The wavelength formula
A radio wave travels at the speed of light, 299,792,458 metres per second. Its wavelength is the distance it covers in one cycle, so it's the speed divided by the frequency:
f (MHz) = 299.79 ÷ λ (metres)
Radio amateurs usually round 299.79 to 300, which is close enough for most purposes. That's where the band names come from: 14 MHz is about 21 m, so it's called the 20m band, and 144 MHz is about 2.08 m, so it's the 2m band.
Velocity factor
Radio waves travel more slowly in a cable than in free space, because of the insulation between the conductors. The velocity factor is the fraction of the speed of light they reach. Solid polyethylene coax such as RG-58 and RG-213 has a velocity factor of about 0.66, foam cables such as LMR-400 and Ecoflex are about 0.85, and ladder line is about 0.9. A quarter-wave of RG-213 at 14.2 MHz is 3.48 m long, not the 5.28 m it would be in free space. Set the velocity factor above when you're cutting a stub, a phasing line or a matching section.
Wavelength isn't antenna length
A wire antenna resonates a few percent shorter than the free-space figure, because of the wire's thickness and the end insulators. A half-wave dipole for 14.2 MHz is about 10.05 m, not the 10.56 m shown above. Use the dipole calculator or the quarter-wave vertical calculator for cutting lengths.
Wavelength across the spectrum
The amateur bands run from 2,200 m (136 kHz) to millimetre waves above 24 GHz. HF covers 3 to 30 MHz (100 m to 10 m), VHF 30 to 300 MHz (10 m to 1 m) and UHF 300 MHz to 3 GHz (1 m to 10 cm). Antennas get smaller as the frequency rises, which is why a full-size 160m dipole is 80 m long and a 70cm one fits in your hand.
Questions
What is the wavelength of 145 MHz?
About 2.07 m in free space. A quarter-wave is 51.7 cm and a half-wave is 1.03 m.
How do I convert MHz to metres?
Divide 300 by the frequency in MHz. For a more exact figure, use 299.79. For example 7.1 MHz is 299.79 ÷ 7.1 = 42.2 m.
Why is 14 MHz called the 20 metre band?
Its wavelength is about 21 m. Band names are a rounded wavelength, so 14 MHz became 20m, 21 MHz 15m and 28 MHz 10m.
What velocity factor should I use for coax?
About 0.66 for solid polyethylene cable such as RG-58 and RG-213, 0.78 to 0.88 for foam cables such as LMR-400, Ecoflex and Aircell, and about 0.9 for ladder line. Check your cable's datasheet.