Article — Wavelength to Energy Calculator
Wavelength to energy calculator: photons made simple
Photon energy is related to wavelength through E = hc / λ, where h is Planck's constant (6.62607015 × 10⁻³⁴ J·s) and c is the speed of light (299,792,458 m/s). A 550 nm green photon carries about 2.25 eV; a 0.1 nm X-ray photon carries 12.4 keV. Shorter wavelength means more energetic photons.
The equation that links wavelength and energy is one of the foundations of quantum mechanics. Max Planck introduced quanta of energy in 1900 to explain blackbody radiation; Einstein extended the idea to light itself in 1905 to explain the photoelectric effect, earning the Nobel Prize for that work. Today, the same equation underlies fibre optics, laser physics, photovoltaics, and medical imaging.
What is photon energy?
Light comes in discrete packets called photons. Each photon carries an amount of energy that depends only on its wavelength — or equivalently, its frequency. Make the wavelength shorter and the photon becomes more energetic; stretch it out and the energy falls. A radio photon at 1 m wavelength carries about 10⁻⁶ eV; a gamma photon at 10⁻¹² m wavelength carries 1 MeV — a difference of 12 orders of magnitude.
This single relationship explains why radio waves are harmless and X-rays are not. A radio photon doesn't have enough energy to break a chemical bond; an X-ray photon can ionise an atom outright. The difference isn't intensity — it's per-photon energy.
The retinas of dark-adapted humans can detect single photons. Experiments by Hecht, Shlaer, and Pirenne in 1942 showed that 5 to 14 photons hitting the rod cells in the eye are enough to register a flash — a sensitivity at the absolute physical limit.
The wavelength to energy formula
The full set of relationships fits on a postcard:
From frequency E = h · νFrom wavelength E = h · c ÷ λWavelength from energy λ = h · c ÷ EFrequency from wavelength ν = c ÷ λPractical shortcut E[eV] = 1240 ÷ λ[nm]The CODATA-recommended constants used by the calculator above: h = 6.62607015 × 10⁻³⁴ J·s, c = 299,792,458 m/s, and 1 eV = 1.602176634 × 10⁻¹⁹ J. Those values are exact in the redefined SI system that took effect in 2019.
Wavelength and energy across the spectrum
The electromagnetic spectrum covers more than 20 orders of magnitude in wavelength. Reading from longest to shortest:
- Radio — λ > 1 mm, E < 0.001 eV. Broadcasting, radar, 5G.
- Microwave — 1 mm to 1 m, E ≈ 10⁻⁶ to 10⁻³ eV. Ovens, satellites.
- Infrared — 700 nm to 1 mm, E ≈ 10⁻³ to 1.77 eV. Heat radiation, fibre optics.
- Visible — 400 to 700 nm, E ≈ 1.8 to 3.1 eV. Vision, photography.
- Ultraviolet — 10 to 400 nm, E ≈ 3.1 to 124 eV. Sterilisation, sunburn.
- X-ray — 0.01 to 10 nm, E ≈ 124 eV to 124 keV. Medical imaging.
- Gamma — λ < 0.01 nm, E > 124 keV. Radioactive decay, cancer therapy.
The 1240 eV·nm shortcut
One useful number to memorise: hc ≈ 1240 eV·nm. That means E[eV] = 1240 / λ[nm] for any wavelength expressed in nanometres. Useful checks:
The 1240 figure is accurate to better than 0.07%. For visible light, the four key wavelengths map to: 400 nm violet → 3.10 eV, 500 nm cyan → 2.48 eV, 600 nm orange → 2.07 eV, 700 nm red → 1.77 eV.
Photon energy and the photoelectric effect
Einstein won the Nobel Prize in 1921 for explaining why light shining on a metal surface knocks out electrons only above a threshold frequency. The cleanest answer is that light comes in photons, each with E = hν, and an electron either absorbs one whole photon or none. Below the threshold energy, no number of incoming photons matters — they each lack the energy to free an electron.
The work function Φ of a metal is the minimum photon energy needed to liberate an electron. Typical values: lithium 2.3 eV, sodium 2.75 eV, zinc 3.6 eV, copper 4.5 eV. UV light easily exceeds these; visible light often does not. The kinetic energy of the ejected electron equals the photon energy minus the work function: KE = hν − Φ.
The Nobel Committee specifically cited Einstein's "discovery of the law of the photoelectric effect", not relativity. Special relativity was still controversial in 1921, while the photoelectric effect had been verified experimentally. Einstein got the prize for the work that proved light is quantised — and that quantum mechanics is real.
Wavelength-to-energy in practice
Knowing photon energy guides equipment selection across many fields.
- Solar cells — silicon absorbs photons above its 1.12 eV bandgap (λ < 1100 nm), so infrared past that wavelength is wasted.
- LEDs — emission wavelength is set by the semiconductor bandgap. Blue InGaN emits at 460 nm (2.7 eV); red GaAlAs at 660 nm (1.9 eV).
- X-ray imaging — diagnostic tubes run at 30–150 kV, producing photons up to 150 keV. Higher voltage means greater penetration.
- Fibre optics — telecom uses 1310 nm and 1550 nm windows where silica fibre is most transparent.
- UV-C disinfection — 254 nm photons (4.9 eV) damage microbial DNA enough to kill bacteria and viruses.
Common photon-energy mistakes
A brighter lamp emits more photons per second, but each photon carries the same E = hc/λ as in a dim lamp of the same wavelength. This was Einstein's key insight — and the reason the classical wave theory of light couldn't explain the photoelectric effect.
Five errors that come up regularly:
- Confusing intensity with photon energy — intensity is photon flux, not per-photon energy.
- Forgetting unit prefixes — nm versus μm differs by a factor of 1000.
- Mixing up frequency and wavelength — they're inversely related: high frequency means short wavelength.
- Using vacuum c in a medium — c drops in matter, so frequency stays constant but wavelength shortens. Photon energy E = hν is still set by the unchanged frequency.
- Forgetting to convert J to eV — most spectroscopy is reported in eV; SI prefers J. Divide J by 1.602 × 10⁻¹⁹ to get eV.
For quick sanity checks, remember 550 nm → 2.25 eV (green light), 300 nm → 4.1 eV (UV-B), 100 nm → 12.4 eV (vacuum UV, hard limit of standard optics). Anything outside that range is in the territory of specialised hardware.