Photon Energy-Wavelength Calculator

Calculate photon energy from wavelength or wavelength from energy using E = hc/λ. Also shows frequency and wavenumber.

Spectroscopy

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Spectral presets

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How to Use

  1. 1
    Choose wavelength or energy as input

    Select whether to start from wavelength (in nm, µm, or m) or from photon energy (in eV, J, or kJ/mol).

  2. 2
    Enter the known value

    Input the wavelength or energy. Common reference points: visible light spans roughly 400 nm (violet) to 700 nm (red); UV-Vis spectroscopy uses 200-800 nm.

  3. 3
    Read all calculated quantities

    The tool returns the complementary property plus frequency (ν = c/λ), wavenumber (ᵜ̃ = 1/λ), and the spectral region classification (microwave, infrared, visible, UV, X-ray).

About

Photon energy and wavelength are the two most fundamental descriptors of electromagnetic radiation in spectroscopy and photochemistry. Their relationship E = hc/λ — where h is Planck's constant and c is the speed of light — encapsulates one of the pivotal discoveries of 20th-century physics: that light is quantized into discrete packets called photons, each carrying an energy inversely proportional to its wavelength.

This relationship is the foundation of all spectroscopic techniques. In UV-Vis spectroscopy, photons with energies matching electronic transition gaps are absorbed, producing the characteristic absorption spectra used to identify chromophores and measure concentrations. In infrared spectroscopy, photons with energies matching molecular vibrational frequencies are absorbed, giving the fingerprint spectra that identify functional groups. In photochemistry, the energy of individual photons determines which chemical bonds can be broken or formed — ultraviolet photons carry enough energy to break C-C bonds and initiate photochemical reactions, while visible photons drive photosynthesis.

This calculator converts seamlessly between wavelength, frequency, wavenumber, energy per photon (in J and eV), and molar energy (kJ/mol), covering the entire electromagnetic spectrum from radio waves to gamma rays. It also identifies the spectral region, making it useful for spectroscopy courses, photochemistry research, and optics engineering.

FAQ

What equation relates photon energy and wavelength?
Photon energy is given by E = hν = hc/λ, where h = 6.626×10⁻³⁴ J·s is Planck's constant, ν is frequency (Hz), c = 2.998×10⁸ m/s is the speed of light, and λ is wavelength (m). Because frequency and wavelength are inversely related through c = λν, shorter wavelength means higher frequency and higher energy. This equation, proposed by Max Planck in 1900 and confirmed by Einstein's explanation of the photoelectric effect, established the quantum nature of light.
What is the photoelectric effect and how is photon energy relevant?
The photoelectric effect is the emission of electrons from a metal surface when illuminated by light of sufficient frequency. Einstein showed in 1905 that light consists of discrete photons, each carrying energy E = hν. Electrons are ejected only when the photon energy exceeds the metal's work function (binding energy), regardless of light intensity. Doubling intensity doubles the number of photons but not their individual energy. This observation was inexplicable by classical wave theory and provided the first direct evidence for light quanta, earning Einstein the 1921 Nobel Prize.
What is wavenumber and how does it relate to energy?
Wavenumber (ᵜ̃, often written ν-bar) is the number of wavelengths per centimeter: ᵜ̃ = 1/λ(cm). It is proportional to energy: E = hcᵜ̃. Wavenumber in cm⁻¹ is the standard unit in infrared and Raman spectroscopy, where absorption peaks are reported as, for example, 1715 cm⁻¹ for a C=O carbonyl stretch. The range of infrared spectroscopy spans approximately 400-4000 cm⁻¹ (2500-25000 nm wavelength).
How many joules is one electron-volt?
One electron-volt (eV) is the kinetic energy gained by a single electron accelerating through a potential difference of one volt: 1 eV = 1.602×10⁻¹⁹ J. In spectroscopy, eV is convenient for X-ray and UV photons: visible light photons range from about 1.8 eV (red) to 3.1 eV (violet), X-ray photons range from 100 eV to 100 keV. In chemistry, energies are often reported as kJ/mol to connect to thermodynamic quantities; 1 eV/photon = 96.485 kJ/mol.
What spectral regions are chemically significant?
UV-Vis spectroscopy (200-800 nm, 1.5-6.2 eV) probes π→π* and n→π* electronic transitions in organic chromophores and d-d transitions in transition metal complexes. Infrared spectroscopy (2.5-25 µm, 400-4000 cm⁻¹) probes molecular vibrations used for functional group identification. NMR spectroscopy uses radio waves (∼100-1000 MHz) to probe nuclear spin transitions. X-ray spectroscopy (0.01-10 nm) ionizes core electrons and is used for elemental analysis (XRF) and crystallography.
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