# 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 $f$:

$\footnotesize E = h \cdot f$

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

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

Where:

• $E$ - Photon energy;
• $h$ - Planck's constant, 6.6261 x 10-34 J⋅s or 4.1357 x 10-15 eV⋅s;
• $c$ - Speed of light, 299792458 m/s;
• $\lambda$ - Wavelength; and
• $f$ - Photon frequency.

Notice that if a photon's frequency $f$ or wavelength $\lambda$ are known, you can directly determine its energy $E$, 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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