Photon Energy and Frequency Calculator
Calculates photon energy from either its wavelength or frequency using Planck's relation. Ideal for optics, spectroscopy, and quantum physics problems involving electromagnetic radiation.
About this calculator
A photon's energy is governed by Planck's relation E = h · f, where h = 6.626 × 10⁻³⁴ J·s is Planck's constant and f is the photon's frequency in Hz. Because frequency and wavelength are related by c = f · λ (where c ≈ 3 × 10⁸ m/s is the speed of light), you can also write E = (h · c) / λ. When given a wavelength, the calculator uses E = (6.626 × 10⁻³⁴ × 3 × 10⁸) / λ; when given a frequency it uses E = 6.626 × 10⁻³⁴ × f. Energies are often converted to electron-volts (1 eV = 1.602 × 10⁻¹⁹ J) for atomic-scale work. This relationship explains why ultraviolet photons carry enough energy to break chemical bonds while radio waves do not.
How to use
Example using wavelength: visible green light at λ = 550 nm = 5.50 × 10⁻⁷ m. Step 1: Select 'wavelength' as input type and enter 5.50 × 10⁻⁷ m. Step 2: E = (6.626 × 10⁻³⁴ × 3 × 10⁸) / 5.50 × 10⁻⁷ = 1.988 × 10⁻²⁵ / 5.50 × 10⁻⁷ ≈ 3.61 × 10⁻¹⁹ J. Step 3: Convert to eV: 3.61 × 10⁻¹⁹ / 1.602 × 10⁻¹⁹ ≈ 2.25 eV. This is consistent with the known ~2.25 eV energy of green photons, which sits comfortably within the visible band.
Frequently asked questions
What is the relationship between photon energy and wavelength?
Photon energy and wavelength are inversely proportional: E = hc / λ. Shorter wavelengths (like X-rays or ultraviolet) correspond to higher-energy photons, while longer wavelengths (like infrared or radio waves) mean lower energy per photon. This inverse relationship is why UV radiation causes sunburn but visible light does not — UV photons carry enough energy (~3–10 eV) to ionize biological molecules, whereas visible photons (~1.8–3.1 eV) generally do not. The product hc ≈ 1240 eV·nm is a convenient shorthand for quick calculations.
How do I convert photon energy from joules to electron-volts?
Divide the energy in joules by the elementary charge e = 1.602 × 10⁻¹⁹ C, since 1 eV is defined as the energy gained by one electron accelerating through a 1 V potential. For example, 3.61 × 10⁻¹⁹ J ÷ 1.602 × 10⁻¹⁹ J/eV ≈ 2.25 eV. Electron-volts are the preferred unit in atomic and solid-state physics because atomic energy levels and band gaps are typically in the range of 1–10 eV. Joules are more convenient in classical optics or when combining with macroscopic quantities.
Why does the speed of light change in a medium and how does that affect photon energy?
In a medium with refractive index n, light travels at v = c / n, and the wavelength shortens to λ_medium = λ_vacuum / n, but the frequency — and therefore the photon energy E = hf — stays constant. Energy is carried by the photon regardless of the medium it traverses; only the spatial oscillation pattern (wavelength) compresses. This is why a photon's color (determined by its energy and frequency) does not change when light enters glass, even though the wavelength does. For energy calculations it is safest to use vacuum wavelength or frequency directly.