Antenna length is one of the most fundamental calculations in RF engineering, and it comes down to one principle: a wire resonates when its electrical length equals the correct fraction of the wavelength at the target frequency. This calculator applies the exact formula — including velocity-factor correction — for three of the most widely used antenna types: the half-wave dipole, the quarter-wave monopole, and the full-wave loop. Enter your frequency (or a physical length you want to reverse-engineer) and get the correct cut dimensions in metres, centimetres, feet, or inches.
How it works
The free-space wavelength at frequency f is:
λ = c / f
where c = 299,792,458 m/s (speed of light in vacuum). For each antenna type the theoretical element length is a fixed fraction of λ:
| Antenna type | Theoretical length | Radiation resistance | Directivity |
|---|---|---|---|
| Half-wave dipole | λ / 2 | ≈ 73 Ω | 2.15 dBi |
| Quarter-wave monopole | λ / 4 | ≈ 36.5 Ω | 5.19 dBi |
| Full-wave loop | λ | ≈ 100 Ω | 3.84 dBi |
In practice every conductor propagates a wave at slightly less than c. The velocity factor (VF) captures this: for bare copper wire in open air VF ≈ 0.95, for coaxial cable 0.66–0.82. The practical element length becomes:
L = k × VF × c / f
where k is the fraction for the chosen type (0.5, 0.25, or 1.0).
For the classic half-wave dipole with VF = 0.95 this collapses to the shorthand every radio amateur knows by heart:
- Length (metres) = 142.5 / f(MHz)
- Length (feet) = 468 / f(MHz) — each arm is 234 / f(MHz)
The calculator performs the full formula with your chosen VF, then also shows the traditional shorthand figures for reference. Use “Show working” to see every arithmetic step.
Worked example — 20-metre amateur radio band
The 20-metre ham band runs from 14.0–14.35 MHz; the calling frequency is 14.200 MHz.
Half-wave dipole:
- λ = 299,792,458 / 14,200,000 = 21.11 m
- Theoretical half-length = 21.11 / 2 = 10.555 m
- With VF = 0.95: L = 0.95 × 10.555 = 10.027 m total, each arm 5.014 m
- Shorthand check: 142.5 / 14.2 = 10.035 m (agrees to within rounding)
Cut two wires of 5.01 m each, connect them at the centre through a 1:1 balun and 50 Ω coax, and you have a resonant 20-metre centre-fed dipole with a feed impedance of roughly 73 Ω and an SWR of approximately 1.5:1 on 50 Ω coax — acceptable without a tuner for most transceivers.
Quarter-wave vertical for 433 MHz ISM (LoRa / Zigbee):
- λ = 299,792,458 / 433,000,000 = 0.6924 m
- Quarter-wave = 0.6924 / 4 = 0.1731 m
- With VF = 0.95: L = 0.95 × 0.1731 = 164.4 mm
- Mount on a ground plane with four radials of the same length and connect to 50 Ω coax directly — feed impedance ≈ 36.5 Ω, SWR on 50 Ω ≈ 1.4:1.
Formula note
The velocity factor correction is the single biggest source of error in antenna construction. Beginners often use the bare 0.5 × c / f formula (equivalent to VF = 1.0), which consistently produces antennas that are 5% too long — resonant about 5% below the target frequency. Starting from VF = 0.95 as the default for wire antennas and then trimming experimentally is standard practice. An antenna analyser (such as the NanoVNA, widely available for under £30) allows you to measure the actual resonant frequency and iterate toward the exact length in a few cuts.