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ISO 5725 Reproducibility Calculator

Compute the ISO 5725 reproducibility limit from stated components s_r and s_L: s_R = √(s_r²+s_L²), R = 2.8·s_R. Runs locally. Not r from a sample, not AIAG GRR, and not combined RSS.

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 reproducibility s_R and limit R from stated s_r and s_L.
Scope
ISO 5725 reproducibility: s_R = √(s_r²+s_L²), R = 2.8·s_R from stated components.
Verification
Engine tested · 8/8 tests · Production surface contract 4/4 · Source checked · v1.0.0
Named expert review
Optional · Not performed
Sources
  • ISO 5725-1 — Accuracy (trueness and precision) of measurement methods and results — Reproducibility standard deviation s_R and reproducibility limit R
  • ISO 5725-2 — Repeatability and reproducibility of standard measurement methods — s_R = √(s_r² + s_L²)
Sources
Evidence
5 boundary · 3 property · Production surface contract 4/4 · Artifact integrity PASS
Production
Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (1 capability; 156 remain CURRENT) @ 2026-09-14T03:54:53.650Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

Reproducibility ss_R = √(s_r² + s_L²)
Reproducibility limitR = 2.8 · s_R
i2.8 is the ISO 5725 conventional factor, not coverage factor k. This page does not take a sample and does not take a single s_R.

How to use

1

Enter s_r

Repeatability standard deviation, already computed. Aliases: sr, s_repeatability, repeatability. Must be ≥ 0.

2

Enter s_L

Between-laboratory or between-condition standard deviation. Aliases: sL, s_lab, s_between. Must be ≥ 0.

3

Read R, then s_R

R is the reproducibility limit. Use Precision when you have repeats and need r = 2.8·s. Use Gauge R&R for EV/AV/PV. Combined RSS is a different contract.

Example calculations

Common configurations with formula and result.

ϟ

3-4-5 components

s_r=3 · s_L=4

s_R=5; R=2.8·5
R=14 · s_R=5
ϟ

No between-lab term

s_r=1 · s_L=0

s_R=1; R=2.8
R=2.8 · s_R=1

ISO 5725 Reproducibility calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
From stated repeatability s_r ≥ 0 and between-laboratory s_L ≥ 0, s_R = √(s_r² + s_L²) and the ISO 5725 reproducibility limit R = 2.8·s_R.
What it calculates
ISO 5725 reproducibility s_R and limit R from stated s_r and s_L.
Inputs
  • s_r
  • s_L
Outputs
  • R
  • s_R
  • s_r
  • s_L
  • factor
Formula
s_R=√(s_r²+s_L²); R=2.8·s_R
Assumptions
  • ISO 5725 reproducibility: s_R = √(s_r²+s_L²), R = 2.8·s_R from stated components.
  • s_r and s_L are ≥ 0. Both zero is valid (R = 0).
  • Not r = 2.8·s from a sample, not AIAG GRR, and not combined RSS.
  • Does not take a single s_R as input.
Units
  • same as s_r / s_L
Boundary conditions
  • missing s_r or s_L → MISSING_REQUIRED_INPUT
  • negative s_r or s_L → VALUE_OUT_OF_RANGE
  • s_L = 0 is valid
Example
s_r=3 s_L=4 → s_R=5 R=14
Validation cases

3 published on this page · 8/8 tests · Production surface contract 4/4 · View evidence

  • s_r=3 s_L=4 → s_R=5 R=14
  • s_r=1 s_L=0 → s_R=1 R=2.8
  • s_r=3 → MISSING_REQUIRED_INPUT
Sources
  • ISO 5725-1 — Accuracy (trueness and precision) of measurement methods and results — Reproducibility standard deviation s_R and reproducibility limit R
    Supports: s_R combines repeatability and between-laboratory variation. R = 2.8·s_R is the conventional reproducibility limit.
  • ISO 5725-2 — Repeatability and reproducibility of standard measurement methods — s_R = √(s_r² + s_L²)
    Supports: This page takes stated s_r and s_L. It does not estimate them from a collaborative study table.
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute the ISO 5725 reproducibility limit from stated repeatability and between-laboratory components.

Supported and not supported

Supported — s_R and R from paired s_r, s_L · s_L = 0 is valid · API engineering.measurement.reproducibility

Not supported — r = 2.8·s from a sample, a single s_R wrap, AIAG GRR, combined RSS, pass/fail

Agent / API notes

Capability id: engineering.measurement.reproducibility · tool id: reproducibility · pin 1.0.0.

{ "s_r": 3, "s_L": 4 }

Aliases: sr / s_repeatability / repeatability for s_r; sL / s_lab / s_between for s_L. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_OUT_OF_RANGE.

Calculator URL stays /calc/engineering/reproducibility. There is no /calc/metrology.

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Frequently asked questions

Key distinctions behind the calculation.

Is this the same as precision / r?

No. Precision takes a sample and reports r = 2.8·s. This page takes two already-stated components s_r and s_L, then R = 2.8·√(s_r²+s_L²). A single s_R is not an input.

Is this Gauge R&R?

No. Gauge R&R composes AIAG EV, AV, and PV. s_L is a between-laboratory (or between-condition) standard deviation of a measurement method, not AV.

Is this ISO 21748 u of a mean?

No. This page reports R = 2.8·s_R of a single result. Uncertainty of a mean from precision takes the same s_r and s_L plus n≥2 and reports u = √(s_L²+s_r²/n).

Is this combined RSS?

No. Combined RSS combines standard uncertainties of a measurement model: u_c = √Σ u_i². This page composes ISO 5725 precision components. Four u_i = 1 give RSS = 2; that is a different contract.

Is 2.8 the coverage factor k?

No. Coverage factor k is a different page. 2.8 is the ISO 5725 conventional factor, the same constant used for r.

Where does this run?

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