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.
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
- ISO 5725-2 — Repeatability and reproducibility of standard measurement methods
- 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- Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (1 capability; 156 remain CURRENT)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.
How to use
Enter s_r
Repeatability standard deviation, already computed. Aliases: sr, s_repeatability, repeatability. Must be ≥ 0.
Enter s_L
Between-laboratory or between-condition standard deviation. Aliases: sL, s_lab, s_between. Must be ≥ 0.
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.
3-4-5 components
s_r=3 · s_L=4
No between-lab term
s_r=1 · s_L=0
ISO 5725 Reproducibility calculator specification
Version 1.0.0 · Engine tested
- Engine tested 8/8 tests · Production surface contract 4/4
- Named expert review Not performed
- Calculation version 1.0.0
- 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 RSupports: 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.
- ISO 5725-1 — Accuracy (trueness and precision) of measurement methods and results — Reproducibility standard deviation s_R and reproducibility limit R
- 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.
Related tools
Other calculators in this family: Measurement precision, Gauge R&R, Type A uncertainty, Uncertainty of a mean from precision, Welch–Satterthwaite ν_eff, Inverse-variance weighted mean, Coverage factor k, Tolerance / Uncertainty Workspace .
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.