Frequency of Light Calculator
Enter a wavelength or a frequency and this calculator instantly finds the other, plus the photon energy in both electronvolts and joules, the electromagnetic spectrum region, and the visible color (if applicable). You can also start from photon energy and work backward to wavelength and frequency. Switch wavelength units between pm, nm, µm, mm, and cm, and frequency units between Hz, kHz, MHz, GHz, THz, and PHz. The "Show your work" panel walks through every arithmetic step with your actual numbers.
How frequency and wavelength of light are related
All electromagnetic radiation, including light, travels through a vacuum at the same speed: c = 299,792,458 m/s, defined exactly by the International System of Units. The frequency and wavelength of any wave are inversely linked through this constant by the equation c = lambda times nu, where lambda is the wavelength in metres and nu is the frequency in hertz. Double the frequency and you halve the wavelength, and vice versa. This calculator applies that relationship in real time so you never have to handle the arithmetic manually. Wavelength is entered in the unit most natural to the spectral region you are working in: picometres for X-rays and gamma rays, nanometres for UV and visible light, micrometres for near-infrared, millimetres or centimetres for microwaves and long-wave infrared.
Photon energy: Planck's relation and electronvolts
Every photon carries a discrete packet of energy determined by its frequency through Planck's relation: E = h times nu, where h = 6.62607015 x 10^-34 J·s is the Planck constant. Combining with c = lambda times nu gives E = hc / lambda. Because photon energies span many orders of magnitude, two units are commonly used. Joules (J) are the SI unit, but photon energies are often tiny fractions of a joule. The electronvolt (eV) is more convenient: 1 eV = 1.602 x 10^-19 J. Visible-light photons carry roughly 1.65 eV (red) to 3.26 eV (violet). UV photons above ~3.4 eV can break chemical bonds, making them germicidal. X-ray photons in the keV range can ionize atoms, which is why they penetrate soft tissue.
Wavenumber and Angstroms: alternate ways to describe light
Spectroscopists often quote the wavenumber rather than wavelength or frequency. The wavenumber (symbol nu-bar or tilde-nu) is the reciprocal of the wavelength expressed in centimetres: tilde-nu = 1 / lambda_cm. It has units of cm^-1 (reciprocal centimetres) and is directly proportional to both frequency and photon energy, which makes it convenient for comparing spectral lines. The Angstrom (1 A = 10^-10 m = 0.1 nm) is a legacy unit still common in atomic physics and X-ray crystallography, where bond lengths and lattice spacings are naturally expressed in Angstroms. This calculator outputs both alongside the SI results.
Solving the equation in any direction
The same three-way relationship (c = lambda times nu, E = h times nu) can be rearranged for any unknown. Enter a wavelength and get the frequency and photon energy; enter a frequency and get the wavelength; enter a photon energy in eV and get both the wavelength and frequency. This bidirectional capability is especially useful in optics and quantum mechanics labs, where you might know the energy level transition (measured in eV) and need to find which wavelength photon causes it, or where you measure a frequency from a spectrum and need to label the color band.
Electromagnetic spectrum - wavelength, frequency, and energy ranges
| Region | Wavelength | Frequency | Energy per photon | Common uses |
|---|---|---|---|---|
| Gamma ray | < 10 pm | > 30 EHz | > 124 keV | Cancer radiotherapy, PET scans, nuclear physics |
| X-ray | 10 pm to 10 nm | 30 PHz to 30 EHz | 124 eV to 124 keV | Medical imaging, security scanners, crystallography |
| Ultraviolet | 10 nm to 380 nm | 790 THz to 30 PHz | 3.3 eV to 124 eV | Sterilization, fluorescence, sunscreen testing |
| Visible | 380 nm to 780 nm | 380 THz to 790 THz | 1.6 eV to 3.3 eV | Human vision, photography, fiber optics |
| Infrared | 780 nm to 1 mm | 300 GHz to 380 THz | 1.2 meV to 1.6 eV | Thermal imaging, TV remotes, fiber telecom |
| Microwave | 1 mm to 10 cm | 3 GHz to 300 GHz | 12 µeV to 1.2 meV | Wi-Fi, radar, microwave ovens, 5G |
| Radio wave | > 10 cm | < 3 GHz | < 12 µeV | AM/FM broadcast, mobile networks, GPS |
Approximate boundaries used in physics and engineering. Values are order-of-magnitude guides; actual boundaries vary by discipline.
Frequently asked questions
What is the formula for the frequency of light?
The fundamental relation is c = lambda times nu, which gives nu = c / lambda. Here c is the speed of light (299,792,458 m/s exactly), lambda is the wavelength in metres, and nu is the frequency in hertz. For visible light at 550 nm (green): nu = 299,792,458 / (550 x 10^-9) = approximately 5.45 x 10^14 Hz, or 545 THz.
What is the frequency range of visible light?
Visible light spans roughly 380 THz (for red light at about 780 nm) to 790 THz (for violet light at about 380 nm). Within that band: red is about 380-490 THz, orange about 490-510 THz, yellow about 510-530 THz, green about 530-600 THz, blue about 600-680 THz, and violet about 680-790 THz. Exact boundaries vary between sources because perception differs among individuals.
Why is frequency sometimes given in THz for light?
Optical frequencies run into the hundreds of terahertz (10^12 Hz), so gigahertz is too small and petahertz is used only for UV and higher. Terahertz sits right in the middle of the visible and near-infrared range, making it the most natural unit. Infrared light at 3 µm, for example, has a frequency of about 100 THz, and green light at 550 nm has a frequency of about 545 THz.
How do I convert wavelength in nm to frequency?
Divide the speed of light by the wavelength in metres. First convert nm to metres by multiplying by 10^-9. Then apply nu = c / lambda = 299,792,458 / lambda_m. For 600 nm: lambda_m = 600 x 10^-9 = 6 x 10^-7 m, so nu = 299,792,458 / (6 x 10^-7) = 4.997 x 10^14 Hz = 499.7 THz.
How is photon energy related to frequency?
Photon energy follows Planck's relation: E = h times nu, where h = 6.626 x 10^-34 J·s. Higher frequency means higher energy per photon. A 545 THz (green) photon has E = 6.626 x 10^-34 x 5.45 x 10^14 = 3.61 x 10^-19 J = 2.25 eV. That's why UV photons (above ~3 eV) can break molecular bonds while radio photons (below 1 µeV) cannot.
What is a wavenumber and how does it relate to frequency?
The wavenumber (tilde-nu) is 1 / lambda expressed in cm^-1. It is directly proportional to both frequency and photon energy. Converting is simple: tilde-nu (cm^-1) = nu (Hz) / c (cm/s) = nu / (2.998 x 10^10). For green light at 545 THz: tilde-nu = 5.45 x 10^14 / (2.998 x 10^10) = 18,179 cm^-1. Wavenumbers are the standard unit in vibrational spectroscopy and Raman spectroscopy.
Does light travel at the same speed in all media?
No. The speed c = 299,792,458 m/s applies only in a perfect vacuum. In any material the speed is reduced by the refractive index n: v = c / n. For glass (n approximately 1.5), light travels at about 2 x 10^8 m/s. When light enters a medium, its frequency stays the same but its wavelength shortens. The formulas in this calculator assume propagation in vacuum, which is appropriate for most physics problems and astronomical contexts.