Photon Energy Calculator

Background.

One photon of green light carries about 3.6 × 10⁻¹⁹ joules. That is so little that a one-watt green beam has to deliver nearly 2.8 × 10¹⁸ of them every second, yet the size of that single packet decides almost everything light can do to matter. Whether a photon can knock an electron out of a metal, lift one across the band gap of a solar cell, break a chemical bond or ionise an atom depends on the energy of that one photon, not on how bright the light is.

The energy follows from the colour alone. Planck's relation E = hν ties it to frequency, and because light in a vacuum always travels at c, the same thing can be written from the wavelength as E = hc/λ. Enter either a wavelength in nanometres, metres or ångströms, or a frequency in hertz, terahertz or petahertz, and you get the photon energy in joules and in electronvolts, together with whichever of wavelength or frequency you did not supply.

All three constants involved are exact. Since the 2019 revision of the SI, the Planck constant, the speed of light and the elementary charge are fixed numbers rather than measurements, so the only uncertainty in the answer is the uncertainty in what you type.

For quick work in your head, divide 1,239.84 by the wavelength in nanometres to get electronvolts. The visible band runs from about 1.65 eV at the deep-red end (750 nm) to 3.26 eV in the violet (380 nm); infrared photons sit below that and ultraviolet ones above, which is the whole story of why one warms your skin and the other burns it.

What is photon energy calculator?

Photon energy is the energy of a single quantum of electromagnetic radiation. Light of a given frequency is absorbed and emitted only in whole packets of size hν, so a beam's total energy is the energy per photon times the number of photons. Physicists and chemists usually quote it in electronvolts: one electronvolt is the energy an electron gains when it moves through a potential difference of one volt, exactly 1.602176634 × 10⁻¹⁹ joules. On that scale the spectrum spreads across many powers of ten. An FM radio photon at 100 MHz, with a wavelength of about 3 m, carries 4.136 × 10⁻⁷ eV. The 1,550 nm infrared used in fibre-optic links carries 0.80 eV, visible light between 1.65 and 3.26 eV, the 254 nm ultraviolet of a germicidal lamp 4.88 eV, and X-rays thousands of electronvolts.

How to use this calculator.

1. 01To start from a wavelength, type it in the Wavelength box and pick nanometres, metres or ångströms; leave Frequency at 0 or blank. Infrared figures in micrometres convert to nanometres by multiplying by 1,000, so 10.6 µm becomes 10,600 nm.
2. 02To start from a frequency, enter it in Hz, THz or PHz. There is no GHz or MHz option: a 2.45 GHz microwave is 2,450,000,000 Hz or 0.00245 THz. Any frequency above zero takes priority, and the wavelength box is then ignored.
3. 03If you have a spectroscopic wavenumber in cm⁻¹, convert it first: wavelength in nanometres = 10,000,000 ÷ wavenumber.
4. 04Enter the vacuum wavelength. A wavelength measured inside glass or water must be multiplied by the refractive index before you use it.
5. 05Read the energy in joules (very small values appear as m × 10ⁿ) and in electronvolts, along with the frequency in hertz and the wavelength in metres. The electronvolt figure is the one to set against a band gap, a work function or an ionisation energy, since tables quote those in eV.

The formula.

Planck's relation is E = hν: the energy of one photon equals the Planck constant h times the frequency ν. In a vacuum, frequency and wavelength are linked by c = λν, so the same energy is E = hc/λ. The constants are h = 6.62607015 × 10⁻³⁴ J·s and c = 299,792,458 m/s, both exact, which makes hc = 1.9864 × 10⁻²⁵ joule-metres. Dividing by the elementary charge, e = 1.602176634 × 10⁻¹⁹ C (also exact), turns joules into electronvolts, and folding the units together gives the handy form E (eV) = 1,239.84 ÷ λ (nm).

When you enter a wavelength, it is converted to metres (1 nm = 10⁻⁹ m, 1 Å = 10⁻¹⁰ m), the energy is hc/λ and the frequency is c/λ. When you enter a frequency, it is converted to hertz (1 THz = 10¹² Hz, 1 PHz = 10¹⁵ Hz), the energy is hν and the wavelength is c/ν. Energy is inversely proportional to wavelength: halve the wavelength and each photon carries twice the energy.

The electronvolt form explains a classic teaching experiment that runs the equation backwards. An LED starts to glow at roughly the voltage at which one electron crossing its junction gains the energy of one emitted photon, so the charge times the voltage, e × V, is close to hc/λ. Plot the turn-on voltage of several LEDs against 1/λ and the points fall near a straight line whose slope is hc/e, about 1.2398 × 10⁻⁶ volt-metres; with c and e known, the slope gives an estimate of h.

The relation itself holds for every photon from radio to gamma rays. What it assumes is the input: λ must be the wavelength the light would have in a vacuum, because c is the vacuum speed. Frequency does not change when light enters glass or water, but wavelength shrinks by the refractive index, so an in-medium wavelength gives an energy that is too high by that factor. The result describes one photon of one wavelength; to get the energy per mole multiply by Avogadro's number, and to get photons per second divide a beam's power by it. A photon also carries momentum, p = E/c = h/λ — about 1.2047 × 10⁻²⁷ kg·m/s at 550 nm — which is the source of the radiation pressure that pushes a solar sail.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Planck, M. (1900). "Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum." Verhandlungen der Deutschen Physikalischen Gesellschaft 2:237–245.
2. [2]BIPM (2019). The International System of Units (SI Brochure), 9th ed.
3. [3]CODATA (2018). "Recommended Values of the Fundamental Physical Constants." Rev. Mod. Phys. 93(2):025010.
4. [4]Einstein, A. (1905). "Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt." Annalen der Physik 322(6):132–148. doi:10.1002/andp.19053220607
5. [5]Eisberg, R. and Resnick, R. (1985). Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles, 2nd ed. John Wiley & Sons. ISBN 978-0-471-87373-0