How to Find Antenna Length From Frequency: Dipole, Quarter-Wave, and Velocity Factor

Every wire antenna is really a piece of metal cut to match a wavelength. Get the length right and the antenna resonates where you want it; get it wrong by a few percent and your radio sees a mismatch it does not like. The good news is that the math is simple, and once you know the relationship between frequency and length you can size a dipole, a quarter-wave vertical, or a full-wave loop in your head.

This guide walks through that relationship, the velocity factor that trips up first-timers, and a full worked example for a 40 metre ham band dipole. If you just want a number fast, the Antenna Length Calculator gives you all four lengths the moment you type a frequency.

Wavelength Is the Whole Story

An antenna does not care about frequency directly. It cares about wavelength, and wavelength is just the speed of light divided by frequency:

wavelength (m) = 300 / frequency (MHz)

That uses 300 as a friendly round number for the speed of light in metres per microsecond. A 100 MHz FM signal has a wavelength of 3 metres. A 14.2 MHz HF signal stretches to about 21 metres. Because frequency sits in the denominator, the two are inversely related: double the frequency and every length on the antenna halves. That single fact explains why a VHF handheld antenna is a stubby few centimetres while an 80 metre band wire fills a backyard.

If you want to see wavelengths for any band without the antenna math layered on top, the Frequency Wavelength Calculator does the plain conversion both directions.

The Half-Wave Dipole and the 143 Rule

The most common antenna on the HF bands is the half-wave dipole: a straight wire one half wavelength long, fed in the centre. You do not cut it to the full free-space half wavelength, though, because real wire behaves slightly differently from a mathematical line in a vacuum. Hams shorthand the practical length as:

dipole length (m) = 142.5 / frequency (MHz)

Many people round 142.5 up to 143, so you will see "143 over f" everywhere in the hobby. The dipole is fed in the middle, so each of the two legs is half of that total span. This is the single most common point of confusion: the formula gives you the tip-to-tip length, not the length of one leg.

A quarter-wave vertical is exactly half of a half-wave dipole, which makes its length about 75 divided by the frequency in MHz (71.25 over f if you want to be precise about the velocity factor). A quarter-wave element needs a ground plane or a set of radials to act as its missing half, which is why a ground-mounted vertical always comes with a bundle of wires fanning out from its base.

Why 142.5 Instead of 150?

A pure half wavelength at, say, 14.2 MHz works out to about 10.55 metres in free space. Yet a real dipole for that frequency resonates closer to 10.0 metres. The difference is the velocity factor.

Two things slow a radio wave down on a physical conductor. The wave travels slightly slower along a wire than through empty space, and the wire ends radiate energy in a way that makes the antenna behave electrically longer than it is physically. To bring resonance back to the target frequency you cut the wire a few percent short. For thin bare wire the standard velocity factor is 0.95, which is exactly what turns the ideal half-wavelength constant of 150 into the practical 142.5 you cut to.

The factor is not fixed. Insulated wire, thick tubing, or wire run close to other conductors slows the wave more, so the factor drops to roughly 0.90 to 0.93. If you build with insulated house wire and cut to the bare-wire number, your antenna will resonate low and you will be chopping length off. That is why a good calculator lets you change the velocity factor rather than baking in 0.95 and pretending every install is identical.

Worked Example: A 40 Metre Dipole at 7.1 MHz

Let me size an antenna I actually strung up last winter for the 40 metre band. I wanted it centred on 7.1 MHz, near the bottom of the phone segment.

First the wavelength: 300 divided by 7.1 is about 42.3 metres. A half wavelength of that is 21.1 metres in free space.

Now apply the practical dipole formula:

142.5 / 7.1 = 20.07 metres tip to tip

So the total span is just over 20 metres, and each leg is half of that, about 10.0 metres. Here is what the antenna math gives at a glance:

Full wavelength: about 42.3 m
Half-wave dipole: about 20.1 m (each leg about 10.0 m)
Quarter-wave vertical: about 10.0 m
Full-wave loop: about 40.1 m of wire

I cut each leg of my dipole at 10.3 metres, a touch long on purpose, hung it at its real height between two trees, then measured SWR. It came in slightly low, so I folded a few centimetres back at each end and re-checked until the dip landed on 7.1 MHz. Cutting long and trimming down matters because adding wire back once you have snipped it is a genuine pain.

That is the workflow the calculator is built for: it gets you inside a few percent, and the antenna analyser handles the final tuning.

From the Calculator to a Real Antenna

A few habits keep antenna projects out of trouble. Always enter the frequency in megahertz, not kilohertz. If you type 7100 thinking in kHz, you will get a millimetre-scale length, which is an obvious tell that the unit is wrong. Treat every computed length as a starting point, not gospel, because height above ground, nearby roofs, wire sag, and insulation all shift resonance. And remember which number you are reading: the half-wave figure is the whole dipole, while one leg or a quarter-wave vertical is half of it.

The same length-from-frequency idea scales across the whole spectrum. A 2 metre VHF dipole at 146 MHz is under a metre tip to tip. A WiFi antenna at 2400 MHz has a quarter-wave element near 31 millimetres, which is why those little stub antennas are so short. A 70 cm UHF whip at 435 MHz lands around 16 centimetres. Punch any of those into the Antenna Length Calculator, switch between metres and feet, and you have a buildable number before you ever pick up the wire cutters.

Made by Toolora · Updated 2026-06-13