Wavelength and Frequency Calculator with Antenna Dimensions

Every antenna dimension in amateur radio comes from one relationship: wavelength is the speed of light divided by frequency. Once that number is in front of you, half waves, quarter waves, spacing between elements, matching stub lengths and the height an antenna needs to be all fall out of it. This page gives the conversion and every derived dimension that follows.

Where the constants come from

Light travels at almost exactly 300 million metres per second in a vacuum, and radio waves are light. A wave at one megahertz completes a cycle in one microsecond, during which it travels 300 metres, so one megahertz has a wavelength of 300 metres. Every other frequency scales inversely: ten megahertz gives 30 metres, a hundred gives three.

In feet, the same speed is about 984 million feet per second, which gives the 984 constant. Halving it gives 492 for a half wavelength and 246 for a quarter, and these are the free-space numbers.

Real antennas are not free-space mathematical lines, and this is where the familiar 468 comes in. Two effects make a wire behave electrically longer than its physical length: end effect, which is the capacitance between the wire ends and everything near them, and the wire's own diameter relative to the wavelength. Together they add roughly five percent, so the physical wire has to be about five percent shorter to resonate where you want it. Ninety-five percent of 492 is 468, and 95 percent of 246 is 234.

Every amateur band, in one table

The band names are approximate and historical. Twenty metres is really 21.2 metres at 14.175 MHz, forty metres is really 42, and fifteen metres is really 14.1. The names were rounded when the allocations were made and have been in use for a century, so there is no prospect of them being corrected and no need. There are 16 amateur bands listed in the full plan and every one of them is named this loosely.

Velocity factor: when wavelength gets shorter

Signals travel more slowly through anything denser than a vacuum, and wavelength shrinks in proportion. Frequency never changes, because that is set by the transmitter; only the physical distance one cycle occupies does.

This matters in exactly two situations. The first is cutting an antenna from insulated wire, where the jacket slows the wave and the antenna needs to be two to four percent shorter than the bare-wire figure. The dipole calculator has that correction built in.

The second is any time you need a specific electrical length of transmission line: a quarter-wave matching transformer, a half-wave repeater line, a phasing harness between stacked antennas, or a coaxial stub used as a filter. There the physical length is the free-space length multiplied by the velocity factor, and getting it wrong by using the free-space figure produces a stub that resonates about a third away from where you wanted it. Worked through on the impedance matching calculator.

What wavelength decides beyond antenna length

• How high the antenna needs to be. Takeoff angle depends on height in wavelengths, not in feet, which is why 35 feet is generous on 20 metres and inadequate on 40. See the antenna height calculator.
• How far radials should run. An eighth of a wavelength on the ground, or a resonant quarter wavelength if elevated. See the radial planner.
• Where to put a common-mode choke. A quarter wavelength down the coax from an end fed antenna is the current maximum on the shield and the most effective position for it.
• How close nearby metal can be. Gutters, fences and siding within a small fraction of a wavelength detune an antenna and absorb power. The higher the band, the smaller that distance is in feet.
• Whether an antenna is physically possible. A full-size 160 metre dipole is 246 feet tip to tip. Knowing that in advance saves an afternoon of planning.

Building at the dimensions this page gives you

Cut two to three percent long and trim, always. The arithmetic lands close and the last couple of percent depends on wire diameter, insulation, height and what is nearby, none of which a formula knows about. A Paladin 14 AWG stranded copper wire, 500 ft$74.50 spool gives enough wire for several antennas plus mistakes, which is the right way to buy it, and a NanoVNA H4 vector network analyzer$89.90 tells you where the resonance actually landed rather than where the formula predicted.

For the trimming procedure and the reason it must be done at final height, see the dipole length calculator. For choosing which antenna to build in the first place, see choosing a first HF antenna.