Last updated: 2026-06-15

Photon Energy

Light travels as discrete packets of energy called photons. The energy carried by a single photon is proportional to its frequency and inversely proportional to its wavelength. This relationship, discovered by Max Planck in 1900 and extended by Albert Einstein in 1905 to explain the photoelectric effect, is one of the foundational results of quantum mechanics. It shows that light is not merely a continuous wave but arrives in quantised bundles whose size depends on colour.

This calculator finds the energy of a photon from either its wavelength or its frequency, and reports the complementary quantity as well.

The Formula

The energy of a photon is:

where $h = 6.626 \times 10^{-34}\ \text{J·s}$ is Planck's constant, $f$ is the frequency in hertz, $c = 299\,792\,458\ \text{m/s}$ is the speed of light in a vacuum, and $\lambda$ is the wavelength in metres. The two expressions are equivalent because $f = c/\lambda$.

Electronvolts Versus Joules

Photon energies expressed in joules are inconveniently small. A green photon at 550 nm carries about $3.6 \times 10^{-19}$ J — a number that is hard to reason about intuitively. The electronvolt (eV) is a more natural unit: $1\ \text{eV} = 1.602 \times 10^{-19}\ \text{J}$. In eV, visible-light photons sit in the range 1.8–3.3 eV, which aligns neatly with typical electronic transition energies in molecules and semiconductors. This calculator defaults to eV for the result.

Visible Light and the Electromagnetic Spectrum

Visible light spans wavelengths from about 380 nm (violet) to 700 nm (red). The corresponding photon energies are:

Beyond visible light, ultraviolet photons carry 3–100 eV, X-ray photons carry thousands of eV, and radio photons carry fractions of a microelectronvolt.

Worked Example

A laser pointer emits light at a wavelength of $\lambda = 500\ \text{nm}$ ($5 \times 10^{-7}\ \text{m}$). The photon energy is:

Entering 500 nm in this calculator reproduces the result. The frequency output of approximately $5.996 \times 10^{14}$ Hz confirms the calculation.

Why Photon Energy Matters

The photon energy determines whether light can trigger a given physical or chemical process. Photosynthesis relies on photons in the red and blue parts of the spectrum carrying just enough energy to excite chlorophyll molecules. Solar cells require photons above a threshold energy to free electrons from a semiconductor. The human eye responds to photons in the 1.8–3.3 eV range because the photoreceptor molecules in the retina have absorption peaks in that window. Below the threshold energy for a given process, increasing the intensity of light — sending more photons — has no effect; only higher-frequency (higher-energy) photons can trigger the transition.

Relationship to Other Quantities

The product $h \cdot c \approx 1240\ \text{eV·nm}$ is a useful shortcut: dividing 1240 by the wavelength in nanometres gives the photon energy in eV directly. This approximation reproduces the exact formula to better than six significant figures. The same constant appears in the photoelectric effect, where the maximum kinetic energy of an ejected electron equals the photon energy minus the work function of the metal.