Wavelength to Energy Calculator

Created by Gabriela Diaz
Reviewed by Anna Szczepanek, PhD
Last updated: May 17, 2022

This is Omni's wavelength to energy calculator, a tool that instantly calculates a photon's energy from its wavelength. By using Planck's equation, this tool will help you determine a photon's energy in joules (J), electronvolts (eV), or its multiples.

In this article, you'll also find the Planck equation, a step-by-step guide on how to calculate the energy from the wavelength of a photon and how to get this result in joules or electronvolts.

The wavelength to energy formula - Planck's equation

Planck's equation, also known as Planck's relation, is an expression that allows you to define a photon's energy E in terms of its wave properties. Planck's relation states that the energy is directly proportional to its frequency ff:

E=hf\footnotesize E = h \cdot f

Or inversely proportional to wavelength λ\lambda, by recalling the relationship between frequency and wavelength, f=c/λf = c / \lambda:

E=hcλ\footnotesize E = \dfrac {h \cdot c}{\lambda}

Where:

  • EE - Photon energy;
  • hh - Planck's constant, 6.6261 x 10-34 J⋅s or 4.1357 x 10-15 eV⋅s;
  • cc - Speed of light, 299792458 m/s;
  • λ\lambda - Wavelength; and
  • ff - Photon frequency.

Notice that if a photon's frequency ff or wavelength λ\lambda are known, you can directly determine its energy EE, since the other elements in the equation are constants.

🙋 The energy of a photon is commonly expressed using the unit electronvolt (eV), but it can also be expressed in other energy units, such as joules (J).

How do I calculate energy from wavelength?

To calculate a photon's energy from its wavelength:

  1. Multiply Planck's constant, 6.6261 × 10⁻³⁴ J⋅s by the speed of light, 299792458 m/s.
  2. Divide this resulting number by your wavelength in meters.
  3. The result is the photon's energy in joules.

More wavelength and energy calculators!

If you enjoyed using this tool and you'd like to get more information about a photon's energy and its wavelength, we invite you to visit more of our related tools:

FAQ

How do I find the energy in joules given the wavelength?

To find the energy in joules given the wavelength of a photon:

  1. Use Planck's equation E = h x c / λ and substitute the values of the wavelength (λ), Planck's constant in joules (h = 6.6261 × 10⁻³⁴ J⋅s), and speed of light (c = 299792458 m/s).
  2. With these units, you'll get an energy result in joules (J).
  3. That's it!

How do I convert wavelength to energy in eV?

In order to convert a wavelength to energy in electronvolts (eV):

  1. Utilize Planck's energy equation E = h × c / λ.
  2. Substitute the values of the wavelength (λ), Planck's constant (h = 6.6261 × 10⁻³⁴ J⋅s), and speed of light (c = 299792458 m/s).
  3. You'll get a result in joules (J).
  4. To go from joules (J) to electronvolts (eV), use the conversion factor 1eV = 1.602176565 × 10⁻¹⁹ J.
  5. Finally, to express your result in electrovolts, divide the energy in joules by the conversion factor: E [J] / 1.602176565e⁻¹⁹ J/eV = E [eV].

How do I calculate the energy of a photon of wavelength 3.5 μm?

To calculate the energy of a photon of wavelength 3.5 μm:

  1. Employ Planck's energy equation, E = h × c / λ.
  2. Use the values of the wavelength λ = 3.5 μm, Planck's constant h = 6.6261 × 10⁻³⁴ J⋅s and speed of light c = 299792458 m/s.
  3. Substitute into Planck's equation, E = 3.5 μm × (6.6261 × 10⁻³⁴ J⋅s) × (299792458 m/s).
  4. After performing the required operations, you'll get that the energy value is E = 354.242 meV.

What is the energy of a 100 nm photon?

The energy of a 100 nm photon is 12.39847 eV or 1.99 × 10⁻¹⁸ J. To get this result:

  1. Employ Planck's equation, E = h × c / λ:
  2. Where λ = 3.5 μm is the wavelength, h = 6.6261 × 10⁻³⁴ J⋅s Planck's constant and c = 299792458 m/s the speed of light.
  3. Replace, E = 3.5 μm × (6.6261 × 10⁻³⁴ J⋅s) × (299792458 m/s) = 12.39847 eV.
  4. To express the result in joules, apply the conversion factor 1eV = 1.602176565 × 10⁻¹⁹ J, E = 12.39847 eV x (1.602176565 x 10⁻¹⁹ J/eV) = 1.99 × 10⁻¹⁸ J.
Gabriela Diaz
Wavelength
mm
Energy
meV
Frequency
GHz
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