Convert between photon energy and wavelength using E = hc/λ. Supports eV, joules, frequency, and nm inputs. Includes EM spectrum reference and common photon energies.
The energy of a photon is directly related to its wavelength through the Planck-Einstein relation E = hc/λ, where h is Planck's constant (6.626 × 10⁻³⁴ J·s), c is the speed of light, and λ is the wavelength. Higher energy photons have shorter wavelengths — gamma rays carry millions of electron volts in wavelengths smaller than atoms, while radio waves carry billionths of an eV in wavelengths measured in meters.
This relationship is foundational to spectroscopy, quantum mechanics, photochemistry, and radiation physics. It explains why UV light causes sunburn (enough energy to break molecular bonds) while radio waves pass harmlessly through your body (too little energy to affect molecules).
This calculator bidirectionally converts between wavelength, frequency, energy in electron volts, and energy in joules. It identifies the electromagnetic spectrum region and provides comprehensive reference tables for common photon sources across the entire electromagnetic spectrum. Check the example with realistic values before reporting.
Converting between wavelength, frequency, and energy involves Planck's constant and the speed of light — tiny and huge numbers that are tedious to handle by hand. Scientists frequently need to switch between nm (optics), eV (atomic physics), cm⁻¹ (spectroscopy), and Hz (radio engineering). This calculator handles all four unit systems and gives immediate spectrum context.
Photon Energy: E = hf = hc/λ Frequency: f = c/λ = E/h Wavelength: λ = hc/E = c/f Wave Number: k = 1/λ (in cm⁻¹) Constants: h = 6.626 × 10⁻³⁴ J·s c = 2.998 × 10⁸ m/s 1 eV = 1.602 × 10⁻¹⁹ J hc = 1240 eV·nm (useful shortcut)
Result: 2.254 eV
Green light at 550 nm: E = hc/λ = (6.626×10⁻³⁴ × 2.998×10⁸)/(550×10⁻⁹) = 3.61×10⁻¹⁹ J = 2.254 eV. The frequency is f = c/λ = 5.45×10¹⁴ Hz.
When Max Planck proposed in 1900 that electromagnetic energy is exchanged in discrete quanta of E = hf, he launched the quantum revolution. Einstein extended this in 1905 to argue that light itself consists of particles (photons) each carrying energy E = hf. This dual wave-particle nature of light resolved paradoxes like the photoelectric effect and ultraviolet catastrophe.
The relation E = hc/λ is simply E = hf combined with c = fλ. It means every photon has a definite energy determined by its wavelength (or equivalently, frequency). This discreteness is what makes quantum mechanics fundamentally different from classical physics.
The energy-wavelength relationship is the foundation of spectroscopy — the study of how matter absorbs, emits, and scatters light. Each chemical element and molecule has a unique set of energy levels, producing characteristic spectral lines. By measuring which wavelengths are absorbed or emitted, scientists can identify substances, determine chemical compositions, and probe molecular structures.
Infrared spectroscopy uses wave numbers (cm⁻¹) as the standard unit because the positions of molecular vibration absorption bands fall at convenient numbers: C-H stretches near 3000 cm⁻¹, C=O stretches near 1700 cm⁻¹, and so on.
The electromagnetic spectrum spans over 20 orders of magnitude in wavelength and energy. Radio waves (wavelengths of meters to kilometers, energies of nano-eV) carry broadcast signals. Microwaves (mm to cm, μeV to meV) heat food and enable wireless communication. Infrared (μm, tenths of eV) is felt as radiant heat. Visible light (400-700 nm, 1.8-3.1 eV) is the narrow window our eyes evolved to detect. Ultraviolet (nm, eV) causes sunburn. X-rays (pm to nm, keV) penetrate tissue for medical imaging. Gamma rays (sub-pm, MeV to GeV) are emitted by nuclear reactions and cosmic events.
Because E = hc/λ — energy and wavelength are inversely proportional. A photon with twice the energy has half the wavelength. This is why gamma rays (high energy) have tiny wavelengths and radio waves (low energy) have long wavelengths.
One electron volt (1 eV) is the energy gained by an electron accelerated through 1 volt, equal to 1.602 × 10⁻¹⁹ joules. It is the standard energy unit in atomic, molecular, and particle physics.
Since hc = 6.626×10⁻³⁴ × 2.998×10⁸ = 1.989×10⁻²⁵ J·m = 1240 eV·nm, you can use E(eV) = 1240/λ(nm) for quick mental calculations.
Wave number (cm⁻¹) is the reciprocal of wavelength in centimeters: k = 1/λ. It is commonly used in infrared spectroscopy and physical chemistry. Higher wave number means higher energy.
Only photons with energy above the ionization threshold (typically 5-25 eV for most atoms, corresponding to UV and shorter wavelengths) can ionize. This is why UV, X-rays, and gamma rays are "ionizing radiation" while visible light and below are not.
Einstein explained the photoelectric effect using E = hf: each photon carries discrete energy. If hf exceeds the work function of a metal, the photon can eject an electron. This was key evidence for the quantum nature of light.