Photon Energy Calculator
Compute the energy of a single photon from its wavelength using Planck's law. Useful for optics, spectroscopy, and photovoltaic studies where knowing per-photon energy is essential.
About this calculator
A photon carries energy determined solely by its wavelength (or equivalently its frequency). The formula is E = hc / λ, where h is Planck's constant (6.626 × 10⁻³⁴ J·s), c is the speed of light (3 × 10⁸ m/s), and λ is the photon's wavelength in meters. Shorter wavelengths (ultraviolet, X-rays) carry more energy per photon, while longer wavelengths (infrared, radio) carry less. This relationship explains why UV radiation can break chemical bonds and cause sunburn while visible light generally cannot. The result is given in joules; for convenience in atomic physics, energies are often converted to electron-volts (1 eV = 1.602 × 10⁻¹⁹ J). Photon energy calculations are central to photoelectric effect analysis, LED design, and solar cell efficiency studies.
How to use
Consider a green laser with a wavelength of 532 nm = 532 × 10⁻⁹ m = 5.32 × 10⁻⁷ m. Enter wavelength = 5.32 × 10⁻⁷ m. The calculator computes: E = (6.626 × 10⁻³⁴ × 3 × 10⁸) / 5.32 × 10⁻⁷ = 1.988 × 10⁻²⁵ / 5.32 × 10⁻⁷ ≈ 3.74 × 10⁻¹⁹ J. Converting to eV: 3.74 × 10⁻¹⁹ / 1.602 × 10⁻¹⁹ ≈ 2.33 eV. This matches the known photon energy for green light and confirms whether a material's work function can be overcome in a photoelectric setup.
Frequently asked questions
How does photon energy change with wavelength across the visible spectrum?
Photon energy and wavelength are inversely proportional: E = hc / λ. Violet light at ~400 nm has roughly twice the photon energy of red light at ~700 nm. This is why violet and UV photons can trigger photochemical reactions — such as vitamin D synthesis or DNA damage — that red or infrared photons cannot. The entire visible spectrum spans photon energies from about 1.77 eV (red) to 3.10 eV (violet). Understanding this gradient is critical in designing photodetectors, solar cells, and phototherapy devices.
What is the difference between photon energy calculated from wavelength versus frequency?
Both approaches yield identical results because wavelength and frequency are related by c = fλ. Using frequency, the formula is E = hf; using wavelength, it is E = hc / λ. Substituting f = c / λ into E = hf immediately gives E = hc / λ. In practice, wavelength is more commonly measured directly with spectrometers, so the wavelength form is more convenient. Frequency-based calculations are preferred in radio-wave and microwave contexts where frequency is the directly measured quantity.
Why is photon energy important for understanding the photoelectric effect?
The photoelectric effect — the ejection of electrons from a metal surface by light — only occurs when each individual photon carries enough energy to overcome the metal's work function (binding energy of the electron). This cannot be achieved by increasing light intensity if the photon energy is too low, only by increasing the frequency (shortening the wavelength). Einstein's 1905 explanation of this threshold behavior using E = hf earned him the Nobel Prize and confirmed the quantum nature of light. Calculating photon energy lets engineers and physicists determine whether a given light source can drive photoemission in a specific material.