Frequency ⇄ Wavelength
Wavelength for any frequency, with velocity factor for cables.
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The engineering
Wavelength is the speed of light divided by frequency. In free space the velocity factor is 1.0; in coax and other transmission lines the wave travels slower — typically 0.66 for solid-PE coax and around 0.82–0.87 for foam dielectric.
The half-wave and quarter-wave rows are what you actually cut: a quarter-wave whip for 146 MHz works out to about 49 cm in free space.
Where this math comes from
This one-line formula compresses two centuries of physics. Ole Rømer showed in 1676 that light has a finite speed at all, timing eclipses of Jupiter's moons. James Clerk Maxwell's 1865 field equations predicted electromagnetic waves traveling at exactly that speed — implying light itself was one — and Heinrich Hertz built the apparatus that proved it in 1887, measuring wavelength and frequency of radio waves directly.
The velocity-factor input comes from Oliver Heaviside, the self-taught telegraph engineer whose 1880s transmission-line equations describe why waves slow down inside cables. Since 1983 the speed of light is no longer measured but *defined* — exactly 299,792,458 m/s — which is the constant in this card.
- 1676Ole RømerFirst demonstration that light has a finite speed, from Jupiter's moons.
- 1865James Clerk MaxwellField equations predict EM waves at the speed of light.
- 1887Heinrich HertzGenerates and measures radio waves — λf = c confirmed on a lab bench.
- 1887Oliver HeavisideTransmission-line theory explains velocity factor in cables.
- 198317th CGPMSpeed of light fixed by definition at 299,792,458 m/s.
See the full timeline of the math behind every calculator →
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