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Antenna Length Calculator

Compute dipole (λ/2) or monopole (λ/4) antenna length from frequency and an empirical length factor. Runs locally in your browser.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance
Input interpretation
Enter values to calculate.
Result
—
Assurance
Engineering
Declared partition coverage
PASS · 5/5 declared partitions (half, quarter, wavelength, length-factor, invalid-domain) · Matrix
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.
Known limitations
  • Free-space / shortened wire element models; not a full EM solver
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Physical antenna length from frequency and empirical length factor k.
Scope
Straight idealized antenna element.
Verification
Engine tested · Source checked · v1.0.3 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
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
Legacy regression
28/28 tests · Production surface contract 4/4
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
Internal · Pass · electrical-engineer
Named expert review
Not performed
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 · Manifest
Sources
Sources
Evidence
5 legacy golden · 10 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 9/9 invalid · Artifact integrity PASS · CalculatorX electrical review
This calculator CURRENT · Public schema 1.0.3 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

Free-space wavelengthλ₀ = c / f
Corrected length scaleS = k · λ₀
Half-wave dipoleL = S / 2
Quarter-wave monopoleL = S / 4
Corrected 1λL = S = k · λ₀
ic = 299792458 m/s (NIST CODATA exact). k defaults to 1 (ideal free-space). Wavelength mode is k·λ₀, not free-space λ₀ when k≠1. S is a design length scale from element shortening — not a claim that free-space EM wavelength became k·λ₀. Not a substitute for antenna modeling (ground plane, loading coils, diameter, end effect).

How to use

1

Choose half-wave, quarter-wave, or corrected 1λ

λ/2 is the total dipole length (each leg is L/2). λ/4 is the monopole radiator over an ideal image plane. kλ₀ is the corrected full-wave element length (equals λ₀ only when k=1).

2

Enter frequency

Use Hz, kHz, MHz, or GHz in the page UI. The API always uses f_Hz. Share links include calculation_version as attribution of the engine that rendered the page — not a historical version lock. Pin reproducibility via REST/MCP CalculatorX-Spec-Version; immutable replay uses snapshots.

3

Optionally set a length factor k

1.00 is free-space. For simple half-wave wire dipoles, k≈0.95 is a common first-cut rule of thumb. Other antenna geometries may require a different empirical factor. This is not coax VF.

Example calculations

Common configurations with formula and result.

ϟ

146 MHz half-wave

f=146 MHz · k=1

L = c/(2f)
L = 1.0267 m (3.3684 ft); each leg 0.5133 m

Antenna Length calculator specification

Version 1.0.3 · Engine tested · Supplemental domain review · Internal · 2026-09-05

Calculation status

Review policy · Evidence · Reviewed by CalculatorX electrical review (electrical-engineer)

Definition
Free-space wavelength λ₀ = c/f. A half-wave dipole total length is k·λ₀/2; a quarter-wave monopole radiator over an ideal image plane is k·λ₀/4; the wavelength tab returns the corrected 1λ length k·λ₀. The length factor k < 1 is an empirical shortening of the physical element, not a transmission-line velocity factor.
What it calculates
Physical antenna length from frequency and empirical length factor k.
Inputs
  • mode half|quarter|wavelength
  • f_Hz>0 finite λ/L
  • length_factor∈(0,1] optional default 1
  • velocity_factor deprecated alias of length_factor
Outputs
  • L_m
  • L_ft
  • L_leg_m
  • lambda_free_space_m
  • corrected_length_scale_m
  • length_factor
  • velocity_factor deprecated
  • lambda_effective_m deprecated
  • lambda_m deprecated
Formula
λ₀=c/f; S=k·λ₀; L=S/2, S/4, or S
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.
Units
  • Hz → m, ft
Boundary conditions
  • f≤0 → VALUE_MUST_BE_POSITIVE
  • non-finite λ/L → VALUE_OUT_OF_RANGE
  • k∉(0,1] → FRACTION_OUT_OF_RANGE
  • invalid mode → INVALID_MODE
  • length_factor ≠ velocity_factor when both sent → CONFLICTING_INPUTS
Example
146 MHz half-wave k=1 → L=1.0267 m total, 0.5133 m each leg
Validation cases

2 published on this page · 28/28 tests · Production surface contract 4/4 · View evidence

  • f=c half k=1 → L=0.5 m
  • f=146e6 half k=1 → L≈1.0267 m
Sources
Last reviewed
2026-09-05
Reviewed by
CalculatorX electrical review (electrical-engineer)
Calculation version
1.0.3

Background

Interpretation and common distinctions.

Compute antenna length from frequency.

Default: 146 MHz half-wave, k=1 → L = 1.0267 m total dipole (0.5133 m each leg).

Supported and not supported

Supported — λ/2 dipole total length · λ/4 monopole radiator (ideal image plane) · corrected 1λ (k·λ₀) · empirical length factor k · API electrical.rf.antenna_length

Not supported — Yagi design, loading coils, NEC modeling, conductor-diameter / end-effect physics, real ground / radial systems

Agent / API notes

Capability id: electrical.rf.antenna_length · tool id: antenna-length · pin 1.0.3.

Prefer length_factor (k). Prefer output corrected_length_scale_m (S = k·λ₀). velocity_factor, lambda_effective_m, and lambda_m are deprecated aliases. Free-space lambda_free_space_m is always c/f. Share URLs may include calculation_version as attribution; REST/MCP CalculatorX-Spec-Version is the reproducibility pin.

Other calculators in this family: Cascaded Noise Figure Calculator, Coax Impedance Calculator, dBm to Watts Calculator, Free-Space Path Loss Calculator, L-section LC Match Calculator, Receiver Sensitivity Calculator, Reflection Coefficient to Impedance Calculator, RF Link Budget Calculator . Explore all RF & Microwave.

→ Cascaded Noise Figure Calculator Compute cascaded noise figure and total gain for a multi-stage RF chain using the Friis formula. Add, remove, or reorder stages. Runs locally in your browser. › → Coax Impedance Calculator Compute coaxial characteristic impedance Z0 from shield inner diameter D, center-conductor diameter d, and dielectric εr. Ideal TEM, μr≈1. Runs locally in your browser. › → dBm to Watts Calculator Convert dBm ↔ watts and dBm ↔ milliwatts with hard validation. Canonical Unit Engine for RF power. › → Free-Space Path Loss Calculator Compute free-space path loss FSPL = 20·log10(d·f) + 20·log10(4π/c) from distance and frequency, with optional antenna gains. Runs locally in your browser. › → L-section LC Match Calculator Narrowband real RL→Z0 L-section match with dual LP/HP solutions. Runs locally in your browser. › → Receiver Sensitivity Calculator Estimate MDS: S = −174 + NF + 10·log10(BW) + SNR_min (dBm). Runs locally in your browser. › → Reflection Coefficient to Impedance Calculator Convert complex Γ ↔ normalized z (Cartesian or polar Γ). Reports VSWR and return loss. Runs locally in your browser. › → RF Link Budget Calculator Compute RF link budget: FSPL, path loss with antenna gains and misc loss, received power, and optional margin above sensitivity. Extends Free-Space Path Loss. ›
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Frequently asked questions

Key distinctions behind the calculation.

Is the length factor the same as coax velocity factor?

No. Transmission-line VF scales the wavelength inside a cable. Here k is an empirical shortening of the radiating element. Free-space λ₀ = c/f does not change with the wire you use. Prefer API field length_factor; velocity_factor is a deprecated alias.

Is the kλ₀ tab the free-space wavelength?

Only when k=1. When k≠1 the tab returns the corrected 1λ length L = k·λ₀. Free-space λ₀ is always shown separately and never depends on k.

Is 1.0267 m the whole dipole or each leg?

For λ/2 mode it is the total dipole length. Each leg is L/2 (0.5133 m at 146 MHz with k=1).

Why not 468/f MHz?

ARRL’s 468/f_MHz is an empirical resonant-wire rule of thumb (about k≈0.95). This calculator defaults to ideal free-space k=1. For simple half-wave wire dipoles, k≈0.95 is a common first-cut rule of thumb. Other antenna geometries may require a different empirical factor. Then trim to SWR.