Verified calculation capability

Capacitance Calculation Capability

Parallel-plate and series/parallel capacitance. · Electrical

Capability ID electrical.capacitance · version 1.1.0

Open calculator REST API MCP Evidence Evidence JSON CVP Manifest Review policy

Model

Parallel plate

Parallel plate: C = ε0·εr·A/d
Parallel: C = C1+C2+…
Series: 1/C = 1/C1+1/C2+…

Inputs / Outputs

Canonical symbols for this capability. Agent schemas remain the contract.

Symbol	Quantity	Unit	Role
`C`	—	F	output

Assumptions / Validity

Declared scope for this capability. Do not use it outside this domain.

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

Not supported

Coaxial/cylindrical exact models
fringing
frequency-dependent or complex permittivity
ESR/ESL
leakage

Example

One numerical check. The calculator page holds worked steps and FAQ.

A=0.01 m², d=0.001 m, er=4 → 354.17 pF

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance. Computational verification is defined by CVP. Supplemental domain review (internal) and named expert review are defined by the Review policy and do not by themselves determine CVP conformance.

CVP: CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Assurance: Engineering
Declared partition coverage: PASS · 4/4 declared partitions (plate, parallel, series, invalid-domain)
Calculation version: 1.1.0
Verification: 17/17 calculation tests · 3/3 legacy golden · 8/8 legacy boundary · 6/6 legacy property
Production surface contract: 4/4
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
Reference: O1 model · 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 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.
CVP suite: 3/3 golden · 9/9 CVP boundary · 12/12 invalid · 5/5 property · 5/5 metamorphic · 7/7 cross-interface · 4/4 CVP contract
Supplemental domain review: Internal · Pass · electrical-engineer
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.1.0 (workspace artifacts agree)
Review-policy tier: Internal engineering review — catalog token expert_verified; supplemental; not CVP status

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

Call this capability

Human page, REST, and MCP share the same engine and calculation_version. Build verified hashes workspace artifacts only. After deploy, attest:production GETs canonical URLs twice — the public/cached view an Agent actually hits, and origin — including every /capabilities/{id} HTML page. Public Capability HTML version must match catalog before production attestation passes. Live Trust rows above fetch /.well-known/calculatorx-production-attestation.json and the output schema const. Build hashes: release integrity. That proves currently published page / engine / schema / evidence / MCP agree — not that a historical version is independently immutable. Reference Calculation Standard — Production surface contract 4/4.

Tool id: capacitance
Engine: capacitance
REST: POST /api/v1/calc/capacitance
MCP: execute_calculation with capability_id: "electrical.capacitance"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.1.0)
Versioned output schema: Immutable pin (1.1.0)

Operations

Declared calculation modes for this capability.

plate
parallel
series

References

Human-readable sources plus CVP reference evidence classes.

Sources

IEC 60050-131 — International Electrotechnical Vocabulary — Capacitance (IEV 131-12-13)
IEC 60050-121 — International Electrotechnical Vocabulary — Electric constant (IEV 121-11-03)
IEC 60050-121 — International Electrotechnical Vocabulary — Relative permittivity (IEV 121-12-13)
NIST CODATA 2022 — Vacuum electric permittivity ε0
Horowitz & Hill — The Art of Electronics, 3rd ed. — Capacitor networks (series/parallel combinations)

Reference evidence classes: O1 model · O2 expected_values · O2 numerical_behavior

Try with an agent

Inspect this capability via same-origin MCP, then call execute_calculation.

curl -sS -X POST 'https://www.calculatorx.com/mcp' \
  -H 'Content-Type: application/json' \
  -H 'MCP-Protocol-Version: 2026-07-28' \
  -H 'Mcp-Method: tools/call' \
  -H 'Mcp-Name: inspect_capability' \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/call","params":{"name":"inspect_capability","arguments":{"capability_id":"electrical.capacitance"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.1.0) when reproducibility matters. Full protocol notes: MCP docs.