What a photon energy calculator does
A photon is a single packet of light. Its energy depends on just one thing: its frequency. Higher frequency means more energy per photon. Because wavelength and frequency are tied together by the speed of light, you can also find the energy from the wavelength. That is what this page computes.
The formula is E = h x f. Here E is energy in joules, f is frequency in hertz, and h is the Planck constant. The Planck constant is 6.62607015 x 10^-34 J s, and that value is exact. You can also write the formula with wavelength: E = h x c / lambda. The speed of light c is 299,792,458 m/s, also exact.
Type in any one value and the other two appear. The result comes out in joules and in electronvolts. One electronvolt is 1.602176634 x 10^-19 J. Electronvolts are handy because visible photons have energies of a few eV, which is a much easier number to read than 0.0000000000000000003 J.
The shortcut chemists use: hc = 1239.84 eV nm
If you work in nanometers and electronvolts, the constants fold into one number. Multiply h by c and convert to eV, and you get hc = 1239.84 eV nm. Then the formula is simply E = 1239.84 / lambda, with lambda in nanometers and E in electronvolts.
This is the version most people use day to day. It skips the powers of ten and gives an answer you can check in your head.
Worked example: a green laser pointer
A common green laser pointer puts out light at 532 nm. What is the energy of one photon?
- Use E = 1239.84 / lambda with lambda = 532 nm.
- E = 1239.84 / 532 = 2.33 eV.
So each green photon carries 2.33 eV. To get the frequency, use f = c / lambda. That gives 563.5 THz, or 5.635 x 10^14 Hz. The same photon in joules is 2.33 x 1.602176634 x 10^-19, which is about 3.73 x 10^-19 J.
Worked example: a 1 nm X-ray photon
Now try a much shorter wavelength. A 1 nm photon sits in the soft X-ray band. Using the same shortcut: E = 1239.84 / 1 = 1239.84 eV, or about 1.24 keV. That is roughly 530 times the energy of the green photon. Shorter wavelength means higher frequency, and higher frequency means more energy per photon.
Why shorter wavelength means more energy
Wavelength and frequency move in opposite directions. As wavelength gets shorter, frequency gets higher. Since E = h x f, energy rises with frequency. So a 400 nm violet photon has more energy than a 700 nm red photon.
This matters for what light can do. Visible photons carry a few eV. That is enough to drive some chemical reactions, like the ones in your eyes or in photosynthesis. It is not enough to knock an electron out of most atoms. That takes several eV or more, which is why ultraviolet light can damage skin and visible light mostly does not.
The bands below are conventional boundaries. Different references draw them slightly differently, and they overlap in practice.
| Band | Wavelength range |
|---|---|
| Radio | longer than 1 m |
| Microwaves | 1 mm to 1 m |
| Infrared | 750 nm to 1 mm |
| Visible | 380 nm to 750 nm |
| Ultraviolet | 10 nm to 380 nm |
| X-rays | 10 pm to 10 nm |
| Gamma rays | shorter than 10 pm |
From eV to wavelength and back
The same shortcut runs in reverse. If you know the energy in eV and want the wavelength in nm, use lambda = 1239.84 / E. A 2.33 eV photon gives 1239.84 / 2.33 = 532 nm, which matches the green laser example.
This reverse step is useful when you read a band gap or an ionisation energy and want to know what wavelength of light goes with it. It also works for the energy needed to break a bond, if that energy is given in eV.
What is a mole of photons?
Chemists sometimes talk about a mole of photons, called an einstein. It is Avogadro's number of photons treated as one batch. To get the energy in that batch, take the energy of one photon in joules and multiply by Avogadro's number. The result is usually reported in kilojoules per mole. This is the unit that lines up with bond energies and reaction energies in a chemistry course.
What the calculator does not do
It does not compute relativistic effects. For photons that is fine, because photons have no mass and always travel at c. The formula E = h x f holds for every photon. If you need the de Broglie wavelength of a particle with mass, that is a different page.
All the formulas used here are published at how we calculate. You can also see the full electromagnetic spectrum or check the wavelength calculator for the v = f x lambda relation.