Public evidence

electrical.capacitance

Machine-checked verification for calculation version 1.1.0 · tier expert_verified

Open calculator API Capability Download JSON CVP Manifest MCP Review policy

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· Ideal parallel plates with a homogeneous isotropic dielectric fully filling the gap. εr is a scalar ≥ 1. Fringing, frequency dependence, dielectric loss, leakage, ESR/ESL and parasitics are neglected. · Protocol · Schema · Production report

Declared partition coverage: PASS · 4/4 declared partitions (plate, parallel, series, invalid-domain)
Versions: Calculation 1.1.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-11.url-canonical-mode
Verification revision: 2026-09-11.url-canonical-mode · 5/5 property · digest 2e5db26b1665

Verification

Legacy regression suite: 17/17 calculation tests · Production surface contract 4/4

Three distinct suites: educational examples on the calculator page, this legacy regression count (17/17 golden + boundary), and the CVP verification suite below. They are not the same number. Property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the CVP Manifest . SKIP (0/0) means that suite has no published vectors.

This calculator CURRENT · Public schema 1.1.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓

CVP verification suite

Protocol checks from the Evidence Manifest. Distinct from the legacy regression suite above. Verification revision 2026-09-11.url-canonical-mode. Calculation version 1.1.0. CVP 1.0.0-proposed. 3/3 golden · 9/9 CVP boundary · 12/12 invalid · 5/5 property · 5/5 metamorphic · 7/7 cross-interface · 4/4 CVP contract. digest 2e5db26b1665.

Golden (oracle-backed) 3 / 3
CVP boundary 9 / 9
Invalid input 12 / 12
Property 5 / 5
Metamorphic 5 / 5
Cross-interface 7 / 7
CVP contract 4 / 4
Interfaces PASS · UI (SSR) / REST / MCP
Interface claim ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 2/2 (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.
Assurance Engineering

release artifacts aligned PASS
schema valid input executes PASS
engine success output validates schema PASS
schema rejects incomplete input PASS

Fingerprint sha256:517e5fb7d116021589bd6cca4b4fa9db355d18438b09c41d81d446cb2237f824

Input schema sha256:898759233c3370b143287de0035df3f80febe06b5568a7e4c0fd11140f2b55b3 · Output schema sha256:b094fddc9f307c4f37eb04e6a6d5e2921190a217ee3a4dc2647c5a57c76ac1fa · Build-time SHA-256 digests prove published artifacts agree with each other (release_integrity.scope=workspace). Production attestation GETs canonical URLs twice (public/cached view and origin), including Capability HTML, via npm run attest:production --write (published at /.well-known/calculatorx-production-attestation.json) and fails if the public Capability page advertises a different calculation_version. This is artifact consistency, not an independent immutable release log.

Build & scope

Engine identity and declared limitations.

Tool: capacitance
Engine: capacitance
Engine build: 2026-09-11
Evidence core: 2026-09-11T14:32:48.551Z
Rendered: 2026-09-16T22:03:43.728Z
Last reviewed: 2026-09-11

Assumptions

Ideal parallel plates with a homogeneous isotropic dielectric fully filling the gap
Relative permittivity is a scalar constant (no frequency dependence or dielectric loss)
Fringing, leakage, ESR/ESL and parasitic capacitance are neglected
Scope is vacuum or conventional passive dielectric: εr ≥ 1

Limitations

Ideal parallel plates; homogeneous isotropic dielectric fully filling the gap; fringing, frequency dependence, dielectric loss, leakage, ESR/ESL and parasitics neglected

Sources

Standards and references supporting this tool specification. Methods are listed separately — they are algorithms, not bibliographic sources.

IEC 60050-131 — International Electrotechnical Vocabulary — Capacitance (IEV 131-12-13)
Supports: Definition C = Q/U
IEC 60050-121 — International Electrotechnical Vocabulary — Electric constant (IEV 121-11-03)
Supports: Vacuum electric permittivity ε0 used in C = ε0·εr·A/d
IEC 60050-121 — International Electrotechnical Vocabulary — Relative permittivity (IEV 121-12-13)
Supports: εr as a scalar ratio; this page does not use complex permittivity
NIST CODATA 2022 — Vacuum electric permittivity ε0
Supports: Engine constant ε0 = 8.8541878188×10⁻¹² F/m
Horowitz & Hill — The Art of Electronics, 3rd ed. — Capacitor networks (series/parallel combinations)
Supports: Parallel sum and series reciprocal sum

Legacy published checks

Golden and boundary cases from the legacy Evidence JSON. CVP property, metamorphic, round-trip, O3, and interface statuses/checks are recorded in the Manifest — including SKIP when a suite has no vectors.

ID	Kind	Status	Detail
`plate`	golden	pass	Expected C_F=3.54167512752e-10 · Actual mode=plate · A_m2=0.01 · d_m=0.001 · er=4 · C_F=3.54167512752e-10 · C_uF=0.000354167512752 · C_nF=0.35416751275200004 · C_pF=354.167512752
`parallel`	golden	pass	Expected C_F=0.000003 · Actual n=2 · mode=parallel · C_F=0.000003 · C_uF=3
`series`	golden	pass	Expected C_F=0.000001 · Actual n=2 · mode=series · C_F=0.000001 · C_uF=1
`bad-d`	boundary	pass	Expected VALUE_MUST_BE_POSITIVE · Actual VALUE_MUST_BE_POSITIVE
`boundary-cap-plate`	boundary	pass	Expected C_F=8.8541878188e-11 · Actual mode=plate · A_m2=0.01 · d_m=0.001 · er=1 · C_F=8.8541878188e-11 · C_uF=0.000088541878188 · C_nF=0.08854187818800001 · C_pF=88.541878188
`boundary-cap-series-three`	boundary	pass	Expected C_F=0.000001 · Actual n=3 · mode=series · C_F=0.000001 · C_uF=1
`boundary-cap-bad`	boundary	pass	Expected VALUE_MUST_BE_POSITIVE · Actual VALUE_MUST_BE_POSITIVE
`boundary-cap-d-zero`	boundary	pass	Expected VALUE_MUST_BE_POSITIVE · Actual VALUE_MUST_BE_POSITIVE
`boundary-cap-er-frac`	boundary	pass	Expected VALUE_OUT_OF_RANGE · Actual VALUE_OUT_OF_RANGE
`boundary-cap-one`	boundary	pass	Expected NEEDS_TWO_INPUTS · Actual NEEDS_TWO_INPUTS
`boundary-cap-mode`	boundary	pass	Expected INVALID_MODE · Actual INVALID_MODE
`property-plate`	property	pass	ε0·A/d
`property-parallel`	property	pass	ΣC
`property-series`	property	pass	½
`property-parallel-commute`	property	pass	C(C1,C2)=C(C2,C1)
`property-parallel-gt-max`	property	pass	Ceq>max(Ci)
`property-series-lt-min`	property	pass	Ceq<min(Ci)