Engineering calculator

Repeatability from Duplicates Calculator

Compute ISO 5725 repeatability s_r from m≥2 duplicate differences. Runs locally. Not Type A from a sample of observations, not r = 2.8·s, and not AIAG GRR EV = R̄/d2.

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 · ISO 5725 s_r = sqrt(Σ d² / (2m)) from m≥2 differences, + O3 mpmath tabulated duplicate sd.

Input interpretation: Enter values to calculate.
Result: —
Verified scope: ISO 5725 s_r = sqrt(Σ d² / (2m)) from m≥2 differences, + O3 mpmath tabulated duplicate sd.
Assurance: Engineering
Declared partition coverage: PASS · 6/6 declared partitions (pairs, alias, awkward, zero, spread, invalid-domain) · Matrix
Deferred: Not r = 2.8 s and not Gauge R&R.
Numerical scope: O2: repeatability from duplicates s_r = sqrt(Σ d² / (2m)) vs a separate-module identity (≤2 ULP). Not r = 2.8 s. ≤2 ULP vs O3 applies only to the published tabulated duplicate-sd vectors. Not r = 2.8 s.
Known limitations: Core CVP does not include live graph, viewport, or pointer interaction.
Model: ISO 5725 repeatability s_r from m≥2 duplicate differences.
Scope: ISO 5725 duplicate-difference repeatability: s_r = √(Σ d_i² / (2m)) from m≥2 pairs. m=1 is rejected.
Verification: Engine tested · Source checked · v1.0.1 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · ISO 5725 s_r = sqrt(Σ d² / (2m)) from m≥2 differences, + O3 mpmath tabulated duplicate sd.· 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 24091842c569
Legacy regression: 8/8 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 · 4/4 CVP boundary · 4/4 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 — Repeatability variance from duplicate differences
ISO 5725-1 — Accuracy (trueness and precision) of measurement methods and results — Repeatability standard deviation s_r
Sources
Evidence: 1 legacy golden · 4 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 4/4 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.

Repeatability ss_r = √(Σ d_i² / (2m))

im is the number of pairs. This page does not take a sample of observations and does not report r = 2.8·s_r. Range-method EV uses R̄/d2 on Gauge R&R.

How to use

Enter d_i

Comma-separated duplicate differences. Aliases: diffs, differences, delta. Negative values are allowed (they are squared). Or send y1 and y2 of equal length.

Read s_r

s_r is the repeatability standard deviation. Use Precision when you have a sample and need r = 2.8·s. Use Gauge R&R for EV from ranges.

Example calculations

Common configurations with formula and result.

6 and 8

d=[6,8]

s_r=√((36+64)/4)

s_r=5 · m=2

From pairs

y1=[10,20] · y2=[4,12]

d=[6,8]

s_r=5 · m=2

One pair rejected

d=[6]

m≥2

VALUE_OUT_OF_RANGE

Repeatability from Duplicates calculator specification

Version 1.0.1 · Engine tested

Calculation status

Engine tested 8/8 tests · Production surface contract 6/6
Named expert review Not performed
Calculation version 1.0.1

Review policy · Evidence

Definition: From m≥2 duplicate differences d_i, s_r = √(Σ d_i² / (2m)). Each pair is two observations under repeatability conditions. m=1 is rejected so this cannot wrap |d|/√2.
What it calculates: ISO 5725 repeatability s_r from m≥2 duplicate differences.
Inputs: d
Outputs: s_r
m
d
Formula: s_r=√(Σd²/(2m))
Assumptions: ISO 5725 duplicate-difference repeatability: s_r = √(Σ d_i² / (2m)) from m≥2 pairs. m=1 is rejected.
d_i may be negative or zero. Both zero is valid (s_r = 0).
Not Type A from a sample of observations, not r = 2.8·s, and not AIAG GRR EV = R̄/d2.
Units: same as d
Boundary conditions: missing d (and no y1+y2) → MISSING_REQUIRED_INPUT
m = 1 → VALUE_OUT_OF_RANGE
y1/y2 length mismatch → INVALID_INPUT
d = [0,0] is valid
Example: d=[6,8] → s_r=5
Validation cases: 3 published on this page · 8/8 tests · Production surface contract 6/6 · View evidence
d=[6,8] → s_r=5 m=2
y1=[10,20] y2=[4,12] → s_r=5
d=[6] → VALUE_OUT_OF_RANGE
Sources: ISO 5725-2 — Repeatability and reproducibility of standard measurement methods — Repeatability variance from duplicate differences
Supports: Each pair contributes d_i²/2 to the within-laboratory variance. Pooled over m pairs, s_r² = Σ d_i² / (2m).
ISO 5725-1 — Accuracy (trueness and precision) of measurement methods and results — Repeatability standard deviation s_r
Supports: This page estimates s_r from already-formed differences. It does not report the conventional limit r = 2.8·s_r.
Calculation version: 1.0.1

Background

Interpretation and common distinctions.

Compute ISO 5725 repeatability from duplicate differences.

Supported and not supported

Supported — s_r from m≥2 differences · y1/y2 pairs · d_i = 0 is valid · API engineering.measurement.duplicate_sd

Not supported — Type A from a sample, r = 2.8·s, m=1 wrap of |d|/√2, AIAG GRR EV

Agent / API notes

Capability id: engineering.measurement.duplicate_sd · tool id: duplicate-sd · pin 1.0.1.

{ "d": [6, 8] }

Aliases: diffs / differences / delta for d; y1+y2 for the two columns. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, INVALID_INPUT, VALUE_OUT_OF_RANGE.

Calculator URL stays /calc/engineering/repeatability-from-duplicates. There is no /calc/metrology.

Other calculators in this family: Measurement precision, ISO 5725 reproducibility, Type A uncertainty, Pooled standard deviation, Cochran's C, Gauge R&R, Uncertainty of a mean from precision, Tolerance / Uncertainty Workspace .

Frequently asked questions

Key distinctions behind the calculation.

Is this Type A uncertainty?

No. Type A takes one sample of observations. This page takes duplicate differences and uses the 2m denominator of ISO 5725.

Is this the same as precision / r?

No. Precision takes a sample and reports s and r = 2.8·s. This page reports only s_r from pair differences and does not multiply by 2.8.

Is this Gauge R&R EV?

No. Gauge R&R range-method EV is R̄/d2. For n=2, d2=1.128, which is not 1/√2. A single pair is rejected here so |d|/√2 cannot wrap that estimator either.

Can I enter the two columns instead of d?

Yes. y1 and y2 of equal length give d_i = y1_i − y2_i. If d is also sent, d is used.

Where does this run?

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