# Antenna Length Calculator

> Computes the free-space wavelength for a frequency and the physical wire length of a half-wave dipole (with the length of each leg), a quarter-wave vertical, a full-wave loop or a 5/8-wave radiator, applying a velocity (end-effect) factor as in the 468/f ft rule.

- Calculator id: `antenna-length` · Category: Engineering & Automotive (`engineering`) · Tool name: `calculate_antenna_length`
- Canonical page: https://tttkmbb.com/engineering/antenna-length · This document: https://tttkmbb.com/engineering/antenna-length.md · JSON definition: https://tttkmbb.com/engineering/antenna-length.json

## Purpose

Computes the free-space wavelength for a frequency and the physical wire length of a half-wave dipole (with the length of each leg), a quarter-wave vertical, a full-wave loop or a 5/8-wave radiator, applying a velocity (end-effect) factor as in the 468/f ft rule.

**Use when:** You are cutting wire or tubing for an amateur-radio, CB, FM, Wi-Fi, LoRa or ISM-band antenna and need the starting length for a given frequency.

**Do not use when:** You need a Yagi, patch, helical or loaded (shortened) antenna design, impedance matching, or just the wavelength without an antenna (use wavelength-frequency).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `frequency_mhz` | number | MHz | required | Operating (centre) frequency in megahertz, e.g. 146 (2 m band), 27.185 (CB channel 19), 433.92 (ISM), 2437 (Wi-Fi channel 6). (> 0, max 1000000) |
| `antenna_type` | enum: half_wave_dipole \| quarter_wave_vertical \| full_wave_loop \| five_eighths_wave |  | optional, default "half_wave_dipole" | Radiator geometry. |
| `velocity_factor` | number |  | optional, default 0.95 | Shortening factor for end effect and conductor thickness: 0.95 for thin wire (the classic 468/f ft rule), 1.0 for the theoretical free-space length, 0.66–0.85 for coaxial-cable elements (coax dielectric). (min 0.3, max 1) |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `wavelength_m` | number | m | λ = 299.792458 / frequency_mhz. |
| `wavelength_ft` | number | ft | λ in feet (1 ft = 0.3048 m). |
| `total_length_m` | number | m | Overall radiator length (tip to tip for a dipole, total wire for a loop). |
| `total_length_ft` | number | ft | Overall length in feet. |
| `total_length_in` | number | in | Overall length in inches. |
| `each_leg_m` | number | m | Length of each of the two dipole legs (half of the total; dipole only). |
| `each_leg_ft` | number | ft | Each dipole leg in feet (dipole only). |
| `each_leg_in` | number | in | Each dipole leg in inches (dipole only). |
| `formula_used` | string |  | Length expression applied for the chosen antenna type. |

## Formula

`wavelength_m = 299.792458 / frequency_mhz; half_wave_dipole: total_length_m = wavelength_m / 2 × velocity_factor (≈ 468 / frequency_mhz ft at 0.95), each_leg_m = total_length_m / 2; quarter_wave_vertical: wavelength_m / 4 × velocity_factor (≈ 234 / f ft); full_wave_loop: wavelength_m × 1.02 (≈ 1005 / f ft, velocity_factor not applied); five_eighths_wave: 0.625 × wavelength_m × velocity_factor`

Free-space lengths scaled by an empirical shortening factor (0.95 for thin wire, per the ARRL 468/f rule) that accounts for end effect; loops are electrically longer than free-space wavelength, hence the 1005/f ft (1.02 λ) rule. Results are starting lengths: cut slightly long, then trim for minimum SWR, because height above ground, wire diameter, insulation and nearby objects shift resonance by a few percent.

## Data Sources

- Wikipedia – Dipole antenna — https://en.wikipedia.org/wiki/Dipole_antenna (reference, retrieved 2026-09-24)
- ARRL Antenna Book for Radio Communications (American Radio Relay League) – dipole and loop length formulas — https://www.worldcat.org/search?q=ARRL+Antenna+Book (textbook, retrieved 2026-09-24)
- Wikipedia – Velocity factor — https://en.wikipedia.org/wiki/Velocity_factor (reference, retrieved 2026-09-24)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/antenna-length?frequency_mhz=…`
- `POST https://tttkmbb.com/api/v1/calculate/antenna-length` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/antenna-length · OpenAPI operationId `calculate_antenna_length` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "antenna-length", "inputs": {…}}`

## Example

- Half-wave dipole for 146 MHz (2 m band), vf 0.95: inputs `{"frequency_mhz":146,"antenna_type":"half_wave_dipole","velocity_factor":0.95}` → `{"wavelength_m":2.0534,"wavelength_ft":6.7368,"total_length_m":0.9754,"total_length_ft":3.2,"total_length_in":38.4,"each_leg_m":0.4877,"each_leg_ft":1.6,"each_leg_in":19.2}`
- Quarter-wave vertical for CB channel 19 (27.185 MHz): inputs `{"frequency_mhz":27.185,"antenna_type":"quarter_wave_vertical"}` → `{"wavelength_m":11.0279,"total_length_m":2.6191,"total_length_ft":8.5929,"total_length_in":103.11}`

```
GET https://tttkmbb.com/api/v1/calculate/antenna-length?frequency_mhz=146&antenna_type=half_wave_dipole&velocity_factor=0.95
```

## Limitations

You need a Yagi, patch, helical or loaded (shortened) antenna design, impedance matching, or just the wavelength without an antenna (use wavelength-frequency). Free-space lengths scaled by an empirical shortening factor (0.95 for thin wire, per the ARRL 468/f rule) that accounts for end effect; loops are electrically longer than free-space wavelength, hence the 1005/f ft (1.02 λ) rule. Results are starting lengths: cut slightly long, then trim for minimum SWR, because height above ground, wire diameter, insulation and nearby objects shift resonance by a few percent. All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**Why is the dipole shorter than half a wavelength?**

Capacitance at the wire ends (end effect) and the finite conductor diameter make a wire resonate at a length about 5 % shorter than λ/2 in free space, which the 0.95 velocity factor and the 468/f ft rule build in.

**Does the velocity factor apply to the loop?**

No. A full-wave loop resonates when its total wire length is slightly longer than one wavelength, so the calculator uses the empirical 1.02 λ (1005/f ft) rule and ignores velocity_factor for loops.

**Does a quarter-wave vertical need anything else?**

Yes, a ground plane: radials or a conductive surface of about the same length as the radiator form the other half of the antenna. The 5/8-wave vertical also needs a base loading coil to match 50 Ω.

## Related

- [Wavelength & Frequency Calculator](https://tttkmbb.com/physics/wavelength-frequency.md) — Wavelength for any frequency and propagation speed.
- [LC Resonance Calculator](https://tttkmbb.com/engineering/lc-resonance.md) — Tuned circuits and traps used with antennas.
- [Length Converter](https://tttkmbb.com/conversion/length.md) — Convert the cut length between metres, feet and inches.