USL, and target.
Verification: Engine tested · Source checked · v1.0.1 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Design-stage Taguchi Cpm from stated μ, σ, LSL, USL, and a target, + O3 mpmath tabulated Cpm.· View Manifest · CVP overview · Specification
Versions: Calculation 1.0.1 · CVP protocol 1.0.0-proposed · Evidence 2026-09-24.o2-o3
Verification revision: 2026-09-24.o2-o3 · 1/1 property · digest 0ea009ab8875
Legacy regression: 7/7 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 · 3/3 CVP boundary · 6/6 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 3/3 cross-interface · 6/6 CVP contract · Manifest
Sources: Chan, Cheng, and Spiring — A new measure of process capability: Cpm — Cpm = (USL−LSL)/(6√(σ²+(μ−T)²))
ISO 22514-2 — Statistical methods in process management — Capability and performance — Capability vs performance; target-based indices
Sources
Evidence: 1 legacy golden · 3 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 6/6 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.

CpmCpm = (USL − LSL) / (6 √(σ² + (μ − target)²))

itarget is a process target, not tolerance span T. This is not Cp/Cpk (those ignore the target in the denominator) and not Pp/Ppk (those use sample s).

How to use

Enter specification limits

LSL and USL in the same unit as μ, σ, and the target. USL must be greater than LSL.

Enter μ, σ, and the target

σ must be greater than zero. The target may sit anywhere; it is not required to be the spec midpoint.

Read Cpm

On target, Cpm equals Cp. Off target, Cpm is smaller. Use Cp/Cpk when you have no target. Use Pp/Ppk for overall sample s.

Example calculations

Common configurations with formula and result.

On target

LSL=0 · USL=12 · μ=6 · σ=1 · target=6

Cpm=12/(6·1)

Cpm=2

Off target

LSL=0 · USL=12 · μ=7 · σ=1 · target=6

Cpm=12/(6√2)

Cpm=√2

Process Capability Cpm calculator specification

Version 1.0.1 · Engine tested

Calculation status

Engine tested 7/7 tests · Production surface contract 6/6
Named expert review Not performed
Calculation version 1.0.1

Review policy · Evidence

Definition: Cpm = (USL − LSL) / (6 √(σ² + (μ − target)²)). Design-stage from a stated mean, σ, two-sided spec, and a target. When μ equals the target, Cpm equals Cp.
What it calculates: Taguchi Cpm from stated μ, σ, LSL, USL, and a target.
Inputs: lsl
usl
mu
sigma
target
Outputs: Cpm
offset
target
Formula: Cpm=(USL−LSL)/(6√(σ²+(μ−target)²))
Assumptions: Taguchi Cpm = (USL−LSL)/(6√(σ²+(μ−target)²)) from stated μ, σ, LSL, USL, and target.
Not Cp/Cpk (those ignore the target in the denominator), not Pp/Ppk, and not a 1.33 verdict.
Units: dimensionless
Boundary conditions: missing target → MISSING_REQUIRED_INPUT
sigma ≤ 0 → VALUE_MUST_BE_POSITIVE
USL ≤ LSL → INVALID_INPUT
Example: lsl=0 usl=12 mu=6 sigma=1 target=6 → Cpm=2
Validation cases: 3 published on this page · 7/7 tests · Production surface contract 6/6 · View evidence
lsl=0 usl=12 mu=6 sigma=1 target=6 → Cpm=2
lsl=0 usl=12 mu=7 sigma=1 target=6 → Cpm=√2
missing target → MISSING_REQUIRED_INPUT
Sources: Chan, Cheng, and Spiring — A new measure of process capability: Cpm — Cpm = (USL−LSL)/(6√(σ²+(μ−T)²))
Supports: Cpm penalizes deviation from a target; it is not Cp and not Cpk
ISO 22514-2 — Statistical methods in process management — Capability and performance — Capability vs performance; target-based indices
Supports: This page is a design-stage target index, not overall sample Pp/Ppk
Calculation version: 1.0.1

Background

Interpretation and common distinctions.

Compute Taguchi Cpm.

Supported and not supported

Supported — Cpm from stated μ, σ, LSL, USL, and a target · API engineering.process.cpm

Not supported — Cp/Cpk, Pp/Ppk, sample s, Cpm≥1.33 verdict, P/T = 1/Cp

Agent / API notes

Capability id: engineering.process.cpm · tool id: cpm · pin 1.0.1.

{ "lsl": 0, "usl": 12, "mu": 6, "sigma": 1, "target": 6 }

Aliases: mean for mu; std for sigma; x_target for target. Do not send T as the target (T is a spec span on TUR / Cg). Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, INVALID_INPUT, VALUE_MUST_BE_POSITIVE.

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

Other calculators in this family: Process capability (Cp/Cpk), Process performance (Pp/Ppk), Process performance (Ppm), Process capability (Cpmk), Process performance (Ppmk), Guard band, Gauge R&R, Tolerance / Uncertainty Workspace .

Frequently asked questions

Key distinctions behind the calculation.

Is Cpm the same as Cp or Cpk?

No. Cp and Cpk do not put (μ − target) in the denominator. When the mean equals the target, Cpm equals Cp. This page does not report Cpk.

Is this Pp/Ppk?

No. Pp/Ppk use overall sample s from observations and have no target. Cpm is design-stage from a stated μ and σ.

Does Cpm≥1.33 mean pass?

This page does not issue that verdict. It reports Cpm only.

Is target the same as tolerance T?

No. target is the process aim. TUR and Cg use T as a specification span. Do not send T as the target.

Where does this run?

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