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Engineering calculator

Cochran's C Calculator

Compute ISO 5725-2 Cochran's C from k≥2 stated laboratory sample standard deviations. Runs locally. Not pooled s_p, not Hartley's F_max, and not a tabulated Ccrit pass/fail.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · ISO 5725-2 C = s_max² / Σ s_i² from k≥2 stated laboratory s_i, + O3 mpmath tabulated Cochran C.
Input interpretation
Enter values to calculate.
Result
—
Verified scope
ISO 5725-2 C = s_max² / Σ s_i² from k≥2 stated laboratory s_i, + O3 mpmath tabulated Cochran C.
Assurance
Engineering
Declared partition coverage
PASS · 6/6 declared partitions (alias, awkward, zero-one, equal, spread, invalid-domain) · Matrix
Deferred
Not a Ccrit verdict and not pooled s_p.
Numerical scope
O2: Cochran C = s_max² / Σ s_i² vs a separate-module identity (≤2 ULP). Not a Ccrit verdict. ≤2 ULP vs O3 applies only to the published tabulated Cochran vectors. Not a Ccrit verdict.
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
ISO 5725-2 Cochran C from k≥2 stated laboratory s_i.
Scope
ISO 5725-2 Cochran C = s_max² / Σ s_i² from k≥2 stated laboratory sample standard deviations. k=1 is rejected.
Verification
Engine tested · Source checked · v1.0.1 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · ISO 5725-2 C = s_max² / Σ s_i² from k≥2 stated laboratory s_i, + O3 mpmath tabulated Cochran C.· 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 9eb4c2d716f3
Legacy regression
9/9 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 · 5/5 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 6/6 CVP contract · Manifest
Sources
  • ISO 5725-2 — Repeatability and reproducibility of standard measurement methods — Cochran's C test
  • ISO 5725-1 — Accuracy (trueness and precision) of measurement methods and results — Repeatability standard deviation s_r
Sources
Evidence
1 legacy golden · 5 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 5/5 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.

Cochran CC = s_max² / Σ s_i²
iThis page takes already-computed laboratory s_i. It does not pool them into s_p, does not form Hartley's F_max = s_max²/s_min², and does not look up Ccrit(p, n, α).

How to use

1

Enter s_i

Comma-separated laboratory sample standard deviations. Aliases: s_i, stdevs, std. Each s_i ≥ 0. This is not a sample of observations.

2

Read C

C is the share of the largest variance. Use Pooled standard deviation when you need s_p. Critical values Ccrit(p, n, α) are tabulated in ISO 5725-2 — this page does not apply them.

Example calculations

Common configurations with formula and result.

ϟ

3, 4, 5

s=[3,4,5]

C=25/(9+16+25)
C=0.5 · s_max=5 · k=3
ϟ

Equal s

s=[5,5]

C=25/50
C=0.5 · k=2
ϟ

One laboratory rejected

s=[3]

k≥2
VALUE_OUT_OF_RANGE

Cochran's C calculator specification

Version 1.0.1 · Engine tested

Calculation status

Review policy · Evidence

Definition
From k≥2 stated laboratory sample standard deviations s_i ≥ 0, C = s_max² / Σ s_i². k=1 is rejected so C cannot wrap identity 1. All-zero s is rejected because the denominator would be zero.
What it calculates
ISO 5725-2 Cochran C from k≥2 stated laboratory s_i.
Inputs
  • s
Outputs
  • C
  • s_max
  • k
  • s
Formula
C=s_max²/Σs²
Assumptions
  • ISO 5725-2 Cochran C = s_max² / Σ s_i² from k≥2 stated laboratory sample standard deviations. k=1 is rejected.
  • s_i ≥ 0. All-zero s is rejected (Σ s² must be > 0).
  • Not pooled s_p, not Hartley's F_max, and not a tabulated Ccrit pass/fail.
Units
  • 1
Boundary conditions
  • missing s → MISSING_REQUIRED_INPUT
  • k = 1 → VALUE_OUT_OF_RANGE
  • s = [0,0] → VALUE_MUST_BE_POSITIVE
  • negative s_i → VALUE_OUT_OF_RANGE
Example
s=[3,4,5] → C=0.5
Validation cases

3 published on this page · 9/9 tests · Production surface contract 6/6 · View evidence

  • s=[3,4,5] → C=0.5 s_max=5 k=3
  • s=[5,5] → C=0.5
  • s=[3] → VALUE_OUT_OF_RANGE
Sources
  • ISO 5725-2 — Repeatability and reproducibility of standard measurement methods — Cochran's C test
    Supports: C = s_max² / Σ s_i² is the test statistic for an unusually large laboratory repeatability variance. Critical values depend on p, n, and α and are not applied here.
  • ISO 5725-1 — Accuracy (trueness and precision) of measurement methods and results — Repeatability standard deviation s_r
    Supports: This page takes already-stated laboratory s_i. It does not estimate s_r from a collaborative-study table.
Calculation version
1.0.1

Background

Interpretation and common distinctions.

Compute ISO 5725-2 Cochran's C from laboratory sample standard deviations.

Supported and not supported

Supported — C from k≥2 stated s_i · s_i = 0 is valid if Σ s² > 0 · API engineering.measurement.cochran

Not supported — pooled s_p, Hartley's F_max, Ccrit pass/fail, Type A from a sample

Agent / API notes

Capability id: engineering.measurement.cochran · tool id: cochran · pin 1.0.1.

{ "s": [3, 4, 5] }

Aliases: s_i / stdevs / std for s. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_OUT_OF_RANGE, VALUE_MUST_BE_POSITIVE.

Calculator URL stays /calc/engineering/cochrans-c. There is no /calc/metrology.

Other calculators in this family: Pooled standard deviation, Measurement precision, ISO 5725 reproducibility, Repeatability from duplicates, Type A uncertainty, Tolerance / Uncertainty Workspace .

s_p Pooled standard deviation › s Measurement precision › R ISO 5725 reproducibility › s_r Repeatability from duplicates › uA Type A uncertainty › WS Tolerance / Uncertainty Workspace ›

Frequently asked questions

Key distinctions behind the calculation.

Is this pooled s_p?

No. Pooled standard deviation combines k≥2 groups into s_p = √(Σ ν_i s_i² / Σ ν_i). This page reports only Cochran's C = s_max² / Σ s_i² and does not need ν_i.

Is this Hartley's F_max?

No. Hartley's F_max is s_max² / s_min². Cochran's C uses the sum of all s_i² in the denominator.

Does C ≥ Ccrit fail a laboratory?

No. ISO 5725-2 tabulates Ccrit against p, n, and α. This page does not apply those tables and does not return pass/fail.

Can I enter a sample of observations?

No. Enter already-computed laboratory s_i. Use Precision or Repeatability from duplicates when you have observations or pair differences.

Where does this run?

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