Verified calculation capability

Antenna length Calculation Capability

λ/2 dipole total length · λ/4 monopole radiator · corrected 1λ (k·λ₀) from frequency and empirical length factor k. · Electrical · Rf

Capability ID electrical.rf.antenna_length · version 1.0.3

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

Model

Free-space wavelength

Free-space wavelength: λ₀ = c / f
Corrected length scale: S = k · λ₀
Half-wave dipole: L = S / 2
Quarter-wave monopole: L = S / 4
Corrected 1λ: L = S = k · λ₀

Solve modes: half · quarter · wavelength

Inputs / Outputs

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

Symbol	Quantity	Unit	Role
`f`	Operating frequency in hertz. Must keep λ₀ and L finite in IEEE-754 binary64.	Hz	input / output
`length_factor`	Empirical length/shortening factor k for the physical element. 1.00 is ideal free-space fractional wavelength. Not a transmission-line velocity factor. Practical resonant wire antennas are often ~0.95 due to diameter, end effect, insulation, and surroundings.	—	input / output
`velocity_factor`	Deprecated alias of length_factor. Prefer length_factor. Kept for URL/API compatibility; must match length_factor when both are sent.	—	input / output
`lambda_free_space`	Free-space wavelength λ₀ = c/f in metres. Independent of k.	m	output
`corrected_length_scale`	Corrected length scale S = k·λ₀ in metres. Design length scale for fractional elements; not a claim that EM wavelength in free space became k·λ₀.	m	output
`lambda_effective`	Deprecated alias of corrected_length_scale_m. Prefer corrected_length_scale_m — k is element shortening, not a medium effective wavelength.	m	output
`lambda`	Deprecated alias of corrected_length_scale_m (same as former lambda_effective_m).	m	output
`L`	Physical antenna length in metres (total dipole length when mode=half; k·λ₀ when mode=wavelength).	m	output
`L_ft`	Physical antenna length L_m in feet.	—	output
`L_leg`	Each dipole leg (L_m/2) when mode=half; null otherwise.	m	output

Assumptions / Validity

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

Assumptions

Straight idealized antenna element.
Frequency is the intended resonant/design frequency.
No loading coils or distributed reactive loading.
No explicit ground, nearby-object, conductor-diameter, or end-effect model.
Correction factor k is a scalar length adjustment, not a transmission-line velocity factor.
Quarter-wave mode is the ideal monopole radiator length over a perfect image plane / ground plane (≈ λ₀/4); radials and real soil are not modeled.
Wavelength mode returns L = k·λ₀ (corrected 1λ), which equals free-space λ₀ only when k=1.
S = k·λ₀ is a corrected design length scale, not a physical EM wavelength in a medium.

Not supported

Yagi design
loading coils
NEC modeling
conductor-diameter / end-effect physics
real ground / radial systems

Example

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

146 MHz half-wave k=1 → L=1.0267 m total, 0.5133 m each leg

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 · 5/5 declared partitions (half, quarter, wavelength, length-factor, invalid-domain)
Calculation version: 1.0.3
Verification: 28/28 calculation tests · 5/5 legacy golden · 10/10 legacy boundary · 13/13 legacy property
Production surface contract: 4/4
Versions: Calculation 1.0.3 · CVP protocol 1.0.0-proposed · Evidence 2026-09-11.o3-cov
Verification revision: 2026-09-11.o3-cov · 13/13 property · digest 3d9fa5324276
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Numerical scope: ≤2 ULP vs O3 applies only to the published tabulated vectors (half, quarter, wavelength/full alias, k≠1, HF/VHF/UHF/LF). It is not a whole-domain antenna-model guarantee.
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.
CVP suite: 4/4 golden · 9/9 CVP boundary · 9/9 invalid · 13/13 property · 10/10 O3 · 5/5 cross-interface · 1/1 CVP contract
Supplemental domain review: Internal · Pass · electrical-engineer
Named expert review: Not performed
Version lock: Supported (409 VERSION_MISMATCH)
Artifact consistency: Build verified · 1.0.3 (workspace artifacts agree)
Review-policy tier: Internal engineering review — catalog token expert_verified; supplemental; not CVP status

This calculator CURRENT · Public schema 1.0.3 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: antenna-length
Engine: antenna-length
REST: POST /api/v1/calc/antenna-length
MCP: execute_calculation with capability_id: "electrical.rf.antenna_length"
Agent input schema: Canonical (MCP / Agent)
Output schema: JSON Schema (latest)
Versioned input schema: Immutable pin (1.0.3)
Versioned output schema: Immutable pin (1.0.3)

References

Human-readable sources plus CVP reference evidence classes.

Sources

Reference evidence classes: O1 model · O3 expected_values · O3 numerical_behavior · 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.rf.antenna_length"}}}'

Inspect the trust tier and required assurance level before execution. Pin calculation_version (1.0.3) when reproducibility matters. Full protocol notes: MCP docs.