Wavelength to Frequency Calculator
Enter a wavelength and get the frequency instantly, or flip it and enter a frequency to solve for wavelength. Choose a medium from the preset list (light in vacuum, sound in air, sound in water, and more) or type your own wave speed. The calculator also shows photon energy in joules and electron volts for electromagnetic waves, and it labels the region of the electromagnetic spectrum.
Formula
Worked example
Visible green light has a wavelength of 500 nm = 5e-7 m. In vacuum (v = 299,792,458 m/s): f = 299,792,458 / 5e-7 = 5.996e14 Hz (about 600 THz). The period is T = 1 / 5.996e14 = 1.668e-15 s (1.668 fs). The angular frequency is omega = 2 * pi * 5.996e14 = 3.768e15 rad/s. Each photon carries E = 6.626e-34 * 5.996e14 = 3.973e-19 J = 2.48 eV.
The wave equation: f = v / lambda
Every wave, whether light, sound, radio, or a ripple in water, obeys the same relationship between frequency, wavelength, and wave speed: frequency equals wave speed divided by wavelength (f = v / lambda). Rearranging gives wavelength equals wave speed divided by frequency (lambda = v / f). The speed depends on the medium, not on the frequency of the wave, which is why the same radio tower can broadcast AM and FM signals at very different frequencies through the same air. This calculator applies the equation in both directions: give it a wavelength and it returns the frequency, or give it a frequency and it returns the wavelength.
Wave speed in different media
Light travels fastest in a vacuum at exactly 299,792,458 m/s (the defined value of the speed of light, c). It slows down in any material medium by a factor called the refractive index: about 0.03% slower in air, 25% slower in water, and 33% slower in common glass. Sound behaves very differently: it cannot travel through a vacuum at all, and its speed depends strongly on the density and stiffness of the medium. In dry air at 20 degrees Celsius, sound travels at about 343 m/s, nearly a million times slower than light. In water, sound travels at roughly 1,481 m/s, and in dense metals like steel or aluminum, it can reach 5,000 m/s or more. This calculator includes 14 preset velocities for the most common combinations of wave type and medium.
Period, angular frequency, and wavenumber
Beyond the basic frequency, three related quantities appear throughout physics and engineering. The period (T = 1 / f) is the time taken to complete one full cycle, measured in seconds. For a 440 Hz note, the period is about 2.27 ms; for visible light at 600 THz, it is about 1.67 femtoseconds. The angular frequency (omega = 2 * pi * f) measures cycles in radians per second rather than cycles per second, which is more natural in many equations. The wavenumber (k = 2 * pi / lambda) is the spatial counterpart of angular frequency: it counts how many radians of wave fit into one metre of space.
Photon energy for electromagnetic waves
Electromagnetic waves carry energy in discrete packets called photons. Each photon has energy E = h * f, where h is Planck's constant (6.626e-34 J*s). Because frequency and wavelength are inversely proportional at fixed speed, shorter wavelengths mean higher frequencies and higher photon energies. Visible violet light at 400 nm carries about 3.1 eV per photon. Infrared at 1000 nm carries about 1.24 eV. Gamma rays at 0.001 nm can carry millions of electron volts per photon, which is why they are ionising and medically dangerous. This calculator shows photon energy in both joules and electron volts whenever a light preset is selected.
Electromagnetic spectrum quick reference
| Region | Wavelength range | Frequency range | Common uses |
|---|---|---|---|
| Radio waves | > 1 mm | < 300 GHz | Broadcasting, radar, astronomy |
| Microwave | 1 mm - 1 m | 300 MHz - 300 GHz | Wi-Fi, mobile networks, ovens |
| Infrared | 700 nm - 1 mm | 300 GHz - 430 THz | Thermal imaging, remote controls |
| Visible light | 400 - 700 nm | 430 - 750 THz | Human vision, photography |
| Ultraviolet | 10 - 400 nm | 750 THz - 30 PHz | Sterilisation, fluorescence |
| X-ray | 0.01 - 10 nm | 30 PHz - 30 EHz | Medical imaging, material testing |
| Gamma ray | < 0.01 nm | > 30 EHz | Nuclear medicine, astronomy |
Approximate frequency and wavelength ranges for major EM bands.
Frequently asked questions
What is the relationship between wavelength and frequency?
Wavelength and frequency are inversely proportional: as one increases, the other decreases, provided the wave speed stays constant. Their product always equals the wave speed: f * lambda = v. For light in vacuum, this product is always c = 299,792,458 m/s regardless of the colour or energy of the light.
Does frequency change when light enters a different medium?
No, frequency stays the same when a wave moves from one medium to another. What changes is the wavelength and the wave speed. Because f = v / lambda and f is fixed, a lower wave speed means a shorter wavelength. This is why light bends (refracts) when it crosses a boundary between media: different frequencies travel at the same speed in vacuum but appear at different colours because the human eye perceives frequency as colour.
How do I convert nm to Hz for visible light?
Divide the speed of light in the relevant medium (usually c = 2.998e8 m/s for air) by the wavelength in metres. First convert nm to m by multiplying by 1e-9. For example, 500 nm = 5e-7 m, and 2.998e8 / 5e-7 = 5.996e14 Hz. The calculator does all unit conversions automatically.
What is the speed of sound used in this calculator?
The calculator uses 343 m/s for dry air at 20 degrees Celsius as the default sound preset. This changes with temperature: approximately 0.6 m/s per degree Celsius near room temperature, so at 40 degrees Celsius it is about 355 m/s. For seawater, the default is 1,520 m/s. Other presets cover rubber, lead, gold, glass, copper, and aluminum. You can also type any custom speed.
What is angular frequency and how is it different from regular frequency?
Regular frequency (f) counts complete cycles per second in hertz. Angular frequency (omega = 2 * pi * f) measures the rate in radians per second, since one full cycle covers 2 * pi radians. Angular frequency is more convenient in many physics equations, such as the description of simple harmonic motion and electromagnetic wave equations, where the factor 2 * pi appears so often it is absorbed into omega.
What is photon energy and why does it depend on frequency?
A photon is the smallest packet of electromagnetic energy. Its energy is proportional to frequency: E = h * f, where h is Planck's constant. Higher-frequency radiation (such as X-rays and gamma rays) carries far more energy per photon than lower-frequency radiation (radio waves), which is why high-frequency radiation can strip electrons from atoms (ionising radiation) while radio waves cannot.