CVP verified calculation capability

AWG to mm / mm² Calculation Capability

Look up American Wire Gauge geometry: unrounded ASTM B258 geometric progression (primary) plus Table 1 SI standard nominals for integer 4/0–56; copper resistance at 20 °C; educational NFPA 70–style ampacity reference (edition not pinned). Accepts 12, 1/0, 4/0, or legacy −3…0.

Electrical Capability ID electrical.awg_to_mm version 1.5.0 CVP VERIFIED CURRENT Engineering

Model

Diameter

Diameter: dₙ (mm) = 0.127 × 92^((36−n)/39)
Area: Aₙ (mm²) = (π/4) × dₙ²
Area (direct): Aₙ (mm²) = 0.012668 × 92^((36−n)/19.5)
Heavy gauges: 4/0, 3/0, 2/0, 1/0 (legacy −3…0)

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`awg`	AWG gauge: 12, "1/0", "4/0", or legacy −3…0	—	input
`a`	Legacy alias for awg	—	input
`field`	mm = primary diameter; mm2 = primary round area πd²/4	—	input
`value`	Primary scalar: diameter_mm when field=mm, area_mm2 when field=mm2	—	output
`unit`	mm or mm² matching field	—	output
`gauge`	Canonical label	—	output
`gauge_n`	Geometric index	—	output
`geometry`	—	—	output
`electrical`	—	—	output
`references`	—	—	output

Assumptions / Validity

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

Assumptions

Solid round conductor of the stated AWG; no insulation.
Standard AWG logarithmic definition with d₃₆ = 0.127 mm (ASTM B258-18(2026); 2026 reapproval of B258-18).
Copper resistance uses ρ = 1.7241×10⁻⁸ Ω·m at 20 °C (NBS Handbook 100 / 100% IACS annealed copper material model).
Ampacity is an educational NFPA 70–style thermal reference (table-like 310.16); edition not pinned; not jurisdiction-usable; not a branch-circuit/OCPD rating.

Example

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

AWG 12 → 2.0525 mm, 3.3088 mm², 5.211 Ω/km @ 20 °C

Open this example in the calculator

Trust

CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · AWG geometry & calculation contract. 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 · AWG geometry & calculation contract· View Manifest · CVP overview · Specification
Verified scope: AWG geometry & calculation contract
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (geometry-formula, geometry-standard-nominal, copper-resistance-model, ampacity-reference-integrity, invalid-domain)
Calculation version: 1.5.0
Verification: 46/46 calculation tests · 13/13 legacy golden · 6/6 legacy boundary · 27/27 legacy property
Production surface contract: 6/6
Versions: Calculation 1.5.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-10.wire-chart-claim-boundary
Verification revision: 2026-09-10.wire-chart-claim-boundary · 5/5 property · digest 42bdfb24710d
Reference: O1 model · O1 model · O2 expected_values · O2 numerical_behavior
Numerical scope: CVP numerical verification covers AWG diameter/area geometry (unrounded formula + ASTM Table 1 identity). Copper resistance is a 20 °C IACS material model. Ampacity is an educational code-context reference and is outside CVP golden numeric verification.
Interfaces: PASS · UI (SSR) / REST / MCP
ui-ssr is query-result HTML, not a live browser session. Human URL alias: /calc/wire/wire-gauge-chart?a=12&mode=awg-mm ≡ /calc/wire/awg-to-mm?awg=12&mode=awg-mm ≡ REST awg-to-mm and wire-gauge-chart ≡ MCP electrical.awg_to_mm.
CVP suite: 6/6 golden · 5/5 CVP boundary · 6/6 invalid · 5/5 property · 2/2 cross-interface · 4/4 CVP contract
Supplemental domain review: Not performed
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.5.0 (workspace artifacts agree)
Review-policy tier: Engine tested — catalog token engine_tested; supplemental; not CVP status

This calculator CURRENT · Public schema 1.5.0 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 6/6.

curl -sS -X POST 'https://www.calculatorx.com/api/v1/calc/awg-to-mm' \
  -H 'Content-Type: application/json' \
  -d '{"inputs":{"awg":-3,"field":"mm"},"calculation_version":"1.5.0"}'

{
  "inputs": {
    "awg": -3,
    "field": "mm"
  },
  "calculation_version": "1.5.0"
}

POST /api/v1/calc/awg-to-mm. This is a POST calculate endpoint — do not GET it.

Full REST contract: REST API docs.

Tool id: awg-to-mm
Engine: awg
REST: POST /api/v1/calc/awg-to-mm
MCP: execute_calculation with capability_id: "electrical.awg_to_mm"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.5.0)
Versioned output schema: Immutable pin (1.5.0)

Operations

Declared calculation modes for this capability.

mm
mm2

References

Human-readable sources plus CVP reference evidence classes.

Sources

ASTM B258-18(2026) — Standard Specification for Standard Nominal Diameters and Cross-Sectional Areas of AWG Sizes of Solid Round Wires Used as Electrical Conductors — Table 1 standard nominal diameters/areas (secondary track: geometry.standard_nominal). 2026 is a reapproval of B258-18; the AWG geometric progression is unchanged.
NBS Handbook 100 — Copper Wire Tables — American Wire Gage geometric progression (No. 0000 = 0.4600 in, No. 36 = 0.0050 in, ratio 92^(1/39)); International Annealed Copper Standard volume resistivity 1.7241 μΩ·cm at 20 °C
100% IACS annealed copper resistivity (20 °C) — Material: annealed copper, 100% IACS; reference temperature 20 °C; ρ = 1.7241×10⁻⁸ Ω·m (NBS Handbook 100)
NFPA 70–style copper ampacity (educational; edition not pinned) — Table-like 310.16 family: copper, not more than three current-carrying conductors, no ambient or bundling correction
NIST Guide to the SI (SP 811) — Millimetre as SI length unit

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

Try with an agent

Inspect, then execute. Same engine as REST and the human calculator.

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.awg_to_mm"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

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: execute_calculation' \
  -d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"execute_calculation","arguments":{"capability_id":"electrical.awg_to_mm","inputs":{"awg":-3,"field":"mm"},"calculation_version":"1.5.0"},"_meta":{"io.modelcontextprotocol/protocolVersion":"2026-07-28","io.modelcontextprotocol/clientInfo":{"name":"calculatorx-docs-example","version":"1.0.0"},"io.modelcontextprotocol/clientCapabilities":{}}}}'

Pin calculation_version (1.5.0) when the result must stay reproducible.

Inspect the trust tier and required assurance level before execution. Full protocol notes: MCP docs.