How to Convert Frequency to Wavelength
Every wave — light, radio, WiFi, sound, or a ripple on water — obeys the same relationship between how fast it travels, how often it oscillates, and how far each cycle spans: the wave equation v = f × λ, where v is the propagation speed, f is the frequency, and λ (lambda) is the wavelength. Rearranged for wavelength, this becomes λ = v / f: for a fixed wave speed, higher frequencies always produce shorter wavelengths, and lower frequencies produce longer ones. This calculator solves that equation directly, plus two related quantities — period and angular frequency — that show up constantly in physics and electrical engineering.
The wave equation and unit conversions
Frequency can be entered in Hz, kHz, MHz, GHz, or THz; the calculator first converts it to Hz (cycles per second) by multiplying by the unit's scale factor (1, 10³, 10⁶, 10⁹, or 10¹²). Wavelength then follows from λ = v / f, using whatever propagation speed you supply. For example, an FM radio signal at 100 MHz (10⁸ Hz) traveling at the speed of light gives λ = 299,792,458 / 100,000,000 ≈ 3 meters. The calculator also reports the period T = 1/f (time for one full cycle), the angular frequency ω = 2πf (radians per second), and the wave number k = 2π/λ (radians per meter) — all standard derived quantities from the same frequency and speed.
Choosing the right propagation speed
The propagation speed depends entirely on the type of wave and the medium it travels through, so picking the right one matters as much as the frequency itself. Electromagnetic waves — radio, microwaves, WiFi, and visible light — travel at c ≈ 299,792,458 m/s in a vacuum, and only slightly slower in air; inside glass or water they slow to v = c / n, where n is the medium's refractive index. Sound waves are far slower and more medium-dependent: about 343 m/s in air at 20°C, roughly 1,481 m/s in water, and several kilometers per second in solids like steel. Because wavelength scales linearly with speed for a fixed frequency, using the wrong speed (for example, the speed of light for an audio frequency) will produce a wavelength that is off by roughly a million times.