Engineering calculator

Type B Uncertainty Calculator

Compute Type B standard uncertainty from a half-width a. Rectangular u_B = a/√3, triangular u_B = a/√6. Runs locally. Not GUM combination and not Monte Carlo.

Instant result

Result

—

Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Type B u_B from half-width a: rectangular a/√3 (uniform alias) and triangular a/√6 + O3 mpmath tabulated u_B.

Input interpretation: Enter values to calculate.
Result: —
Verified scope: Type B u_B from half-width a: rectangular a/√3 (uniform alias) and triangular a/√6 + O3 mpmath tabulated u_B.
Assurance: Engineering
Declared partition coverage: PASS · 6/6 declared partitions (rectangular, triangular, uniform-alias, default-dist, half-width-alias, invalid-domain) · Matrix
Deferred: Not GUM RSS of several uᵢ, not trapezoidal / U-shaped, not Monte Carlo, and not a standalone Combined/Expanded page.
Numerical scope: O2: u_B = a/√3 (rectangular) or a/√6 (triangular) vs separate-module identities (≤2 ULP). Not GUM combination, not trapezoidal, not Monte Carlo. ≤2 ULP vs O3 applies only to the published tabulated Type B vectors (rectangular, triangular, default, uniform alias, a=1, a=0.5 triangular, scale, half_width). It is not a whole-domain Type B guarantee and does not cover trapezoidal.
Known limitations: Core CVP does not include live graph, viewport, or pointer interaction.
Model: Type B u_B from half-width a under a rectangular or triangular assumption.
Scope: Type B: a is the half-width of the assumed distribution
Verification: Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Type B u_B from half-width a: rectangular a/√3 (uniform alias) and triangular a/√6 + O3 mpmath tabulated u_B.· View Manifest · CVP overview · Specification
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-16.o2-o3
Verification revision: 2026-09-16.o2-o3 · 3/3 property · digest 47360ca02434
Legacy regression: 8/8 tests · Production surface contract 4/4
Trust layers: Verification VERIFIED · Production CURRENT · overall VERIFIED
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: 5/5 golden · 4/4 CVP boundary · 7/7 invalid · 3/3 property · 2/2 metamorphic · 8/8 O3 · 4/4 cross-interface · 4/4 CVP contract · Manifest
Sources: JCGM 100:2008 (GUM) — Evaluation of measurement data — 4.3.7 Rectangular distribution
JCGM 100:2008 (GUM) — Evaluation of measurement data — 4.3.9 Triangular distribution
Sources
Evidence: 1 legacy golden · 4 legacy boundary · legacy regression suite · 5/5 oracle-backed golden · 7/7 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.

Rectangularu_B = a / √3

Triangularu_B = a / √6

ia is the half-width of the assumed distribution. This evaluates one Type B component, not GUM RSS of several uᵢ. Not Monte Carlo.

How to use

Enter half-width a

a must be greater than zero, in the same unit as the quantity.

Choose the assumed distribution

Rectangular (uniform) is the default. Triangular is the other seeded form.

Read u_B

Combine several u's on Uncertainty propagate. Type A from a sample is a different page.

Example calculations

Common configurations with formula and result.

Rectangular a=3

default

u_B=3/√3

u_B=√3 ≈ 1.73205

Triangular a=3

same half-width

u_B=3/√6

u_B=√(3/2) ≈ 1.22474

Type B Uncertainty calculator specification

Version 1.0.0 · Engine tested

Calculation status

Engine tested 8/8 tests · Production surface contract 4/4
Named expert review Not performed
Calculation version 1.0.0

Review policy · Evidence

Definition: From a half-width a, rectangular u_B = a/√3 (default) or triangular u_B = a/√6.
What it calculates: Type B u_B from half-width a under a rectangular or triangular assumption.
Inputs: a
distribution
Outputs: u_B
a
distribution
Formula: u_B = a/√3 (rectangular) or a/√6 (triangular)
Assumptions: Type B: a is the half-width of the assumed distribution
Rectangular (default, including uniform alias) u_B = a/√3; triangular u_B = a/√6
Not GUM combination of several uᵢ
Not Monte Carlo
Units: same as a
Boundary conditions: missing a → MISSING_REQUIRED_INPUT
a ≤ 0 → VALUE_MUST_BE_POSITIVE
distribution not rectangular or triangular → INVALID_INPUT
Example: a=3 distribution=rectangular → u_B=3/√3
Validation cases: 2 published on this page · 8/8 tests · Production surface contract 4/4 · View evidence
a=3 distribution=rectangular → u_B=3/√3
a=0 → VALUE_MUST_BE_POSITIVE
Sources: JCGM 100:2008 (GUM) — Evaluation of measurement data — 4.3.7 Rectangular distribution
Supports: If the quantity is modeled as rectangular with half-width a, u = a/√3
JCGM 100:2008 (GUM) — Evaluation of measurement data — 4.3.9 Triangular distribution
Supports: If the quantity is modeled as triangular with half-width a, u = a/√6
Calculation version: 1.0.0

Background

Interpretation and common distinctions.

Compute Type B standard uncertainty from a half-width.

Supported and not supported

Supported — rectangular u_B = a/√3 · triangular u_B = a/√6 · API engineering.uncertainty.type_b

Not supported — GUM RSS of several uᵢ, Type A from a sample, Monte Carlo, trapezoidal / U-shaped

Agent / API notes

Capability id: engineering.uncertainty.type_b · tool id: type-b · pin 1.0.0.

{ "a": 3, "distribution": "rectangular" }

distribution defaults to rectangular. uniform is accepted as an alias. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, INVALID_INPUT, VALUE_MUST_BE_POSITIVE.

Calculator URL stays /calc/engineering/type-b-uncertainty. There is no /calc/metrology.

Other calculators in this family: Type A uncertainty, Welch–Satterthwaite ν_eff, Type B degrees of freedom, Coverage factor k, Uncertainty propagate, Guard band, Tolerance / Uncertainty Workspace .

}

Frequently asked questions

Key distinctions behind the calculation.

Is this the same as Uncertainty propagate?

No. This page evaluates one Type B u_B from a half-width. Uncertainty propagate combines already-evaluated standard uncertainties (GUM). The type_b field on that page is only A/B metadata.

Why rectangular vs triangular?

GUM Type B often models a bound ±a as rectangular (u=a/√3) or triangular (u=a/√6). Uniform is an alias of rectangular.

Where does this run?

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