Two names for the same place
Ask where a repeater is and you will be told “146.52”. Ask what band that is and you will be told “two metres”. Both describe the same signal: one by how fast it alternates, the other by how far it travels in one alternation.
They are locked together by the speed of light. A radio wave travels about 300 000 000 metres per second — in a vacuum, and near enough in air. In the time one cycle takes, the wave advances one wavelength.
The formula, in the form you will actually use
Wavelength in metres equals 300 divided by frequency in megahertz. And backwards:
The 300 is the speed of light, 299 792 458 m/s, rounded so you can do this without a calculator. The rounding costs about 0.07% — irrelevant for naming a band, and worth remembering only if you are cutting a precision matching stub.
Why the band names make sense once you check them
| Band name | Actual range | 300 / centre |
|---|---|---|
| 80 metres | 3.5 – 4.0 MHz | 80 m |
| 40 metres | 7.0 – 7.3 MHz | 42 m |
| 20 metres | 14.0 – 14.35 MHz | 21 m |
| 10 metres | 28.0 – 29.7 MHz | 10.4 m |
| 2 metres | 144 – 148 MHz | 2.05 m |
| 70 centimetres | 420 – 450 MHz | 0.69 m |
The names are rounded to friendly numbers, and 40 metres is the sloppiest of them — genuinely closer to 42. Nobody minds. The names are labels for neighbourhoods, not measurements.
The relationship, stated three ways
Because the two are inversely proportional:
- Higher frequency, shorter wavelength. This is the sentence the pool asks for, and it asks in both directions.
- Double the frequency, halve the wavelength.
- A 2 metre antenna is physically about a tenth the size of a 20 metre antenna, because 146 MHz is about ten times 14 MHz.
That last point is the practical payoff. Antenna size scales with wavelength, so a full-size half-wave dipole for 2 metres is about a metre long and fits indoors, while the same antenna for 80 metres is around 40 metres long and needs a field. This one fact shapes what is realistic to put up at any given location.
Inside a cable, it shrinks
The 300 assumes free space. Inside a coaxial cable, waves travel more slowly — typically 66% of light speed for solid polyethylene dielectric, up to about 95% for open-wire line. That ratio is the velocity factor, and it means an electrical half-wavelength of coax is physically shorter than a half-wavelength in air.
It only matters when the length of the line is doing a job — a matching stub, a phasing line, a quarter-wave transformer. For a plain feed line whose only job is carrying power from A to B, length is a loss question, not a wavelength question.
Worked examples
What is the wavelength at 146 MHz? 300 / 146 = 2.05 metres. Hence “the 2 metre band”.
What frequency corresponds to a 20 metre wavelength? 300 / 20 = 15 MHz. The 20 metre band actually sits at 14.0–14.35 MHz, which is why the name is a round-number label rather than a specification.
A GMRS main channel sits at 462.5500 MHz. What is its wavelength? 300 / 462.55 = 0.649 metres, about 65 cm. A quarter-wave whip for it is therefore around 16 cm — recognisably the length of the stubby antenna on a GMRS handheld. (Consumer radios label this one “channel 15”, but the channel numbers are a manufacturer convention; Part 95 lists frequencies, not numbers.)
Check yourself
- What is the wavelength of a 7.15 MHz signal?
- A signal has a 0.35 metre wavelength. What frequency is it, and which amateur band is nearby?
- If frequency triples, what happens to wavelength?
Answers
- 300 / 7.15 = 42 metres — the 40 metre band.
- 300 / 0.35 = 857 MHz. Above the 70 cm amateur band; this is land-mobile and cellular territory.
- It falls to one third. The two are inversely proportional.