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Wavelength Calculator

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Wavelength is speed divided by frequency, and the interesting part is the speed. In air a radio wave travels at essentially the speed of light, but in coaxial cable it is a third slower, and a quarter-wave stub cut for free space will be far too long once it is made of RG-58. This converts in both directions, in whichever medium applies, and gives the practical antenna lengths — already shortened for end effect, so they are lengths to cut rather than figures to adjust.

What do you know?

Air slows radio waves by about 0.03%, which is below the precision of anything you would cut by hand.

Try:

How to use the wavelength calculator

  1. 1Choose whether you know the frequency or the wavelength.
  2. 2Enter the value and pick its unit.
  3. 3Choose the medium: air for radio, one of the coax options if the wave is inside a cable, or sound in air.
  4. 4Read the wavelength, the half and quarter fractions, and the antenna lengths underneath.
  5. 5The band row identifies which part of the radio spectrum a frequency sits in, and what it is usually used for.

Examples

The 2.4 GHz band

Input
2.4 GHz in air
Result
12.49 cm, quarter wave 3.12 cm

The reason a Wi-Fi antenna is a few centimetres long, and why the band penetrates walls less well than 5 GHz penetrates nothing at all.

An amateur band dipole

Input
7.1 MHz in air
Result
42.2 m wavelength; a half-wave dipole is 20.06 m, or 10.03 m per leg

The end-effect shortening is already applied. A dipole cut to the theoretical 21.1 m would resonate below the band.

The same frequency inside cable

Input
7.1 MHz in solid-dielectric coax
Result
27.9 m — a third shorter than in air

Which is why a quarter-wave matching section has to be cut using the cable's velocity factor rather than the free-space figure.

About the wavelength calculator

One relationship, three quantities

Speed equals frequency times wavelength, so fixing any two fixes the third. For electromagnetic waves in a vacuum the speed is a defined constant — 299,792,458 metres per second exactly, since the metre has been defined from it since 1983 — which makes the conversion between frequency and wavelength exact rather than measured.

The convenient consequence is that wavelength in metres is roughly 300 divided by the frequency in megahertz. That approximation is good to a hundredth of a percent and it is what most people in radio actually use: 100 MHz is about 3 metres, 300 MHz is about 1 metre, and 2.4 GHz is about 12.5 centimetres.

Radio bands are frequently named by wavelength rather than frequency for exactly this reason. The amateur 20 metre band, the 40 metre band and the 2 metre band are named for what an antenna for them has to be, which is the number that matters when you are deciding whether it will fit in the garden.

Why antennas are the length they are

An antenna is most efficient when it resonates at the frequency being used, and resonance happens when the element is a specific fraction of a wavelength. A half-wave dipole is the classic case: current is maximum at the centre where the feedline connects and falls to zero at the ends, which produces a feedpoint impedance of about 73 ohms in free space — conveniently close to the 50 ohms that transmitters and coaxial cable are built around.

A quarter-wave vertical does the same job with half the wire by using a ground plane as a mirror. The earth, a car roof or a set of radial wires reflects the missing half, so the antenna behaves electrically like a full dipole while being physically half the size. Its feedpoint impedance is around 36 ohms, which is why matching arrangements are more common on verticals than on dipoles.

Shortening an antenna below a quarter wave is possible and always costs something. Loading coils and capacitive hats let a 2 metre whip work on a band that wants 10 metres of wire, but the radiation resistance falls, the losses stay, and the bandwidth narrows sharply. That trade — size against efficiency and bandwidth — is the central constraint of antenna design, and it is set entirely by the wavelength this page calculates.

Frequently asked questions

Why is a real antenna shorter than a half wavelength?
Because of end effect. Capacitance between the tips of the elements and everything around them makes the wire behave as though it were electrically longer than its physical length, so a wire cut to exactly half a wavelength resonates slightly below the target frequency. The standard correction is about 5%, which is where the traditional formula of 468 divided by the frequency in megahertz comes from, against the 492 that a true half wave would give.
What is velocity factor and when does it matter?
It is how much slower a wave travels in a material than in a vacuum, expressed as a fraction. Solid polyethylene coax is around 0.66 and foam is around 0.83. It matters any time the physical length of a cable is part of the circuit rather than just a way of getting a signal from one place to another — quarter-wave matching sections, phasing lines, delay lines and stubs all have to be cut using the cable's own velocity factor.
Why does frequency change how well a signal travels?
Largely because the wavelength decides what counts as an obstacle. A wave passes around objects much smaller than its wavelength and is blocked or reflected by objects much larger, so a 100 metre longwave signal is barely affected by a building while a 12 centimetre Wi-Fi signal is stopped by a wet wall. It is also why lower frequencies need physically larger antennas, and why the useful spectrum for small devices starts in the hundreds of megahertz.
Does this work for sound as well as radio?
Yes, with the medium set to sound in air. The relationship is identical but the speed is about 343 metres per second rather than 300 million, so audio wavelengths are room-sized: a 100 Hz tone is 3.4 metres long and a 10 kHz tone is 3.4 centimetres. That difference is behind most of what makes room acoustics awkward — bass wavelengths are comparable to the dimensions of the room itself, so they set up standing waves that treble never does.
How accurate does an antenna length need to be?
More accurate at higher frequencies, since the tolerance is a fraction of the wavelength rather than a fixed distance. A centimetre either way is nothing on an 80 metre dipole and is a significant fraction of a 2.4 GHz element. In practice antennas are cut slightly long and trimmed while measuring, because the surroundings — height above ground, nearby metal, the feedline itself — shift the resonant point by more than the arithmetic error.

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