Engineering calculator

Measurement Error Calculator

Compute the VIM signed measurement error ε = ylab − xref and the relative error ε/xref. Runs locally. Not percent error, not En, and not a z-score.

Instant result

Result

—

Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Signed measurement error ε = ylab − xref, plus the relative error when the reference is not zero, + O3 mpmath tabulated measurement error.

Input interpretation: Enter values to calculate.
Result: —
Verified scope: Signed measurement error ε = ylab − xref, plus the relative error when the reference is not zero, + O3 mpmath tabulated measurement error.
Assurance: Engineering
Declared partition coverage: PASS · 6/6 declared partitions (positive, negative, zero-or-equal, alias, awkward, invalid-domain) · Matrix
Deferred: Not percent error, not En, and not a z-score.
Numerical scope: O2: signed measurement error vs a separate-module subtraction (≤2 ULP). Not percent error, not En, and not a z-score. ≤2 ULP vs O3 applies only to the published tabulated measurement-error vectors. Not percent error.
Known limitations: Core CVP does not include live graph, viewport, or pointer interaction.
Model: VIM signed measurement error and relative error ε/xref.
Scope: VIM measurement error ε = ylab − xref (signed). Relative error is ε/xref when xref ≠ 0.
Verification: Engine tested · Source checked · v1.0.1 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Signed measurement error ε = ylab − xref, plus the relative error when the reference is not zero, + O3 mpmath tabulated measurement error.· 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 34ab16e68069
Legacy regression: 6/6 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 · 2/2 CVP boundary · 3/3 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 6/6 CVP contract · Manifest
Sources: JCGM 200:2012 — International vocabulary of metrology (VIM) — 2.16 measurement error; 2.17 relative measurement error
ISO 13528 — Statistical methods for use in proficiency testing by interlaboratory comparison — z, zeta, and En are different contracts
Sources
Evidence: 1 legacy golden · 2 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 3/3 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.

Measurement errorε = ylab − xref

Relative errorε_rel = ε / xref (xref ≠ 0)

iThis is the VIM signed error. It is not percent error (×100). It is not En, zeta, or z-score — those divide by U, u, or σ_pt.

How to use

Enter ylab and xref

Measured value and reference, in the same unit. xref may be zero; then ε is still defined and ε_rel is omitted.

Read ε, then ε_rel

ε is signed. Use Percent error when you want a ×100 laboratory percent. Use En / zeta / z when you need a proficiency-testing score.

Example calculations

Common configurations with formula and result.

Centered relative

ylab=2.5 · xref=2

ε=0.5; ε_rel=0.5/2

ε=0.5 · ε_rel=0.25

Zero reference

ylab=2.5 · xref=0

ε=2.5; ε_rel undefined

ε=2.5 · ε_rel=—

Measurement Error calculator specification

Version 1.0.1 · Engine tested

Calculation status

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

Review policy · Evidence

Definition: ε = ylab − xref. Relative error is ε / xref when xref ≠ 0. ylab is the measured quantity value and xref the reference quantity value. The result is signed and is not multiplied by 100.
What it calculates: VIM signed measurement error and relative error ε/xref.
Inputs: ylab
xref
Outputs: error
abs_error
relative
Formula: ε=ylab−xref; ε_rel=ε/xref (xref≠0)
Assumptions: VIM measurement error ε = ylab − xref (signed). Relative error is ε/xref when xref ≠ 0.
Not percent error (×100), not En, not zeta, not z-score, and not an ILAC G8 spec decision.
Units: same as ylab/xref; relative is dimensionless
Boundary conditions: missing ylab or xref → MISSING_REQUIRED_INPUT
relative op with xref = 0 → INVALID_INPUT
Example: ylab=2.5 xref=2 → ε=0.5 ε_rel=0.25
Validation cases: 2 published on this page · 6/6 tests · Production surface contract 6/6 · View evidence
ylab=2.5 xref=2 → ε=0.5 ε_rel=0.25
ylab=2.5 xref=0 relative op → INVALID_INPUT
Sources: JCGM 200:2012 — International vocabulary of metrology (VIM) — 2.16 measurement error; 2.17 relative measurement error
Supports: ε = measured quantity value minus a reference quantity value; relative error = ε / reference
ISO 13528 — Statistical methods for use in proficiency testing by interlaboratory comparison — z, zeta, and En are different contracts
Supports: This page does not compute a PT score; it reports the raw signed error
Calculation version: 1.0.1

Background

Interpretation and common distinctions.

Compute the VIM signed measurement error.

Supported and not supported

Supported — signed ε = ylab − xref · relative ε/xref when xref ≠ 0 · API engineering.measurement.error

Not supported — percent error (×100), En, zeta, z-score, ILAC G8 spec decision, bias from a sample of repeats (that is Accuracy)

Agent / API notes

Capability id: engineering.measurement.error · tool id: measurement-error · pin 1.0.1.

{ "ylab": 2.5, "xref": 2 }

Aliases: y / x / measured for ylab; X / ref / reference for xref. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, INVALID_INPUT.

Calculator URL stays /calc/engineering/measurement-error. There is no /calc/metrology.

Frequently asked questions

Key distinctions behind the calculation.

Is this the same as percent error?

No. Percent error is a math page that reports a percentage, often |O−T|/|T|×100. This page reports the signed VIM error and ε/xref without ×100.

Is ε the same as En, zeta, or z?

No. Those divide the difference by expanded U, combined standard u, or scheme σ_pt. This page does not divide by an uncertainty.

What happens when xref is 0?

ε is still ylab. Relative error is omitted (null). The relative op returns INVALID_INPUT.

Where does this run?

Locally in the browser by default. REST and MCP call the same metrology-engine measurement_error ops.