Converting wavelength to photon energy
Light behaves as a stream of photons, and each photon carries an energy set by its wavelength: the shorter the wavelength, the more energetic the photon. A 400 nm violet photon carries about 3.1 eV, while a 700 nm red photon carries about 1.8 eV. This inverse relationship explains why ultraviolet light can break chemical bonds and damage skin while radio waves, with wavelengths of metres, deposit only tiny energy per photon.
Use this calculator to convert a wavelength into photon energy in joules and electronvolts, together with the frequency and the energy per mole of photons. It suits spectroscopy problems, checking whether a light source can excite a semiconductor with a given band gap, photochemistry, and photoelectric-effect homework. Choose the wavelength unit from nanometres, micrometres, ångströms, millimetres or metres.
Formula and constants
E = h × c / λ and f = c / λ
- h is the Planck constant, 6.62607015 × 10⁻³⁴ J·s.
- c is the speed of light in vacuum, 299,792,458 m/s.
- λ is the wavelength in metres; the calculator converts your chosen unit automatically.
- To express energy in electronvolts divide joules by 1.602176634 × 10⁻¹⁹. A handy shortcut is E(eV) = 1239.84 / λ(nm).
- Energy per mole of photons is E × 6.02214076 × 10²³ divided by 1000 for kJ/mol.
Worked example
For green light at 500 nm, λ = 500 × 10⁻⁹ m = 5.00 × 10⁻⁷ m. Then E = 6.62607 × 10⁻³⁴ × 299,792,458 / 5.00 × 10⁻⁷ = 3.9729 × 10⁻¹⁹ J. Dividing by 1.602177 × 10⁻¹⁹ gives 2.4797 eV, matching the shortcut 1239.84 / 500. The frequency is 299,792,458 / 5.00 × 10⁻⁷ = 5.9958 × 10¹⁴ Hz, or 599.58 THz. Multiplying the photon energy by Avogadro's number gives 239.25 kJ/mol. These are the values the calculator returns.
Common mistakes and how to interpret the result
- Selecting the wrong unit. Entering 500 with micrometres selected describes infrared light, not green, and the energy will be a thousand times smaller.
- Mixing up wavelength and wavenumber. Spectroscopists often quote cm⁻¹, which is 1 / λ in centimetres, not a wavelength.
- Forgetting the medium. The wavelength in glass or water is shorter than in vacuum. Use the vacuum wavelength here; the photon energy does not change when light enters a medium.
- Comparing per-photon and per-mole values. Joules and eV are for one photon; kJ/mol is for a mole of them, so the numbers are on a very different scale.