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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 Engine tested · Source checked · 6/6 tests · Production surface contract 4/4 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
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 · 6/6 tests · Production surface contract 4/4 · Source checked · v1.0.0
Named expert review
Optional · Not performed
Sources
Sources
Evidence
3 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.

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

1

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.

2

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.

ϟ

Centered relative

ylab=2.5 · xref=2

ε=0.5; ε_rel=0.5/2
ε=0.5 · ε_rel=0.25
ϟ

Zero reference

ylab=2.5 · xref=0

ε=2.5; ε_rel undefined
ε=2.5 · ε_rel=—

Measurement Error calculator specification

Version 1.0.0 · Engine tested

Calculation status

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 4/4 · 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
1.0.0

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 1.0.0.

{ "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.

Other calculators in this family: Percent error, Maximum permissible error MPE, Normalized error En, Zeta-score, Proficiency-testing z-score, Type A uncertainty, Measurement bias (trueness), MSA linearity, MSA hysteresis, Tolerance / Uncertainty Workspace .

% Percent error › MPE Maximum permissible error MPE › En Normalized error En › ζ Zeta-score › z Proficiency-testing z-score › uA Type A uncertainty › δ Measurement bias (trueness) › lin MSA linearity › H MSA hysteresis › WS Tolerance / Uncertainty Workspace ›
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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.