Photon Energy Calculator

What the photon energy calculator does

Light comes in tiny indivisible packets called photons, and each one carries a definite amount of energy set by its wavelength or frequency. This calculator converts freely between a photon's wavelength, its frequency, and its energy, so you can enter any one and get the other two.

Below is what a photon is, the equation behind it, how photon energy varies across the spectrum, and a worked example.

How to use it

1. Choose what you are entering: wavelength, frequency, or energy.
2. Enter that one value, with its unit.
3. Press Calculate for the other two, plus the energy in joules, or Reset to clear it.

What a photon is

A photon is a single particle of light, the smallest possible quantity of electromagnetic energy. For a long time light was understood purely as a wave, and in many ways it behaves like one, spreading, bending, and interfering. But at the start of the twentieth century, physicists discovered that light also comes in discrete chunks: you cannot have half a photon, only whole ones. This was one of the founding insights of quantum physics, and it earned Einstein his Nobel Prize for explaining how light knocks electrons out of metals one photon at a time.

Each photon carries a fixed amount of energy, and remarkably, that energy depends only on the photon's colour, that is, its wavelength or frequency, and nothing else. A photon of blue light always carries more energy than a photon of red light, no matter how bright or dim the source. Brightness is just the number of photons; the energy of each one is set by its place in the spectrum. This calculator computes that energy and relates it to the photon's wavelength and frequency.

The equation it uses

A photon's energy is its frequency multiplied by Planck's constant, which can also be written in terms of wavelength:

E = h f = h c ÷ λ

Here E is the energy, f is the frequency, λ is the wavelength, c is the speed of light, and h is Planck's constant, a tiny fundamental number that sets the scale of all quantum effects. The first form shows energy rising in step with frequency; the second, using the fact that frequency is the speed of light divided by wavelength, shows energy falling as wavelength grows. The calculator uses these relationships to move between energy, frequency, and wavelength in any direction.

Energy across the spectrum

Because energy rises with frequency, the different parts of the electromagnetic spectrum carry very different photon energies, and this is what makes some kinds of light harmless and others dangerous. Radio waves and infrared, at low frequencies, have feeble photons that can do little more than gently warm what they strike. Visible light photons are more energetic, enough to trigger the chemistry of vision and photosynthesis.

Climb higher in frequency and the photons become powerful enough to cause damage. Ultraviolet photons carry enough energy to break chemical bonds, which is why they cause sunburn and can harm the eyes and skin. X-rays and gamma rays, higher still, carry so much energy per photon that they tear electrons from atoms and can damage living cells, which is the basis of both their medical usefulness and their hazard. The whole difference comes down to the energy each photon delivers, and this calculator shows exactly how that energy scales with the light's wavelength or frequency.

Why energy is measured in electronvolts

The energy of a single photon is an extraordinarily small number in everyday units. A visible photon carries only a few ten-thousand-billion-billionths of a joule, an awkward quantity to write or compare. So physicists working at this scale use a more convenient unit, the electronvolt, which is the energy an electron gains moving through one volt. In these units, a visible photon carries a few electronvolts, a tidy, human-sized number.

The electronvolt is natural here because it matches the scale of atomic and quantum processes. The energy needed to free an electron from an atom, or to bridge the gap in a solar cell or an LED, is a few electronvolts, the same range as visible photon energies, which is no coincidence, since it is photons in this range that drive those processes. The calculator reports the energy in electronvolts and their multiples, alongside the value in joules, so you can work in whichever suits the problem.

Units and precision

The calculator takes wavelength in units from ångströms to metres, frequency from hertz to terahertz, and energy in electronvolts and their multiples, and it reports the results in those units plus the energy in joules. It uses the exact modern value of Planck's constant and the speed of light, so the conversions are accurate across the whole spectrum. Results carry several significant figures.

A worked example

Take a photon of green light with a wavelength of 550 nanometres.

Its energy is E = h c ÷ λ = (6.626 × 10⁻³⁴ × 299,792,458) ÷ (550 × 10⁻⁹) ≈ 3.6 × 10⁻¹⁹ joules, which is about 2.25 electronvolts, at a frequency of around 545 terahertz. For contrast, an ultraviolet photon at 200 nanometres carries about 6.2 electronvolts, enough to break chemical bonds, while a low-energy infrared photon carries only a fraction of an electronvolt. The shorter the wavelength, the more energetic the photon.

Questions people ask

How do you calculate the energy of a photon?

Multiply its frequency by Planck's constant, E = hf, or equivalently divide Planck's constant times the speed of light by the wavelength, E = hc/λ.

Does a photon's energy depend on brightness?

No. The energy of each photon depends only on its wavelength or frequency. Brightness is the number of photons; a blue photon always carries more energy than a red one, however dim the light.

Why is ultraviolet light harmful but infrared is not?

Because ultraviolet photons carry enough energy to break chemical bonds, while infrared photons carry far less and can only gently warm what they strike. The damage depends on the energy per photon.

What is an electronvolt?

The energy an electron gains moving through one volt, a small unit suited to atomic and quantum scales. Visible photons carry a few electronvolts each, matching the energies of atomic processes.

References

A quick note on where the physics comes from. Photon energy and Planck's relation are standard quantum physics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The value of Planck's constant follows the US National Institute of Standards and Technology. The HyperPhysics link is worth a quick click to confirm it lands where you expect.

1. OpenStax, University Physics Volume 3, Section 6.2, Photoelectric Effect. https://openstax.org/books/university-physics-volume-3/pages/6-2-photoelectric-effect
2. HyperPhysics, Photon Energy. http://hyperphysics.phy-astr.gsu.edu/hbase/mod2.html
3. National Institute of Standards and Technology (NIST), Fundamental Physical Constants, Planck constant. https://physics.nist.gov/cgi-bin/cuu/Value?h