Wavelength and Frequency Calculator

Wavelength and frequency are inversely related through wave speed: v = lambda × f, where v is the wave speed (m/s), lambda is the wavelength (m), and f is the frequency (Hz). For electromagnetic waves in a vacuum, v equals c (the speed of light, approximately 299,792,458 m/s), giving c = lambda × f. Because c is constant, doubling the frequency halves the wavelength. For sound waves, the wave speed depends on the medium and temperature, and the same inverse relationship holds.

The electromagnetic (EM) spectrum spans a vast range of wavelengths. Radio waves have wavelengths from millimetres to kilometres (frequencies below 300 GHz). Microwaves cover roughly 1 mm to 30 cm. Infrared runs from about 700 nm to 1 mm. Visible light falls between approximately 380 nm (violet) and 700 nm (red). Ultraviolet extends from about 10 nm to 380 nm. X-rays cover roughly 0.01 nm to 10 nm. Gamma rays are shorter than 0.01 nm. The boundaries are approximate and overlap between adjacent regions.

All electromagnetic waves are oscillations of coupled electric and magnetic fields and travel at the same speed in a vacuum, c = 299,792,458 m/s exactly, by definition (since 1983 the metre is defined in terms of c). This constancy follows from Maxwell's equations of electromagnetism and was confirmed by the Michelson-Morley experiment. In a medium other than vacuum, EM waves slow down; the ratio c/v is the refractive index of the medium. Different wavelengths slow by different amounts (dispersion), which is why a prism separates white light into a spectrum.

The human audible range is approximately 20 Hz to 20,000 Hz (20 kHz). At 20 Hz, the wavelength in air at 20°C is about 17.2 m (a very long wave). At 20 kHz, the wavelength is about 1.7 cm. Below 20 Hz is infrasound (produced by earthquakes, large machinery, and some animals). Above 20 kHz is ultrasound, used in medical imaging, sonar, and cleaning equipment. Bats and dolphins communicate using ultrasound up to approximately 150 kHz.

The relationship c = lambda × f is fundamental to antenna design (antenna length is typically a fraction of the wavelength of the target frequency), radio communications (frequency allocations correspond to specific wavelength bands), optical fibre design, medical imaging (MRI uses radio frequency, X-ray imaging uses very short EM wavelengths), and spectroscopy (atomic emission lines at specific wavelengths identify elements). In acoustics, room design depends on wavelengths of target frequencies relative to room dimensions to avoid standing waves and resonance problems.