Photon Energy Calculator
Enter any one of wavelength, frequency, wavenumber or energy and this calculator returns the full set: photon energy in electronvolts, joules and kilojoules per mole, plus the matching frequency and wavelength. Switch units freely, see which part of the spectrum the photon falls in, and optionally convert a beam power into a photon flux.
Formula
Worked example
For 500 nm green light: E = hc/λ = (6.626×10⁻³⁴ × 2.998×10⁸) ÷ (500×10⁻⁹) = 3.973×10⁻¹⁹ J ≈ 2.48 eV ≈ 239 kJ/mol, at a frequency of about 599 THz.
How photon energy is calculated
Light is delivered in discrete packets called photons, and each photon carries an energy set entirely by its frequency. The calculator uses the Planck relation E = h·f, where h is the Planck constant (6.626×10⁻³⁴ joule-seconds) and f is the frequency in hertz. When you supply a wavelength instead, it substitutes f = c/λ to get the equivalent form E = h·c/λ, using the speed of light c = 2.998×10⁸ metres per second. A spectroscopic wavenumber (reciprocal centimetres) plugs straight into E = h·c·(1/λ). The result is reported in joules, electronvolts, and kilojoules per mole, alongside the matching frequency, wavelength and wavenumber so every common form is available at once.
Four ways in, every quantity out
You can start from any one of four quantities: wavelength, frequency, wavenumber, or the energy itself. Entering an energy works backwards, the calculator solves for the wavelength and frequency a photon of that energy would have, which is handy when you know a band gap in eV and want the corresponding colour. Each numeric field carries a unit switch, so wavelength accepts nanometres, micrometres, ångströms and more, frequency accepts hertz through terahertz, and energy accepts eV, keV, meV, joules or kilojoules per mole. Whichever you choose, the full set of outputs updates together.
Joules, electronvolts and energy per mole
A single photon carries an extraordinarily small amount of energy in joules, typically around 10⁻¹⁹ J for visible light, which is awkward to work with. Physicists favour the electronvolt, the energy an electron gains crossing a one-volt potential, equal to 1.602×10⁻¹⁹ joules. Visible-light photons range from roughly 1.65 eV (deep red) to 3.26 eV (violet), ultraviolet sits above that, and X-rays reach thousands of electronvolts. Chemists prefer energy per mole: multiply the per-photon joule value by Avogadro number and divide by 1000 to get kilojoules per mole, often called an einstein, which compares directly against bond energies.
From beam power to photon flux
Turn on the beam option to convert a radiant power, the optical watts coming out of a laser or lamp, into a photon flux. The flux is simply the beam power divided by the energy of one photon, giving the number of photons emitted each second. A 1 milliwatt green laser pointer, for instance, throws out on the order of 10¹⁵ photons every second. The optional cost estimate prices the radiant energy delivered over one hour at your electricity rate; it is a floor figure, since real lamps and lasers are far from 100 percent efficient at turning wall power into light.
Why shorter wavelengths are more energetic
Because frequency and wavelength are tied together by f = c/λ, the photon energy E = hc/λ is inversely proportional to wavelength: halve the wavelength and you double the energy. This is why ultraviolet light, X-rays and gamma rays, all with short wavelengths, can break chemical bonds and damage living tissue, while infrared and radio photons, with long wavelengths, mostly deposit gentle heat. The same relationship explains the photoelectric effect, where only photons above a threshold energy can eject electrons from a metal, regardless of how bright the light is.
Photon energy across the spectrum
| Region | Wavelength | Frequency | Energy (eV) | Band |
|---|---|---|---|---|
| Radio / microwave | > 1 mm | < 300 GHz | < 0.001 | Low |
| Infrared | 750 nm - 1 mm | 300 GHz - 400 THz | 0.001 - 1.65 | Low |
| Visible light | 380 - 750 nm | 400 - 790 THz | 1.65 - 3.26 | Moderate |
| Ultraviolet | 10 - 380 nm | 790 THz - 30 PHz | 3.26 - 124 | High |
| X-ray / gamma | < 10 nm | > 30 PHz | > 124 | High |
Approximate wavelength, frequency and photon energy for each band.
Frequently asked questions
What can I enter, and what units are supported?
Pick the quantity you know from the dropdown: wavelength, frequency, wavenumber, or energy. Each field has a unit switch, so wavelength accepts nm, µm, mm, pm, ångströms or metres; frequency accepts Hz up to THz; and energy accepts eV, keV, meV, joules, or kJ/mol. The calculator converts to SI internally and returns the photon energy in joules, electronvolts and kJ per mole, plus the matching frequency, wavelength and wavenumber.
Can I solve backwards from an energy to a wavelength?
Yes. Choose Energy as the input quantity and enter a value (for example a 2.48 eV band gap). The calculator inverts E = hc/λ to give the wavelength (about 500 nm here) and the frequency (about 599 THz), so you can find the colour or photon a given energy corresponds to.
How do I get the energy of a mole of photons?
The calculator already reports it as kilojoules per mole. It multiplies the single-photon joule value by Avogadro number (6.022×10²³) and divides by 1000. One mole of photons is called an einstein, and expressing light energy this way lets you compare it directly against chemical bond energies, which are also tabulated in kJ/mol.
How does the beam power to photon flux conversion work?
Toggle on the beam option and enter the optical power. The photon flux, in photons per second, is the radiant power divided by the energy of a single photon at your wavelength. It assumes a monochromatic beam. The optional cost figure prices the radiant energy delivered in one hour at your electricity rate and ignores source inefficiency, so real running costs are higher.