Article — Photon Energy Calculator
Photon energy calculator for wavelength and frequency
A photon's energy is its frequency multiplied by the Planck constant, E = hf, or equivalently hc divided by wavelength, E = hc/λ. In practical units, E in electronvolts equals 1239.84 divided by wavelength in nanometres. A green 550 nm photon carries 2.25 eV; a 50 keV X-ray photon carries about 22,000 times more.
Photon energy is the bridge between waves and quanta. Higher-frequency light delivers more energy per particle, not more particles per second. That is why ultraviolet causes sunburn while bright red light from a 100 W lamp does not, no matter how much you turn it up.
What is photon energy
Max Planck introduced the quantum hypothesis in 1900 to explain blackbody radiation. He proposed that energy is exchanged in discrete packets proportional to frequency. Einstein extended this in 1905 to explain the photoelectric effect, treating light itself as a stream of particles with energy E = hf. The work earned him the 1921 Nobel Prize.
Each photon carries a fixed energy set by its frequency. A million photons of red light contain the same energy as a million separate red-light events, not the same as one ultraviolet photon. This particle nature is what makes light able to free electrons from metal, knock molecules into excited states, or break chemical bonds.
Since the 2019 SI redefinition, the Planck constant has an exact value: h = 6.62607015 × 10-34 J·s. The kilogram is now defined in terms of h, rather than h being measured against a metal cylinder.
The photon energy formula
Two equivalent equations describe photon energy, plus a working shortcut you will use most often.
E = h f E = hc / λE (eV) = 1239.84 / λ (nm) λ (nm) = 1239.84 / E (eV)h = 6.62607015e-34 J·s c = 299,792,458 m/sA worked example. Visible green light at λ = 550 nm. Using the shortcut: E = 1239.84 / 550 = 2.254 eV. To convert to joules, multiply by 1.602×10-19: E = 3.61 × 10-19 J. The frequency is c / λ = 2.998×108 / 5.50×10-7 = 5.45 × 1014 Hz, or 545 THz.
Photon energy across the visible spectrum
Human vision spans roughly 380 to 750 nm. The energy per photon at the ends of that range differs by a factor of two.
The blue end carries more energy per photon, which is why blue-light filters get pitched as eye-comfort upgrades and why excess UV (just past violet) causes skin damage that red light cannot. Energy density on the retina depends on photon flux (photons per second per square metre) and the energy of each, and the product is what your eye registers as brightness.
UV and X-ray photon energies
Above 3 eV photons can break chemical bonds. The threshold for ionization is roughly 10 eV, which is where UV-C and far-UV start. Diagnostic X-rays operate at 20 to 150 keV; gamma rays from radioactive decay sit above 100 keV.
- UV-A 320-400 nm = 3.1 to 3.9 eV (tanning, polymer curing)
- UV-B 280-320 nm = 3.9 to 4.4 eV (sunburn, vitamin D synthesis)
- UV-C 100-280 nm = 4.4 to 12.4 eV (germicidal at 254 nm)
- Soft X-ray 0.1-10 nm = 124 eV to 12.4 keV (XPS spectroscopy)
- Diagnostic X-ray 0.025-0.06 nm = 20 to 50 keV (medical imaging)
- Cobalt-60 gamma = 1.17 and 1.33 MeV (sterilization, cancer therapy)
UV-C and X-rays can strip electrons from atoms and damage DNA. UV-C germicidal lamps need shielding; you should never look at the bare tube. Brief skin exposure from a household germicidal lamp causes severe sunburn-like injury within seconds.
Applications of photon energy
The numbers matter in fields well beyond physics labs.
In solar cells, photons must carry at least the bandgap energy of the semiconductor to free a charge carrier. Silicon has a bandgap of 1.12 eV, so photons below 1100 nm contribute (above that, they pass through unused). The solar spectrum peaks near 500 nm, which is why silicon and the sun are a reasonable match. Tandem cells use stacked materials with different bandgaps to capture a wider slice.
In spectroscopy, each molecule has a fingerprint of vibrational and electronic energy levels. UV-Vis spectroscopy probes electronic transitions in the 2 to 6 eV range; infrared spectroscopy maps vibrations at 0.05 to 0.5 eV. The match between photon energy and molecular gap is what gives you a measurable peak.
The eye's peak sensitivity at 555 nm corresponds to 2.234 eV per photon. The match with the solar spectrum's peak is no accident: vertebrate vision evolved under sunlight.
Photon energy and the photoelectric effect
Einstein's 1905 paper showed that a photon must carry at least the work function of a metal to free an electron from its surface. Below that threshold, no current flows no matter how intense the light. Above it, the kinetic energy of the freed electron equals the photon energy minus the work function.
Cesium has a work function of 1.95 eV, so red light around 635 nm (1.95 eV) is roughly the cutoff. Aluminium needs 4.3 eV, which means only UV will eject electrons. Silver sits at 4.7 eV. These thresholds explain why early photocell designs used alkali metals like cesium and potassium.
Common photon energy mistakes
Most errors come from unit handling and from confusing photons with classical waves.
- Mixing nanometres and metres — the shortcut 1239.84 / λ uses nm and eV. Plug in metres and you are off by 109.
- Forgetting that frequency is invariant — light slows in glass, so wavelength shrinks, but frequency (and therefore photon energy) stays the same.
- Confusing E = hf with E = mc² — photons have no rest mass. Use E = hf or E = pc, not E = mc².
- Misreading laser power as photon energy — a 1 W green laser puts out roughly 2.77 × 1018 photons per second, each at 2.25 eV. Power = photons/s × energy/photon.
- Treating eV per mole as eV per photon — 1 eV per photon = 96.485 kJ per mole of photons, a factor of Avogadro's number.
Memorize 1240 eV·nm. Any wavelength in nm, divided into 1240, gives energy in eV. Works for radio (gigantic nm, tiny eV), visible (hundreds of nm, units of eV), and X-rays (fractions of nm, keV).