Engineering calculator

Maximum Permissible Error Calculator

Decide whether a measured value meets the VIM maximum permissible measurement error: pass iff |ylab−xref| ≤ MPE. Runs locally. Not an ILAC G8 spec decision, not En, and not ε-only.

Instant result

Result

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Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · MPE ratio |ylab − xref| / MPE, with equality counted as pass, + O3 mpmath tabulated MPE.

Input interpretation: Enter values to calculate.
Result: —
Verified scope: MPE ratio |ylab − xref| / MPE, with equality counted as pass, + O3 mpmath tabulated MPE.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (alias, awkward, pass, fail, invalid-domain) · Matrix
Deferred: Not En and not an ILAC G8 guard band.
Numerical scope: O2: MPE ratio vs a separate-module identity (≤2 ULP). Not En. ≤2 ULP vs O3 applies only to the published tabulated MPE vectors. Not En.
Known limitations: Core CVP does not include live graph, viewport, or pointer interaction.
Model: VIM MPE decision: pass iff |ylab−xref| ≤ MPE, plus |ε|/MPE.
Scope: VIM maximum permissible measurement error: pass iff |ylab−xref| ≤ MPE
Verification: Engine tested · Source checked · v1.0.1 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · MPE ratio |ylab − xref| / MPE, with equality counted as pass, + O3 mpmath tabulated MPE.· 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 c1588f98a65e
Legacy regression: 9/9 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 · 5/5 CVP boundary · 5/5 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) — 4.26 maximum permissible measurement error (maximum permissible error, limit of error)
ISO 14253-1 — Geometrical product specifications (GPS) — Inspection by measurement of workpieces and measuring equipment — Decision rules vs MPE of a measuring equipment
Sources
Evidence: 1 legacy golden · 5 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 5/5 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.

Errorε = ylab − xref

Decision|ε| ≤ MPE → pass

iMPE is a stated maximum permissible measurement error. This page does not compare y to LSL/USL and does not divide by U.

How to use

Enter ylab and xref

Measured value and reference, in the same unit as MPE.

Enter MPE

Must be greater than zero. U, Ulab, and T are not aliases.

Read the decision

|ε| ≤ MPE is pass, including equality. ratio = |ε|/MPE. Use Measurement error when you only need ε; use En when you divide by expanded U.

Example calculations

Common configurations with formula and result.

Pass

ylab=2.5 · xref=2 · MPE=1

|0.5| ≤ 1

pass · ratio=0.5

Fail

ylab=4 · xref=2 · MPE=1

|2| ≤ 1

fail · ratio=2

Maximum Permissible Error calculator specification

Version 1.0.1 · Engine tested

Calculation status

Engine tested 9/9 tests · Production surface contract 6/6
Named expert review Not performed
Calculation version 1.0.1

Review policy · Evidence

Definition: Pass if |ylab − xref| ≤ MPE. ylab is the measured quantity value, xref the reference, and MPE the maximum permissible measurement error. Equality is pass. ratio = |ε|/MPE.
What it calculates: VIM MPE decision: pass iff |ylab−xref| ≤ MPE, plus |ε|/MPE.
Inputs: ylab
xref
MPE
Outputs: MPE
error
abs_error
ratio
decision
Formula: ε=ylab−xref; pass iff |ε|≤MPE; ratio=|ε|/MPE
Assumptions: VIM maximum permissible measurement error: pass iff |ylab−xref| ≤ MPE
Equality is pass. ratio = |ε|/MPE
Not an ILAC G8 spec decision on y, not En, and not ε without a limit
U, Ulab, and T are not aliases for MPE
Units: same as ylab/xref/MPE; ratio and decision are dimensionless
Boundary conditions: missing ylab, xref, or MPE → MISSING_REQUIRED_INPUT
MPE ≤ 0 → VALUE_MUST_BE_POSITIVE
Ulab or T without MPE → MISSING_REQUIRED_INPUT
Example: ylab=2.5 xref=2 MPE=1 → error=0.5 ratio=0.5 pass
Validation cases: 4 published on this page · 9/9 tests · Production surface contract 6/6 · View evidence
ylab=2.5 xref=2 MPE=1 → error=0.5 ratio=0.5 pass
ylab=2.5 xref=2 MPE=0.5 → ratio=1 pass
ylab=4 xref=2 mpe=1 → ratio=2 fail
ylab=2.5 xref=2 MPE=0 → VALUE_MUST_BE_POSITIVE
Sources: JCGM 200:2012 — International vocabulary of metrology (VIM) — 4.26 maximum permissible measurement error (maximum permissible error, limit of error)
Supports: MPE is the extreme value of measurement error permitted by specifications or regulations. Pass iff |ε| ≤ MPE.
ISO 14253-1 — Geometrical product specifications (GPS) — Inspection by measurement of workpieces and measuring equipment — Decision rules vs MPE of a measuring equipment
Supports: MPE is a stated error limit of the measuring equipment, not an ILAC G8 specification decision on the workpiece characteristic y
Calculation version: 1.0.1

Background

Interpretation and common distinctions.

Decide whether a measured value meets the VIM maximum permissible measurement error.

Supported and not supported

Supported — |ylab − xref| ≤ MPE · ratio = |ε|/MPE · equality is pass · API engineering.conformity.mpe

Not supported — ILAC G8 specification decision on y, En, zeta, z-score, ε without a limit, TUR≥4 verdict

Agent / API notes

Capability id: engineering.conformity.mpe · tool id: mpe · pin 1.0.1.

{ "ylab": 2.5, "xref": 2, "MPE": 1 }

Aliases: y / x / measured for ylab; X / ref / reference for xref; mpe for MPE. U, Ulab, and T are not aliases. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE.

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

Other calculators in this family: Measurement error, Conformity decision, Normalized error En, Zeta-score, Measurement bias (trueness), Test uncertainty ratio TUR, Tolerance / Uncertainty Workspace .

Frequently asked questions

Key distinctions behind the calculation.

Is this the same as the decision-rule page?

No. Decision-rule compares a measured y to specification limits LSL/USL, optionally with a guard band. This page compares the signed measurement error to a stated MPE. There is no specification interval here.

Is |ε| ≤ MPE the same as En?

No. En divides ylab−xref by √(Ulab²+Uref²). This page does not take U. Use Normalized error when you have expanded uncertainties for a proficiency test.

Is equality a pass?

Yes. |ε| = MPE is pass. MPE must be greater than zero.

Where does this run?

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