E = hν Calculator

Enter a photon's energy to get its frequency, or its frequency to get its energy.

E = hν

Schematic: more energy means more tightly packed waves, but the number of waves drawn is illustrative, not to scale. Height doesn't change, because a photon's energy depends on its frequency alone.

Region of the spectrumVisible
Wavelength550.1 nm
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Light comes in packets of energy called photons, and the energy of each one is set by a single property: its frequency. Type a value into either field above and the other updates instantly. Numbers like 5.45e14 work too.

The formula

The Planck relation, also called the Planck–Einstein relation, is:

E=hνE = h\nu

Here EE is the photon’s energy, ν\nu (the Greek letter nu) is its frequency, and hh is the Planck constant:

h=6.62607015×10−34 J⋅sh = 6.62607015 \times 10^{-34}\ \text{J·s}

To go the other way, divide by hh :

ν=Eh\nu = \frac{E}{h}

The relation is a straight proportion, so doubling the frequency doubles the energy.

Worked example

Green light has a frequency of about 5.45×10145.45 \times 10^{14} Hz, so one photon carries:

E=(6.626×10−34)(5.45×1014)E = (6.626 \times 10^{-34})(5.45 \times 10^{14}) E≈3.61×10−19 JE \approx 3.61 \times 10^{-19}\ \text{J}

Dividing by 1.602×10−191.602 \times 10^{-19} joules per electronvolt gives about 2.25 eV.

Reading the photon drawing

The moving wave packet is a schematic. Raise the frequency and its waves pack more tightly, and the marker slides right along the spectrum bar. The number of waves drawn isn’t to scale, since real frequencies span far too wide a range to draw literally. The packet’s height stays the same because a single photon’s energy depends only on its frequency. A brighter light of the same colour has more photons, not more energetic ones.

To work with wavelength as an input as well, use the Photon Energy & Wavelength Calculator.

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Changelog

  • 2026-11-02Published.