Photon Energy Calculator

Convert wavelength or frequency to photon energy in Joules (J) and electronvolts (eV). Interactive Planck‑curve graph, real‑time visualization, and detailed quantum physics insights.

 
Typical visible range: 380–750 nm
⚡ Quick examples:
Client-side only: All calculations use exact physical constants (CODATA 2018). No data stored or transmitted.

Quantum foundation: Planck‑Einstein relation

The energy of a single photon is directly proportional to its frequency and inversely proportional to its wavelength. This cornerstone of quantum mechanics is expressed as E = h·ν = h·c / λ, where h is the Planck constant, c the speed of light in vacuum, ν the frequency, and λ the wavelength.

Planck constant h
6.62607015 × 10⁻³⁴ J·s (exact)
Speed of light c
299 792 458 m/s (exact)
1 eV = 1.602176634 × 10⁻¹⁹ J

This calculator uses the internationally recognized CODATA 2018 values. Photon energy determines many physical phenomena: photoelectric effect, LED colour, absorption spectra, gamma‑ray astronomy, and photovoltaic efficiency.

Step‑by‑step derivation

Given wavelength λ in meters: E (J) = hc / λ → E (eV) = (hc) / (λ · e) ≈ 1239.84198 eV·nm / λ(nm). For frequency ν (Hz): E = h·ν.

  • Wavelength to energy: λ = 500 nm → E = 1239.84 / 500 = 2.4797 eV.
  • Frequency to energy: ν = 5×10¹⁴ Hz → E = (6.626×10⁻³⁴)(5×10¹⁴) = 3.313×10⁻¹⁹ J = 2.07 eV.

Applications across science & technology

Spectroscopy & Astrophysics

Astronomers measure redshifted photon energies to infer velocities of distant galaxies. The Lyman‑alpha line (121.6 nm) corresponds to 10.2 eV, crucial for studying the intergalactic medium.

Photovoltaics & LED design

Solar cells absorb photons with energy greater than the semiconductor bandgap (e.g., silicon ~1.12 eV ⇒ λ ≤ 1100 nm). LED emission wavelength is directly related to the bandgap energy: λ (nm) ≈ 1240 / Eg(eV).

Medical imaging & radiation safety

X‑ray photons (λ ~ 0.01–0.1 nm) carry keV to MeV energies, enabling radiography and cancer therapy. Our calculator helps estimate exposure parameters.

Frequently Asked Questions (FAQ)

Because photon energy and wavelength are inversely proportional: E ∝ 1/λ. Ultraviolet and X‑ray photons are more energetic, while radio photons have extremely low energy.

Yes. Our wavelength input defaults to nm, but you can enter values in any unit and convert manually. 1 µm = 1000 nm, 1 Å = 0.1 nm. The calculator accepts numeric values directly.

Joule is the SI unit of energy; electronvolt (eV) is the kinetic energy gained by an electron through a 1‑volt potential difference. 1 eV = 1.602×10⁻¹⁹ J. eV is more convenient for atomic and quantum scales.

Using exact defined constants (h, c, e), the computed energy is limited only by input precision and double‑precision floating point (±1e‑15 relative error).
Scientific authority & references
This tool implements the Planck‑Einstein relation following “The International System of Units (SI)” and NIST CODATA recommended values. Updated April 2026. For deeper reading: NIST Reference on Constants, Eisberg & Resnick “Quantum Physics”.
Used by students, researchers and engineers for accurate photon energy conversion. The interactive graph visualizes the ultraviolet catastrophe region and validates Einstein’s photoelectric law.