Frequency Wavelength Converter

Frequency and wavelength are two complementary ways to characterize electromagnetic radiation and periodic waves. Frequency (f) counts how many complete cycles occur per second, measured in hertz (Hz). Wavelength (λ) measures the spatial distance between successive identical points in the wave, measured in meters or submultiples. They are connected through the universal equation λ = c / f, where c = 299,792,458 m/s is the speed of light in vacuum. This inverse relationship means that as frequency increases, wavelength decreases proportionally — and vice versa. This converter allows you to express electromagnetic radiation in frequency or wavelength units interchangeably across the entire spectrum, from cosmic-scale radio waves to quantum-mechanical Compton scales.

The hertz (Hz) is the SI unit of frequency, equal to one cycle per second. The electromagnetic spectrum spans an enormous range of frequencies. Extremely Low Frequency (ELF) radio waves used for submarine communication operate at 3–300 Hz. AM radio broadcasts at 530–1700 kHz (kilohertz). FM radio uses 87.5–108 MHz (megahertz). WiFi (2.4 GHz, 5 GHz) and 5G cellular (sub-6 GHz, mmWave at 24–100 GHz) operate in the gigahertz range. Radar systems use 1–110 GHz (L-band through W-band). Millimeter-wave imaging systems operate at 30–300 GHz.

Terahertz (THz) radiation — spanning 0.1–10 THz (wavelengths 30 µm to 3 mm) — occupies the gap between microwave and infrared, sometimes called the "terahertz gap." It is used in materials science (terahertz spectroscopy), security screening (non-ionizing imaging through clothing), pharmaceutical quality control (tablet coating thickness), and non-destructive testing. The full SI prefix series from exahertz (EHz = 10¹⁸ Hz) down to attohertz (aHz = 10⁻¹⁸ Hz) covers the full range from gamma rays through geological-timescale oscillations.

Visible light occupies the frequency range 405–789 THz, corresponding to wavelengths of 380–740 nm. The human eye's peak sensitivity is at 555 nm (540 THz) — the green-yellow region where the photopic luminosity function reaches its maximum. This is why the candela (SI unit of luminous intensity) is defined at 540 THz: 1 cd = 1/683 W/sr at that frequency. Ultraviolet (UV) light spans 10–400 nm (750 THz–30 PHz); infrared (IR) covers 740 nm–1 mm (300 GHz–405 THz).

In optical fiber communications, the standard C-band operates at 191.7–196.1 THz (1530–1565 nm wavelength). Fiber laser engineers specify their sources in both THz and nm, switching between representations depending on whether they are discussing frequency-domain (spectral) or time-domain (dispersion) properties. DWDM (Dense Wavelength Division Multiplexing) channel spacing is specified in GHz (typically 12.5, 25, 50, or 100 GHz spacing between adjacent channels).

In spectroscopy and analytical chemistry, wavelength in nanometers (nm) is used for UV-Vis spectroscopy, while wavenumber (cm⁻¹ = 10⁷/λ(nm)) is standard in infrared and Raman spectroscopy. Nuclear magnetic resonance (NMR) spectrometers are identified by their ¹H Larmor frequency (e.g., 400 MHz, 600 MHz, 1 GHz NMR), which is proportional to magnetic field strength. X-ray crystallography uses wavelengths in ångströms (0.1 nm) or picometres for characterizing crystal lattice spacings.

The Compton wavelengths of the electron, proton, and neutron represent the quantum length scale at which relativistic quantum mechanical effects become significant for each particle. The electron Compton wavelength (λ_Ce = 2.426 × 10⁻¹² m = 2.426 pm) appears in quantum electrodynamics (QED) calculations of electron energy levels, Compton scattering cross-sections, and the fine structure constant. The proton and neutron Compton wavelengths (≈1.321 × 10⁻¹⁵ m) govern nuclear structure calculations and pion exchange models. This converter includes all three for completeness in high-energy physics applications.

In astronomy and astrophysics, electromagnetic radiation is described across wavelengths from femtometre-scale gamma rays to kilometre-scale radio waves. The cosmic microwave background (CMB) peaks at about 1.9 mm wavelength (160 GHz). Pulsar timing residuals involve nanohertz-frequency gravitational waves being detected by pulsar timing arrays (PTAs). The wavelength series from exametres (10¹⁸ m, larger than the observable universe) to nanometres covers all practically encountered astrophysical radiation scales.

This frequency-wavelength converter supports all 35 units — the complete Hz SI prefix series (EHz to aHz), cycle/second, 13 wavelength scales (exametres to nanometres), and 3 Compton wavelengths — with instant, 12-significant-digit precision, completely free.