Photon Energy Calculator (E = hf)

How is photon energy calculated?

Light is carried in packets of energy called photons. The energy of one photon depends only on the frequency of the light:

E = h × f = h × c / λ

Here h is the Planck constant (6.62607015 × 10⁻³⁴ J·s), c the speed of light (299 792 458 m/s), f the frequency and λ the wavelength. The higher the frequency, in other words the shorter the wavelength, the larger the photon energy. A violet photon carries more energy than a red one.

Electronvolts and a shortcut

In joules the energy of a single photon is a very small number, so the electronvolt (eV) is used instead: 1 eV = 1.602176634 × 10⁻¹⁹ J. With the wavelength in nanometres there is a handy shortcut:

E (eV) = 1239.84 / λ (nm)

Example

For green light with a wavelength of 500 nm, E = 1239.84 / 500 = 2.48 eV, which is 3.97 × 10⁻¹⁹ J. Its frequency is 299 792 458 / (500 × 10⁻⁹) = 5.996 × 10¹⁴ Hz.

Number of photons

A source with light power P emits an energy of P × t in a time t. Dividing by the energy of one photon gives the photon count: N = P × t / E. A 5 mW red laser (632.8 nm) emits about 1.6 × 10¹⁶ photons every second.

Limits

The wavelength is the vacuum value. The photon count is for monochromatic light and is only a rough guide for broad spectrum sources such as bulbs. In the photoelectric effect an electron is released only if the photon energy exceeds the work function of the metal, a comparison you can make with the "From energy" tab.