Everything in amateur radio starts with one relationship: frequency and wavelength are tied together by the speed of light. Once that clicks, band names, antenna lengths and the way signals travel all start to make sense.
What a radio wave is
A radio wave is an electromagnetic wave: a changing magnetic field induces a changing electric field and the reverse, and together they form the wave. Unlike sound, it needs no medium, so it can travel through air and through the vacuum of space (NASA). The electric and magnetic fields are at right angles to each other (Technician pool, T3B01), and the wave travels at a right angle to both (Extra pool, E3A04).
Radio, light and X-rays are the same physical thing, electromagnetic energy, described at different frequencies. Heinrich Hertz showed experimentally that radio waves travel at the speed of light, and the unit of frequency is named after him (NASA). In a vacuum that speed is exactly 299,792,458 meters per second (NIST). Radio work rounds it to 300,000,000 m/s (Technician pool, T3B11), and all radio frequencies travel at the same speed in free space (Technician pool, T3B12).
Frequency and wavelength
Frequency is how many complete cycles pass a point each second, measured in hertz (Hz). Wavelength, written with the Greek letter lambda (λ), is the distance between one crest of the wave and the next (NASA). Wavelength gets shorter as frequency increases (Technician pool, T3B05). The form used on the exams is (ARRL Radio Mathematics):
λ (meters) = 300 / f (MHz), and turned around, f (MHz) = 300 / λ (meters).
Sources: CODATA value: speed of light in vacuum (NIST); 2026-2030 Technician question pool (T3B06) (NCVEC Question Pool Committee)
A few worked values, using that formula and the band limits in 47 CFR 97.301:
| Frequency | Wavelength | Band it falls in |
|---|---|---|
| 3.55 MHz | 300 / 3.55 = 84.5 m | 80 meters |
| 7.15 MHz | 300 / 7.15 = 42 m | 40 meters |
| 14.2 MHz | 300 / 14.2 = 21.1 m | 20 meters |
| 28.4 MHz | 300 / 28.4 = 10.6 m | 10 meters |
| 146.52 MHz | 300 / 146.52 = 2.05 m | 2 meters |
| 446 MHz | 300 / 446 = 0.67 m (67 cm) | 70 centimeters |
Try it yourself: drag the slider to see how the wavelength, the length of a half-wave dipole and the license classes that may transmit change across the spectrum.
- Wavelength
- 21.1 m
- Half-wave dipole
- 10 m (33 ft)
- Band
- 20 m
- Who may transmit here
- Amateur Extra
The 300 is a rounded speed of light: 300 divided by the exact value, 299.792458 (in millions of meters per second), is about 1.0007, so the answer comes out about 0.07 percent long. That is much smaller than the difference of about 5 percent between the free-space and practical dipole formulas later in this guide.
Why bands are named by wavelength
The FCC’s own band table in 47 CFR 97.301 lists each amateur band under a wavelength name. The names are round labels, not exact values. In ITU Region 2, which includes the United States (47 CFR 97.303), the 40 meter band runs from 7.000 to 7.300 MHz, which works out to 42.9 to 41.1 m. The 2 meter band, 144 to 148 MHz, is 2.08 to 2.03 m. The 70 centimeter band, 420 to 450 MHz, is 71 to 67 cm. Besides frequency, amateur bands are identified by their approximate wavelength in meters (Technician pool, T3B07), so “20 meters” and “14 MHz” point to the same band. The band chart shows every band and who may use it.
Regions of the spectrum
The radio spectrum is divided into numbered bands, each covering a tenfold range of frequency. The FCC’s table in 47 CFR 2.101 gives them the names used with the ITU, and Part 97 repeats the ones hams use in 97.3(b). In each range below, the lower limit is excluded and the upper limit is included (47 CFR 2.101). The last column places the bands of 47 CFR 97.301 in each range.
| Name | Frequency range | Metric name | Amateur bands in it |
|---|---|---|---|
| LF (low frequency) | 30 to 300 kHz | kilometric | 2200 m |
| MF (medium frequency) | 300 to 3,000 kHz | hectometric | 630 m, 160 m |
| HF (high frequency) | 3 to 30 MHz | decametric | 80 m through 10 m |
| VHF (very high frequency) | 30 to 300 MHz | metric | 6 m, 2 m, 1.25 m |
| UHF (ultra high frequency) | 300 to 3,000 MHz | decimetric | 70 cm, 33 cm, 23 cm, 13 cm |
| SHF (super high frequency) | 3 to 30 GHz | centimetric | 5 cm, 3 cm, 1.2 cm |
| EHF (extremely high frequency) | 30 to 300 GHz | millimetric | 6 mm through 1 mm |
Sources: 47 CFR 2.101, Frequency and wavelength bands (eCFR); 47 CFR 97.301, Authorized frequency bands (eCFR); 47 CFR 73.14 (AM) and 73.201 (FM broadcast) (eCFR); 47 CFR 15.247 (2400 to 2483.5 MHz) (eCFR); GPS SPS Performance Standard (L1 1575.42 MHz) (GPS.gov)
The regions behave differently. MF and HF signals can be returned to Earth by the ionosphere, which provides communication over medium and long ranges. Above about 30 MHz, signals normally travel point to point and pass through the ionosphere into space, with occasional exceptions such as sporadic E, meteor trails and aurora (ITU-R ionosphere handbook, chapter 3). That is why long-distance ionospheric propagation is far more common on HF than on VHF and higher frequencies (Technician pool, T3C02). The propagation guide covers how this works.
What gets in the way
On VHF and UHF, a signal often reaches you by several paths at once. The copies reinforce or cancel each other, so moving an antenna only a few feet can change the signal strength a lot (Technician pool, T3A01). On a mobile signal that shows up as rapid flutter, which hams call “picket fencing” (Technician pool, T3A06), and on data modes it raises the error rate (Technician pool, T3A10).
Rain matters at microwave frequencies, where precipitation can decrease range (Technician pool, T3A07). For microwave links the ITU notes that multipath fading is the main cause of outages below about 10 GHz, while precipitation becomes the main cause above 10 GHz (ITU-R point-to-point handbook, section 3). On 10 and 6 meters, fog and rain have little effect on the signal (Technician pool, T3A12).
Polarization
The polarization of a radio wave is defined by the orientation of its electric field (Technician pool, T3B02), and an antenna’s polarization is described the same way (Technician pool, T9A03), so an antenna oriented vertically is called vertically polarized (ARRL, Choosing a Ham Radio) and one oriented horizontally is horizontally polarized.
On line-of-sight VHF and UHF paths, polarization matters. If one station’s antenna is vertical and the other’s is horizontal, the received signal is reduced (Technician pool, T3A04). For repeater and FM voice work, the ARRL advises orienting the antenna vertically to match the signals from repeaters and other hams (ARRL, Choosing a Ham Radio), while long-distance CW and SSB contacts on VHF and UHF normally use horizontal polarization (Technician pool, T3A03). Match the people you want to talk to.
On HF skywave paths the rule relaxes. The Earth’s magnetic field splits a wave in the ionosphere into two components with different polarization (ITU-R ionosphere handbook, chapter 3), and because signals propagated by the ionosphere are elliptically polarized, either a vertically or a horizontally polarized antenna can be used (Technician pool, T3A09).
Wavelength sets antenna size
Common antennas such as the half-wave dipole and the quarter-wave vertical are a set fraction of a wavelength long, so the band you pick decides how big the antenna is. In free space a half wavelength in feet is 492 / f (MHz) (ARRL Radio Mathematics). A practical wire dipole is cut about 5 percent shorter, using 468 / f; the General exam’s answers for dipole length, such as 33 feet at 14.250 MHz and 132 feet at 3.550 MHz, follow that formula (General pool, G9B10 and G9B11). That gives:
- A half-wave dipole for 7.15 MHz: 468 / 7.15 = about 65 feet.
- A half-wave dipole for 146 MHz: 468 / 146 = about 3.2 feet.
- A quarter-wave whip for 446 MHz: 234 / 446 = about 0.52 feet, or 6.3 inches.
This is why a quarter-wave vertical for 2 meters is only about 19 inches long (Technician pool, T9A08) while a 40 meter dipole is about 65 feet. When there is not room for a full-size antenna, it can be electrically lengthened with inductors (loading coils) in the radiating elements (Technician pool, T9A02), but shortened antennas cost efficiency: a handheld’s short flexible antenna has low efficiency compared with a full-size quarter-wave antenna (Technician pool, T9A04). The antennas and feed lines guide explains the formulas, and the antenna calculator does the arithmetic for any frequency.