This all-in-one online Photon Energy Calculator performs calculations using a formula that relates the wavelength (or frequency) of a photon to its energy. You can enter the value of any known parameter in an input field of this calculator and find the missing parameters.
Photon Energy and Planck’s Equation
Photon energy is the energy carried by a single photon – the smallest discrete unit or quantum of electromagnetic radiation. This energy is directly related to the photon’s frequency or inversely related to its wavelength. Understanding how to calculate photon energy is essential in fields ranging from quantum mechanics and spectroscopy to photovoltaics and optical communications.
The energy of a photon is described by Planck’s equation, named after the German physicist Max Planck, who is considered one of the founders of quantum theory. The equation is:
$$E = h\cdot f$$
where:
• \(E\) is the energy of the photon (in joules),
• \(h\) is Planck’s constant (6.62607015 × 10-34 J·s),
• \(f\) is the frequency of the photon (in hertz, Hz).
This equation shows that the energy of a photon is directly proportional to its frequency. High-frequency electromagnetic waves (like gamma rays or X-rays) carry more energy per photon than lower-frequency waves (such as radio or microwaves).
Since the frequency and wavelength of a wave are related by the speed of light (\(c = λ\cdot f\)), Planck’s equation can also be written in terms of wavelength:
$$E = \frac{h\cdot c}{λ}$$
where:
• \(c\) is the speed of light in vacuum (299,792,458 m/s),
• \(λ \) is the wavelength of the photon (in meters).
This alternate form makes it easier to calculate photon energy when the wavelength, rather than frequency, is known. Our Photon Energy Calculator allows you to find the energy of a photon both by its frequency and by its wavelength.
How to Calculate the Energy of a Photon
To determine the energy of a photon, you need either its frequency or wavelength. The process involves plugging values into either form of Planck’s equation. The easiest way to make these calculations is with our calculator. However, it is necessary to understand the units of measurement used.
Wavelength is typically measured in meters (m) in the SI system. However, shorter units are more practical in optics and atomic physics. These include millimeters (mm) = 10⁻³ m, micrometers (µm) = 10⁻⁶ m, nanometers (nm) = 10⁻⁹ m, and ångströms (Å) = 10⁻¹⁰ m. For example, visible light wavelengths range from approximately 400 nm (violet) to 750 nm (red).
Frequency is measured in hertz (Hz), which represents one cycle per second (s⁻¹). In practice, frequency is often expressed in larger units such as kilohertz (kHz) = 10³ Hz, megahertz (MHz) = 10⁶ Hz, gigahertz (GHz) = 10⁹ Hz, and terahertz (THz) = 10¹² Hz, especially in radio, microwave, and communication applications. In spectroscopy or rotational systems, you might also encounter revolutions per minute (RPM), which must be converted to Hz by dividing by 60 (since 1 Hz = 60 RPM) to be used in photon energy calculations.
Energy is measured in joules (J) in the SI system, but photon energy is more commonly expressed in electronvolts (eV) in atomic, optical, and particle physics. One electronvolt is equal to 1.60218 × 10⁻¹⁹ J. For higher-energy photons, units like kiloelectronvolts (keV) = 10³ eV, megaelectronvolts (MeV) = 10⁶ eV, and gigaelectronvolts (GeV) = 10⁹ eV are frequently used. For example, ultraviolet photons have energies in the range of a few eV, while gamma-ray photons can exceed several MeV.
Careful unit conversion and consistency are crucial for accurate photon energy calculations, especially when switching between SI base units and commonly used derived units across various scientific disciplines.
Photon Energies Across the Electromagnetic Spectrum
The electromagnetic (EM) spectrum encompasses all types of electromagnetic radiation, from long-wavelength, low-energy radio waves to short-wavelength, high-energy gamma rays. The photon energy varies dramatically across this spectrum.
Related calculators
Check out our other physics calculators such as Resonant Frequency Calculator or Wavelength Calculator.