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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
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Source checked · 8/8 tests · Production surface contract 4/4 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
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 · 8/8 tests · Production surface contract 4/4 · Source checked · v1.0.0
Named expert review
Optional · Not performed
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
5 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.

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

1

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.

2

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.

ϟ

6 and 8

d=[6,8]

s_r=√((36+64)/4)
s_r=5 · m=2
ϟ

From pairs

y1=[10,20] · y2=[4,12]

d=[6,8]
s_r=5 · m=2
ϟ

One pair rejected

d=[6]

m≥2
VALUE_OUT_OF_RANGE

Repeatability from Duplicates calculator specification

Version 1.0.0 · Engine tested

Calculation status

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 4/4 · 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
1.0.0

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 1.0.0.

{ "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 .

s Measurement precision › R ISO 5725 reproducibility › uA Type A uncertainty › s_p Pooled standard deviation › C Cochran's C › GRR Gauge R&R › u Uncertainty of a mean from precision › WS 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.