Engineering calculator

Measurement Bias Calculator

Compute VIM trueness as the signed bias = x̄ − xm from repeats on a master. Runs locally. Not a single-shot measurement error, not Type A u_A, and not Cg.

Instant result

Result

—

Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary Engine tested · Source checked · 9/9 tests · Production surface contract 4/4 · v1.0.0

Input interpretation: Enter values to calculate.
Result: —
Model: VIM trueness as signed bias = x̄ − xm from repeats on a master.
Scope: VIM trueness: signed bias = x̄ − xm from repeats on a master. s may be zero.
Verification: Engine tested · 9/9 tests · Production surface contract 4/4 · Source checked · v1.0.0
Named expert review: Optional · Not performed
Sources: JCGM 200:2012 — International vocabulary of metrology (VIM) — 2.13 measurement accuracy; 2.14 measurement trueness; 2.18 measurement bias
ISO 5725-1 — Accuracy (trueness and precision) of measurement methods and results — Trueness as bias of the mean versus a reference
Sources
Evidence: 5 boundary · 4 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.

Meanx̄ = Σxᵢ / n

Sample ss = √(Σ(xᵢ − x̄)² / (n − ddof))

Biasbias = x̄ − xm

ibias is signed. s may be zero. This is not a single-shot ε, not Type A u_A = s/√n, and not Type-1 Cg (no T).

How to use

Enter repeats on a master

Comma, space, or semicolon separated. JSON arrays also work. Sample s needs at least two values when ddof=1.

Enter xm

Master / reference value in the same unit. Aliases: xref, ref, x_m.

Read bias, then x̄ and s

bias is signed. Use Measurement error for a single ylab. Use Type A when you need u_A. Use Gauge capability when you have T.

Example calculations

Common configurations with formula and result.

Offset repeats

values=6,7,8 · xm=8

x̄=7; bias=7−8

bias=−1 · s=1

Centered, s=0

values=8,8,8 · xm=8

x̄=8; bias=0; s=0

bias=0 · s=0

Measurement Bias calculator specification

Version 1.0.0 · Engine tested

Calculation status

Engine tested 9/9 tests · Production surface contract 4/4
Named expert review Not performed
Calculation version 1.0.0

Review policy · Evidence

Definition: From n repeats on a master, mean x̄, sample s (ddof=1 default), and signed bias = x̄ − xm. VIM accuracy is qualitative; this page reports the quantity used for trueness.
What it calculates: VIM trueness as signed bias = x̄ − xm from repeats on a master.
Inputs: values
xm
ddof
Outputs: bias
abs_bias
xbar
s
xm
n
Formula: bias=x̄−xm
Assumptions: VIM trueness: signed bias = x̄ − xm from repeats on a master. s may be zero.
Not a single-shot measurement error, not Type A u_A = s/√n, and not Type-1 Cg (no T).
Units: same as values / xm
Boundary conditions: missing values or xm → MISSING_REQUIRED_INPUT
n=1 with ddof=1 → VALUE_OUT_OF_RANGE
s=0 is valid
Example: values=[6,7,8] xm=8 → bias=−1 s=1
Validation cases: 3 published on this page · 9/9 tests · Production surface contract 4/4 · View evidence
values=[6,7,8] xm=8 → bias=−1 s=1
values=[8,8,8] xm=8 → bias=0 s=0
values=[1] xm=8 → VALUE_OUT_OF_RANGE
Sources: JCGM 200:2012 — International vocabulary of metrology (VIM) — 2.13 measurement accuracy; 2.14 measurement trueness; 2.18 measurement bias
Supports: Accuracy is qualitative; trueness is closeness of the mean to a reference; bias is the estimate of a systematic measurement error
ISO 5725-1 — Accuracy (trueness and precision) of measurement methods and results — Trueness as bias of the mean versus a reference
Supports: This page reports signed bias of the sample mean; it does not report a precision index as the product
Calculation version: 1.0.0

Background

Interpretation and common distinctions.

Compute VIM trueness as the signed measurement bias of a sample mean.

Supported and not supported

Supported — signed bias = x̄ − xm from repeats on a master · s may be zero · API engineering.measurement.accuracy

Not supported — single-shot measurement error ε, Type A u_A, Type-1 Cg/Cgk, percent error (×100), pass/fail

Agent / API notes

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

{ "values": [6, 7, 8], "xm": 8 }

Aliases: sample for values; xref / ref / x_m / X for xm. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, INVALID_INPUT, VALUE_OUT_OF_RANGE.

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

Other calculators in this family: Measurement error, MSA linearity, MSA hysteresis, Gauge capability (Cg/Cgk), Type A uncertainty, Measurement precision, Process performance (Pp/Ppk), Percent error, Tolerance / Uncertainty Workspace .

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Frequently asked questions

Key distinctions behind the calculation.

Is this the same as measurement error?

No. Measurement error is a single ylab minus xref. This page takes repeats, then signed bias of the mean versus a master.

Is this Type A uncertainty?

No. Type A reports u_A = s/√n of the mean. This page reports bias versus xm and does not report u_A.

Is this the same as Cg/Cgk?

No. Gauge capability needs a characteristic tolerance T and a fraction frac. This page does not take T and does not issue a Cg≥1.33 verdict.

Does s = 0 fail?

No. Perfect repeats still have a defined bias. n = 1 with ddof = 1 is VALUE_OUT_OF_RANGE because sample s is undefined.

Where does this run?

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