Frequency to Wavelength: The 300 Divided by MHz Rule and Band Names
Hams call bands by wavelength, call antennas by fractions of a wavelength and call frequencies by megahertz, and for a newcomer this mixture is confusing. Why is 14 MHz called 20 meters? How long is a quarter wave on 2 meters? What does HF actually mean? All of this rests on one very simple relation between frequency to wavelength: divide 300 by the frequency in megahertz and you have the wavelength in meters. This guide explains where the rule comes from, how accurate it is, how to use it for antennas, why band names are rounded and what the standard names such as HF, VHF and UHF mean. It also provides a table that you can print and keep in the shack.
The Basic Relation
A radio wave travels through free space at the speed of light, about 300 million meters per second. The Wikipedia article on wavelength says that for electromagnetic radiation in free space the phase speed is the speed of light, about 3 times ten to the eighth meters per second, and that in a medium the speed is lower, which makes the wavelength shorter for the same frequency. The wavelength is the distance the wave travels in one cycle, so it equals the speed divided by the frequency. If the frequency is given in megahertz, which is millions of cycles per second, the millions cancel and you get a simple formula: the wavelength in meters is 300 divided by the frequency in MHz.
The exact figure for the speed of light is 299.792458 million meters per second, so the rule with 300 gives a result that is too large by about 0.07 percent. That is much smaller than any practical error in cutting a wire, so for amateur purposes 300 is fine. To go the other way, divide 300 by the wavelength in meters to get the frequency in megahertz. A wave of 21 meters corresponds to about 14.3 MHz, and a wave of 2 meters to 150 MHz.
Examples
- At 7.1 MHz, the wavelength is 300 divided by 7.1, which is 42.3 meters.
- At 14.2 MHz it is 21.1 meters, half as long, because the frequency is twice as high.
- At 145 MHz it is 2.07 meters, and a quarter wave is about 52 centimeters.
- At 435 MHz it is 0.69 meters, and a quarter wave is about 17 centimeters.
Notice the pattern: when the frequency doubles, the wavelength halves. That is why the bands in an octave relationship, such as 40 and 20 meters or 20 and 10 meters, share antenna sizes in simple ratios, and why a dipole cut for 40 meters also works on 15 meters as a third harmonic, a fact on which many multiband antennas rely. Our article on the fan dipole and the one on the G5RV show what uses of the relation are possible.
Table for the Amateur Bands
The table gives the free-space wavelength for a frequency inside each band, with the lengths of a half wave and a quarter wave. The frequencies are examples, so recalculate for your own working frequency. Practical antennas are shorter than these figures, as we explain below.
| Band name | Example frequency | Wavelength | Half wave | Quarter wave |
|---|---|---|---|---|
| 160 m | 1.85 MHz | 162.1 m | 81.0 m | 40.5 m |
| 80 m | 3.65 MHz | 82.1 m | 41.1 m | 20.5 m |
| 40 m | 7.1 MHz | 42.2 m | 21.1 m | 10.6 m |
| 30 m | 10.125 MHz | 29.6 m | 14.8 m | 7.4 m |
| 20 m | 14.2 MHz | 21.1 m | 10.6 m | 5.3 m |
| 17 m | 18.118 MHz | 16.5 m | 8.3 m | 4.1 m |
| 15 m | 21.2 MHz | 14.1 m | 7.1 m | 3.5 m |
| 12 m | 24.94 MHz | 12.0 m | 6.0 m | 3.0 m |
| 10 m | 28.5 MHz | 10.5 m | 5.3 m | 2.6 m |
| 6 m | 50.15 MHz | 5.98 m | 2.99 m | 1.49 m |
| 2 m | 145 MHz | 2.07 m | 1.03 m | 0.52 m |
| 70 cm | 435 MHz | 0.69 m | 0.34 m | 0.17 m |
| 23 cm | 1296 MHz | 0.23 m | 0.12 m | 0.06 m |
Why Band Names Are Rounded
You will notice that the names of the bands do not match the table exactly. The 20 meter band is at about 14 MHz, where the wavelength is 21 meters. The 40 meter band is at 7 MHz, where the wavelength is 42 meters. The 80 meter band is at 3.5 to 3.8 MHz and has a wavelength of about 80 meters, and the 160 meter band at 1.8 MHz has 166 meters at the lower end. The names are traditional labels that were fixed in the early days and then kept; they are rounded and sometimes only roughly right. The 60 meter band, at about 5.3 MHz, has a wavelength near 56 meters, and the 30 meter band is nearly exactly 30 meters.
The lesson is to use the name for conversation and the frequency for calculation. If someone tells you that a quarter wave for 20 meters is 5 meters, they are using the name; your own calculation from the frequency of the part of the band that you use gives 5.3 meters. The difference is small for a quarter wave but would grow for a longer element. Our IARU band plan article shows the actual frequency limits of each band in each region.
The Standard Names: LF, MF, HF, VHF, UHF
Above the amateur band names sits the ITU naming scheme for the radio spectrum. The Wikipedia article on the radio spectrum explains that, as a matter of convention, the ITU divides the radio spectrum into bands, each beginning at a wavelength that is a power of ten in meters and each covering a decade of frequency or wavelength, and each with a traditional name. For amateurs, the useful ones are as follows.
- LF, low frequency: 30 to 300 kHz, wavelengths of 10 km to 1 km. The 2200 meter band lies here.
- MF, medium frequency: 300 kHz to 3 MHz, 1 km to 100 m. The 630 meter and 160 meter bands are in this range.
- HF, high frequency: 3 to 30 MHz, 100 m to 10 m. The classic short-wave bands, from 80 to 10 meters, are here.
- VHF, very high frequency: 30 to 300 MHz, 10 m to 1 m. The 6 meter, 4 meter and 2 meter bands belong here.
- UHF, ultra high frequency: 300 MHz to 3 GHz, 1 m to 10 cm. The 70 centimeter and 23 centimeter bands are examples.
- SHF, super high frequency: 3 to 30 GHz, 10 cm to 1 cm, with the 13 cm, 6 cm, 3 cm bands for microwave enthusiasts.
The boundaries make the scheme easy to remember. HF starts at the 100 meter wavelength and ends at 10 meters, and, curiously, the 160 meter band is in the medium frequency range, not HF. Similarly, 10 meters is at the top of the HF range, and 6 meters is the first amateur band in VHF. Our guides to the 6 meter band and the 2 meter band are good next steps if you want to explore those ranges.
From Free-Space Wavelength to a Real Antenna
A wavelength in the table applies to the wave in free space. A wire antenna is shorter than the calculated half wave, typically by about 5 percent, because of the end effect and the properties of the wire, as explained in our article on the velocity factor. A coaxial cable carries the wave at a lower speed than free space, so a quarter-wave stub of cable is shorter than a free-space quarter wave by the velocity factor, which is about 0.66 for solid polyethylene dielectric and higher for foam. A mast or a tree changes the result a little again. The free-space figure is therefore the beginning of the calculation, not the end.
In practice you do this: find the frequency where you want the antenna to work, calculate the wavelength with 300 divided by that frequency, multiply by the fraction that your antenna uses and then apply the correction factor for the type of antenna. For a dipole the correction is about 0.95, for a vertical monopole made of a thin wire about 0.95 to 0.97 and for coax about the velocity factor of the cable. Then measure and trim.
Wavelength and Everyday Radio Decisions
The size of the wavelength affects more than the length of an antenna. At very low frequencies, the wavelength is so long that an amateur antenna is a tiny fraction of it, and the efficiency is low. At VHF and UHF the wavelength is so short that antennas become small and can be mounted in a car or a handheld. The distance at which a nearby object affects an antenna is also measured in wavelengths: a house that is far from a 2 meter antenna in wavelengths may be very close to a 160 meter antenna. Ground effects, the spacing of radials, the safe distance for RF exposure and the height above ground are all expressed in fractions of a wavelength, and knowing the wavelength of your working frequency makes all of them easier to estimate.
Wavelength also tells you what size of obstacles matter. A wall or a hill affects signals strongly when it is large compared with the wavelength, so UHF signals are blocked by buildings that low HF signals simply diffract around. This is one of the reasons why the propagation of signals on different bands is so different, a subject that our article on HF propagation develops further.
Quick Mental Math
You do not need a calculator for most estimates. Remember a few anchor points: 300 divided by 30 is 10, so 30 MHz is a 10 meter wave; 300 divided by 3 is 100, so 3 MHz is a 100 meter wave; and 300 divided by 150 is 2, so 150 MHz is a 2 meter wave. For anything between, scale in proportion. A 14 MHz signal is a little under half of 30 MHz, so the wavelength is a little over twice 10 meters, which is about 21 meters. With practice you can estimate the length of a half-wave dipole, a quarter-wave vertical or a coaxial stub in a few seconds, and the estimate is good enough to decide whether an idea fits in the garden.
Another helpful trick is to work in feet when a handbook does. A wavelength in feet is about 984 divided by the frequency in megahertz, so a half wave in a real dipole is about 468 divided by the frequency, as discussed in our article on the dipole length formula. Keep the units consistent, and write them next to the numbers in your notes; mixing feet and meters is one of the most common errors in antenna building.
Common Mistakes
- Using kilohertz in the formula. The rule of 300 works only with megahertz. For kilohertz, divide 300,000 by the number.
- Forgetting the correction. Cutting a dipole to the free-space half wave leaves it too long. Apply the factor for wire, tubing or coax.
- Trusting the band name. A quarter wave for the 40 meter band is not 10 meters; use the frequency of the part of the band that you actually use.
- Mixing up half and full wavelength. A dipole is half a wavelength end to end and a quarter wavelength per leg.
- Ignoring height. Heights and spacings are also expressed in wavelengths, so a given height is higher on 10 meters than on 160 meters in electrical terms.
The Bottom Line
To convert frequency to wavelength, divide 300 by the frequency in megahertz; the answer is in meters. A half wave is half of it, a quarter wave a quarter, and the relation also works backwards from wavelength to frequency. The rule is accurate to better than a tenth of a percent in free space, but real antennas and cables need correction factors, and band names such as 20 meters are traditional rounded labels, not exact wavelengths. Learn the ITU names, with HF from 3 to 30 MHz and VHF from 30 to 300 MHz, keep the table close to your workbench and use the actual working frequency for each calculation.
Frequently Asked Questions
How do I convert frequency to wavelength?
Divide 300 by the frequency in megahertz to get the wavelength in meters. For example, 7.1 MHz gives about 42.3 meters.
Why is 14 MHz called the 20 meter band?
The name is a traditional rounded label. The exact free-space wavelength at 14.2 MHz is about 21.1 meters.
How long is a quarter wave on 2 meters?
About 52 centimeters in free space at 145 MHz. Practical antennas are cut slightly shorter, following the maker’s dimensions.
What frequencies are HF?
High frequency covers 3 to 30 MHz according to the ITU naming scheme, which corresponds to wavelengths from 100 meters to 10 meters.
Is the 160 meter band HF?
No. It lies in the medium frequency range, which runs from 300 kHz to 3 MHz, although amateurs usually group it with the HF bands in practice.
Why is a coax stub shorter than a free-space wavelength?
The wave travels more slowly in the cable than in free space, by the velocity factor, so the same number of wavelengths takes up less physical length.