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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
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Source checked · 7/7 tests · Production surface contract 4/4 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
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 · 7/7 tests · Production surface contract 4/4 · Source checked · v1.0.0
Named expert review
Optional · Not performed
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
4 boundary · 3 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.

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

1

Enter specification limits

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

2

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.

3

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.

ϟ

On target

LSL=0 · USL=12 · μ=6 · σ=1 · target=6

Cpm=12/(6·1)
Cpm=2
ϟ

Off target

LSL=0 · USL=12 · μ=7 · σ=1 · target=6

Cpm=12/(6√2)
Cpm=√2

Process Capability Cpm calculator specification

Version 1.0.0 · Engine tested

Calculation status

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 4/4 · 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
1.0.0

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 1.0.0.

{ "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 .

Cp Process capability (Cp/Cpk) › Pp Process performance (Pp/Ppk) › Ppm Process performance (Ppm) › Cpmk Process capability (Cpmk) › Ppmk Process performance (Ppmk) › GB Guard band › GRR Gauge R&R › WS Tolerance / Uncertainty Workspace ›
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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.