Photon Energy Calculator

Use E = hf and E = hc/λ to convert between wavelength, frequency, and photon energy.

Starting values — Photon Energy Calculator

Input mode	Wavelength-driven
Wavelength (nm)	530
Frequency (THz)	565.65

Change any control above and the results recompute from these.

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All of human vision is a single octave 🖖

The wavelength axis here runs from 0.01 nm to metres — more than ten orders of magnitude — and the strip your eyes respond to is a sliver of it. In energy the whole visible range is narrower still: 400 nm reads 3.10 eV and 700 nm reads 1.77 eV, a span of just 1.75×. That is less than a doubling, which in sound would be a single octave; hearing covers about ten. Because E = hc/λ is a reciprocal, equal steps in wavelength are nowhere near equal steps in energy, which is why this chart has to use a logarithmic axis to show gamma rays and radio on one screen at all.

Why photon energy is measured in electron-volts 🖖

A single photon carries so little energy that joules give unwieldy numbers like 10⁻¹⁹ J, so physicists switch to the electron-volt (eV) — the energy one electron gains crossing a 1-volt gap. A handy shortcut hides inside E = hc/λ: with wavelength in nanometres, E(eV) ≈ 1240 / λ(nm). Plug in green light at 530 nm and you get about 2.3 eV per photon — right in the few-eV range that matches chemical-bond energies, which is exactly why our eyes evolved to see it.

One bright photon beats a billion weak ones 🖖

Einstein won his 1921 Nobel Prize not for relativity but for realising that light ejects electrons from metal only if each photon clears an energy threshold — a matter of wavelength, not brightness. A blazing red lamp will never release an electron that a faint ultraviolet glow frees instantly, because piling on more low-energy photons simply doesn't add up. It's the same reason UV light tans and damages your skin while a far more powerful radio transmitter leaves it untouched.

Problem solved in full

Energy of one photon of green light with a wavelength of 530 nm 5 steps
Green light has a wavelength of 530 nm. Find the energy of one such photon, and then find the longest wavelength that can still break an oxygen molecule in two. This is the Green light state, with c = 2.998 × 10⁸ m/s, h = 6.626 × 10⁻³⁴ J s, e = 1.602 × 10⁻¹⁹ C and N_A = 6.022 × 10²³ mol⁻¹.
1. Wavelength is what an instrument measures; frequency is what the quantum rule consumes. Every calculation of this kind therefore opens with the same conversion, and it is the one step that contains no quantum mechanics at all.
  
  $f = \frac{c}{λ} = \frac{2.9979 \times 1 0 ^{8}}{5.30 \times 1 0 ^{- 7}} = 5.656 \times 1 0^{14} Hz$
2. Planck's constant carries the entire quantum content: it turns a rate into an energy, and it is the same number for a radio wave and for a gamma ray. The answer is minute in joules because the joule was sized for kilograms and metres, not for one photon.
  
  $E = h f = (6.626 \times 1 0^{- 34}) (5.656 \times 1 0^{14}) = 3.748 \times 1 0^{- 19} J$
3. The electronvolt fixes that — one electron pushed through one volt — and on that scale the tool's whole visible band, 380 nm to 750 nm, lands between 3.26 and 1.65 eV. Since E and λ always multiply to hc, the conversion collapses to E = 1239.84/λ with λ in nanometres, which is worth memorising: any wavelength becomes an energy in one division.
  
  $E_{eV} = \frac{E}{e} = \frac{3.748 \times 1 0 ^{- 19}}{1.6022 \times 1 0 ^{- 19}} = 2.3393 eV (\frac{h c}{e} = 1239.84 eV nm; \frac{1239.84}{530} = 2.3393)$
4. Chemistry never deals in single photons, so scale up by Avogadro's number. A mole of green photons is called an einstein, and its energy is directly comparable with a bond enthalpy out of a data book — which is the only reason this row is worth printing.
  
  $E_{mol} = \frac{E N _{A}}{1000} = \frac{( 3.748 \times 1 0 ^{- 19} ) ( 6.022 \times 1 0 ^{23} )}{1000} = 225.7105 kJ mo l^{- 1}$
5. So compare it with one. Breaking O=O costs 498 kJ/mol, and because energy per mole times wavelength is the same constant for every photon, turning that cost back into a wavelength is a single division.
  
  $E_{mol} λ = 225.7105 \times 530 = 119627 kJ mo l^{- 1} nm ⟹ λ_{m a x} = \frac{119 627}{498} = 240 nm$
Answer

The tool prints 3.748 × 10⁻¹⁹ J, 2.3393 eV and 225.7105 kJ/mol for green light — less than half of what the oxygen bond costs. No visible photon does better: the red end of the band carries 160 kJ/mol and the violet end 315, both far short of 498. Splitting O₂ needs 240 nm, well inside the ultraviolet, which is why the reaction that builds the ozone layer runs 30 km up where that light still exists and never at ground level where it has all been absorbed. Even the tool's own Ultraviolet state at 250 nm falls short at 478.5 kJ/mol, about 4% under the bond — and 4% under is as useless as half. Photon energy is a threshold, not a budget: a billion green photons arriving together will not break the one bond that a single 240 nm photon breaks.

$E λ = h c = 1239.84 eV nm = 119627 kJ mo l^{- 1} nm$

References (2)

The quantisation the tool computes with: A. Einstein, "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt." Annalen der Physik 322(6), 132–148, 1905.
The values of h, c and e behind E = hc/λ and the eV conversion: E. Tiesinga, P. J. Mohr, D. B. Newell and B. N. Taylor, "CODATA recommended values of the fundamental physical constants: 2018." Reviews of Modern Physics 93(2), 025010, 2021.

By the 42Math team · Updated 2026-09-03

Reviewed against published sources. Corrections welcome. Editorial policy · Corrections

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Example problems

Red light - 650 nm carries 1.9077 eV per photon, the low-energy end of what your eyes register at all.
Green light - 530 nm and 2.3396 eV - the worked problem's case, and just under half the 5.162 eV it takes to split an oxygen molecule.
Ultraviolet - 250 nm carries 4.9600 eV, exactly 2.6 times a red photon because the ratio of energies is the ratio of wavelengths. Still 10 nm too long to break O₂, which needs 240.2 nm.
FM radio - 100 MHz gives 4.14 × 10⁻⁷ eV per photon, about 5.7 million times less than green light. No number of them adds up to a single chemical bond.