# Energy to Wavelength Calculator

Created by Jack Bowater
Reviewed by Gabriela Diaz
Last updated: Jun 09, 2023

Many, many problems in physics and chemistry require you to use an energy-to-wavelength calculator. Do you have an energy transition between two states and wonder what wavelength of light this corresponds to? Have you the energy of two waves that have undergone a constructive or destructive interaction and want to find the new wavelength? If so, you've found the right place in Omni's energy-to-wavelength calculator, which will help you learn how to calculate wavelength from energy for a photon or wave!

## The energy to wavelength formula

The energy to wavelength formula relies upon two other equations: the wave speed equation and the Planck–Einstein relation. The wave speed equation looks like this:

$v = f \times \lambda$

, where:

• $v$ - Wave speed, in m/s;
• $f$ - Frequency of the wave, in s; and
• $\lambda$ - Wavelength, in m.

In most cases, we are looking at how a wave travels through a vacuum. In this case, $v$ is actually equal to the speed of light, 299,792,458 meters per second, which we denote as $c$.

The next equation we need to consider is the Planck-Einstein relation:

$E = h \times f$

, where:

• $E$ - Photon energy, in J;
• $h$ - Planck's constant, equal to 6.62607015×10−34 J Hz−1; and
• $f$ - Frequency of the wave, in s.

Manipulation of the formulas is then required. First, replace $v$ with $c$. Then rearrange the wave speed equation so that frequency is in terms of wavelength. We then substitute this formula into the Planck-Einstein equation. Finally, we must rearrange this substituted formula to get the wavelength in terms of energy:

$\lambda = \frac{h \times c}{E}$

## How do I calculate wavelength from energy?

To calculate wavelength from the energy of a photon:

1. Convert the photon's energy into joules.
2. Divide the speed of light, equal to 299,792,458 meters per second, by the photon's energy.
3. Multiply the resulting number by Planck's constant, which is 6.626×10−34 J/Hz.
4. Congratulations, you have just found your photon's wavelength in meters.

## Our other photon energy and wavelength calculators

We hope this tool provides you with everything you need to solve your problem. However, if for some reason it does not, please check out our other relevant tools:

## FAQ

### How do I calculate energy from wavelength?

To calculate photon energy from wavelength:

1. Make sure your wavelength is in meters.
2. Divide the speed of light, approximately 300,000,000 m/s, by the wavelength to get the wave's frequency.
3. Multiply the frequency by Planck's constant, 6.626×10−34 J/Hz.
4. The resulting number is the energy of a photon!

### What happens to energy when the wavelength is shortened?

When the wavelength is shortened, the photon's energy increases. This is because photon energy is proportional to a constant over the wavelength. Therefore, as the wavelength gets smaller, the constant is divided up by less, and so photon energy increases.

### When wavelength increases, what happens to the energy?

As the wavelength increases, the energy of the photon decreases. This can be seen if you examine the relationship between the two values - energy is inversely proportional to wavelength. When you increase wavelength, then, the constant is divided by more, and so the energy decreases.

Jack Bowater
Energy
μeV
Wavelength
mm
Frequency
GHz
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