How this instrument works
Photon energy and wavelength are locked together by two older ideas stacked on each other: the Planck-Einstein relation E = hf, which says a photon's energy depends only on its frequency, and the wave equation c = fλ, which ties frequency to wavelength through the speed of light. Substitute f = c ⁄ λ into the first equation and frequency drops out entirely, leaving E = hc ⁄ λ — energy computed straight from wavelength, with nothing else measured. Because h (6.62607015×10⁻³⁴ J·s) and c (299792458 m/s) are both fixed by the 2019 SI redefinition rather than measured, their product hc is itself a fixed number, 1.986445857×10⁻²⁵ J·m, and every result on this page is just that one constant divided by whatever wavelength gets entered.
The inverse relationship is the part people misjudge. A longer wavelength sounds like it should carry more of everything, but longer waves oscillate more slowly, and slower oscillation means less energy per quantum — a radio photon a metre long carries only about a millionth of an electronvolt, while an X-ray photon a few nanometres long carries roughly a thousand electronvolts, a difference of nine orders of magnitude packed into a wavelength difference of the same nine orders of magnitude. Visible light sits in a narrow band in between, roughly 380 to 700 nanometres, corresponding to photon energies from about 1.77 eV at the red end to 3.26 eV at the violet end — a range fixed by what a human retina evolved to detect, not by anything special about those wavelengths physically.
The formula wants λ measured in vacuum, or air close enough to vacuum for most purposes, because c is specifically the speed of light in vacuum. Light slows down inside glass, water, or any transparent medium, and its wavelength shortens by the same factor its speed drops by — yet its frequency, and therefore its energy, does not change at all, since frequency is set by the source, not by whatever material the light happens to be crossing. A spectroscopist reading a line off a published emission-line table, or a chemist checking a laser's spec sheet, is already working with the vacuum figure; feeding a shorter in-medium wavelength into this formula instead would quietly overstate the photon's true energy.
- Enter Wavelength in nanometers — switch the unit menu to micrometers for infrared sources beyond about 1000 nm.
- Use the vacuum wavelength, not the shorter value light takes on inside glass, water, or any other transparent medium.
- Read Photon energy in joules; because a single photon carries so little energy, the figure appears in scientific notation.
- To compare against electronvolt figures common in spectroscopy tables, divide the joule reading by 1.602176634×10⁻¹⁹ J per eV.
Worked example — a 500 nm green photon
Green light sits near the peak of human eye sensitivity, and 500 nanometers is the reference wavelength most often used to represent it in optics textbooks and camera sensor datasheets. Enter 500 into Wavelength — internally the field stores it as 5×10⁻⁷ m — and the instrument first multiplies the two exact SI constants: hc = 6.62607015×10⁻³⁴ J·s × 299792458 m/s = 1.986445857×10⁻²⁵ J·m.
Dividing that constant by the wavelength gives Photon energy = 1.986445857×10⁻²⁵ ⁄ 5×10⁻⁷ = 3.9728917143×10⁻¹⁹ J. Converted by hand — dividing by 1.602176634×10⁻¹⁹ J per electronvolt — that comes to about 2.48 eV, squarely inside the 1.77-to-3.26 eV band that spans the whole visible spectrum, and the exact figure this formula returns for any 500 nm source, from a laser pointer to a green traffic-light LED.
The relationship scales predictably in both directions. Halve the wavelength to 250 nm — deep ultraviolet, short enough to break chemical bonds and cause sunburn — and the energy exactly doubles to 7.9457834286×10⁻¹⁹ J. Double the original wavelength instead, to 1000 nm in the near-infrared, and the energy exactly halves to 1.98644585715×10⁻¹⁹ J — a clean check that the reading behaves exactly as the inverse proportionality demands.
Questions
Why does photon energy divide by wavelength instead of multiplying?
Because energy comes from frequency (E = hf), and frequency is inversely tied to wavelength through c = fλ — substituting f = c ⁄ λ turns the relation into E = hc ⁄ λ. A longer wavelength means a lower frequency, and a lower frequency always means less energy per photon; the division is where that inverse relationship shows up in the arithmetic.
Does the wavelength have to be measured in vacuum?
Yes, or air, which is close enough for almost every practical case. Light's frequency stays fixed as it crosses into glass or water, but its wavelength shortens because the light slows down — so plugging in a medium's shorter wavelength would overstate the true photon energy. Published spectral-line and laser wavelengths are essentially always vacuum figures already.
How do I get the answer in electronvolts instead of joules?
Divide the joule reading by 1.602176634×10⁻¹⁹, the exact CODATA value of one electronvolt. The 500 nm example on this page, 3.9728917143×10⁻¹⁹ J, works out to about 2.48 eV — the scale spectroscopists and semiconductor engineers reach for so a single-photon result doesn't need a string of leading zeros to be readable.
Why is the result such a tiny number?
Because a single photon carries an almost immeasurably small amount of energy on the everyday joule scale — a 1-watt green laser still emits on the order of 10¹⁸ such photons every second. The formula reports energy per photon, not the total power of a beam, which is why the figure needs scientific notation to be readable at all.
How is this different from the photoelectric effect calculator?
This page reports the full energy a photon carries, hf. The photoelectric effect calculator takes that same hf and subtracts the toll a metal surface charges to release an electron, called the work function, leaving only the kinetic energy the ejected electron walks away with — a downstream step that only matters once the photon actually strikes something.
Does E = hc ⁄ λ apply outside the visible spectrum?
Yes, across the entire electromagnetic spectrum with no change in form. A one-metre radio wavelength works out to roughly a millionth of an electronvolt per photon, while a one-nanometre X-ray wavelength works out to roughly 1,240 eV — the same formula, the same constants, just a wavelength nine orders of magnitude shorter.