Wavelength / Frequency Converter

Converting between wavelength and frequency comes up in radio engineering, optics, and physics homework — and remembering whether to use c (speed of light) or some other speed for non-electromagnetic waves trips people up.

Enter wavelength or frequency and pick the medium (vacuum, air, water, glass) — the calculator returns the other. For electromagnetic waves, c = 299,792,458 m/s in vacuum, slightly slower in air. For sound, the speed varies with temperature and medium and is configurable. Output covers ranges from radio (km wavelengths) to gamma rays (sub-picometer).

Energy is also shown alongside, since photon energy = h × f and is what people often actually want when working in spectroscopy or quantum mechanics. Units are picked sensibly per range — you'll get GHz for radio, THz for infrared, eV or keV for X-rays — so the numbers stay readable instead of cluttering the screen with scientific notation.

The relationship is c = fλ, where c is the wave speed, f is frequency, and λ is wavelength. For light in vacuum, c is exactly 299,792,458 m/s (a defined constant since 1983 — the meter is now defined in terms of c, not the other way around). In other media, light travels slower: in water about 0.75c, in glass about 0.67c. Frequency stays the same when light enters a new medium, but wavelength compresses proportionally to the speed reduction. This is why a stick in water looks bent — refraction is the geometric consequence of speed change.

The pain this addresses: physics homework and engineering work that bounces between frequency-domain and wavelength-domain descriptions of the same wave. RF engineers think in MHz/GHz. Optical engineers think in nanometers. Spectroscopists think in either, plus wavenumbers (cm⁻¹). Astronomy uses different units for different wavelength regimes — millimeters for microwave, microns for IR, angstroms for visible UV. Converting between them by hand involves remembering c and doing repeated division. The tool handles the bookkeeping.

Worked example: a WiFi router uses 2.4 GHz. What's the wavelength? λ = c/f = 3×10⁸ / 2.4×10⁹ = 0.125 m = 12.5 cm. That's why 2.4 GHz signals struggle to penetrate thick walls — the wavelength is comparable to common building materials' thickness, and water in the walls (and humans) absorbs in this band (incidentally, this is also roughly the resonant frequency of water, which microwave ovens exploit at 2.45 GHz). 5 GHz WiFi has 6 cm wavelength — better resolution, worse penetration.

Where units get philosophically tricky: photon energy. E = hf, with h being Planck's constant. Wavelength and energy are inversely related: short wavelengths = high energy. UV light at 200 nm has photon energy of about 6.2 eV, enough to break chemical bonds (which is why UV causes sunburn — the photons damage DNA directly). Visible light at 500 nm has 2.5 eV — enough to drive photosynthesis but not break most bonds. Infrared at 10 μm is 0.124 eV — only enough to vibrate molecules, which is heat. The same wave, three different units describing it: frequency, wavelength, photon energy.