Wavelength Calculator

The one formula behind every answer here

Every electromagnetic wave obeys the same relationship: the speed of light equals frequency times wavelength, or c = f × λ. Rearranged, that gives the two things people actually search for — wavelength from frequency (λ = c / f) and frequency from wavelength (f = c / λ). Because c is fixed at 299,792,458 metres per second in a vacuum, the two quantities are locked together: double the frequency and the wavelength halves. There is no third variable to guess at.

The calculator adds two things a bare formula does not give you. The first is photon energy, E = h × f, using Planck's constant h = 6.62607015 × 10^-34 J·s, reported both in joules and in electronvolts. The second is a band label, so you immediately know whether you are looking at a radio wave, a microwave, infrared, visible light, ultraviolet, X-rays or gamma rays.

Worked example: your FM station

Take an FM broadcast at 98.5 MHz. That is 98,500,000 Hz, so λ = 299,792,458 / 98,500,000 = 3.044 m. The period is 1 / f = 10.15 nanoseconds, and the photon energy is a minuscule 6.53 × 10^-26 J, or 0.41 microelectronvolts. This is why radio is treated as a smooth wave and never as individual photons: a single FM photon carries almost nothing. The 3 m figure also explains antenna hardware. A quarter-wave whip for that band is about 76 cm, which is exactly the length of the telescopic aerial on an old hi-fi tuner, and a dipole is around 1.5 m tip to tip.

A tour of the spectrum with everyday anchors

Start at the long end. AM radio near 1000 kHz has a 300 m wavelength — longer than a city block, which is why AM bends around hills and buildings. FM sits at 3 m. Wi-Fi at 2.4 GHz gives 12.5 cm, roughly the width of your hand, and 5 GHz gives 6 cm; shorter waves carry more data but get stopped by walls more easily. A microwave oven runs at 2.45 GHz, the same 12 cm ballpark, which is why the metal mesh in the door — with holes a couple of millimetres across — blocks the microwaves while letting visible light through.

Keep going and wavelengths collapse. A TV remote emits at about 940 nm in the near infrared. Green light sits near 530 nm, right where the human eye is most sensitive, at a frequency of 566 THz and a photon energy of 2.34 eV. Red is about 700 nm and 1.77 eV; violet is about 400 nm and 3.10 eV. That energy jump is the whole story of sunburn and photochemistry: UVB photons at 300 nm carry 4.13 eV, enough to break chemical bonds in DNA, while a red photon simply cannot. Below 10 nm you are in X-ray territory (keV energies, used precisely because they pass through soft tissue), and below 10 picometres, gamma rays.

Photon energy intuition

A useful shortcut for optics work: E (in eV) ≈ 1240 / λ (in nm). Plug in 620 nm and you get 2.0 eV; plug in 1240 nm and you get 1.0 eV. That single constant lets you sanity-check any laser, LED or solar-cell number in your head. A silicon solar cell has a band gap of 1.12 eV, which corresponds to 1107 nm — light with a longer wavelength than that passes straight through and generates no current, which caps silicon's theoretical efficiency.

Electromagnetic waves versus sound

The relationship v = f λ holds for any wave, but only electromagnetic waves travel at c. Sound is a mechanical pressure wave needing a medium, moving at roughly 343 m/s in air at 20 °C, 1480 m/s in water and 5100 m/s in steel. A 440 Hz concert A is therefore 0.78 m long in air, not the 681 km you would get by wrongly using the speed of light. If you are calculating room modes, speaker spacing or ultrasound, substitute the correct speed for the medium instead of using this tool.

Limitations worth knowing

Results assume a vacuum. In glass, water or fibre, light slows to c / n and the wavelength shrinks by the same factor while the frequency stays constant — a 1550 nm telecom laser is about 1063 nm inside a fibre with n = 1.4585. Band boundaries are conventions, not physical walls: sources differ on whether visible light stops at 700 nm or 780 nm, and the microwave/infrared border is drawn at 1 mm here. Finally, for waveguides and antennas, the guided wavelength differs from the free-space value, so use this figure as the starting point rather than the final dimension.