# Wavelength to Frequency & Frequency to Wavelength Calculator

A wavelength is a measurement of the distance between two equal peaks of Crest or Troughs. Here crest is high point whereas the troughs are low points in a wave. The best example of a wave is light, sound, etc. The frequency can be determined by the number of repetitions/Cycles for each unit time. In the EM spectrum, there are different types of waves with unstable frequencies as well as wavelengths. This article discusses an overview of what is Wavelength & Frequency, how they are related and its conversions from wavelength to frequency and frequency to wavelength.

**Wavelength to Frequency & Frequency to Wavelength **

The conversion of wavelength to frequency and frequency to wavelength mainly include what is wavelength, frequency, frequency to wavelength conversion and wavelength to frequency conversion with examples.

## How are Wavelength & Frequency Related?

Electromagnetic or EM waves travels with light speed, and the speed of light is 299,792,458 m/sec. The frequency & wavelength of light can be decided using the following formula.

**f = c / λ and λ = c / f**

Where ‘c’ = speed of light in m/sec,

‘λ’ = wavelength in meters

‘f’ = frequency is in cycles/sec.

The calculation of photon energy can be done using this formula:

**e = h*f**

**e = c * h/ λ**

Where ‘e’ = energy in joules

‘f’ = frequency is in cycles/sec.

‘h’ = Planck’s constant and the value of this is 6.6260695729 x 10-34 J*Secs)

‘λ’ = wavelength in meters

### Convert Frequency to Wavelength

In Northern latitudes, the night display like “Aurora Borealis” is caused due to ionizing radiation which interacts with the magnetic field of the earth as well as the higher atmosphere. The individual green color can be caused because of the interaction between radiation and oxygen. So the frequency of this is 5.38 x 1014 Hz. Calculate the wavelength of this light?

Frequency (f) is how many signals flow through a defined point for every second and wavelength is the distance between two crests or troughs in a wave.

The speed of light can be calculated by multiplying frequency and wavelength. So, if we know the value of frequency otherwise the wavelength one can calculate the remaining value.

**Speed of light = frequency x wavelength**

The frequency value of light = 5.38 x 1014 Hz.

We know the standard value of light speed = 3 x 108 m/sec

What is the wavelength (λ) of this light?

Thus,

**λ = c / f**

Substitute the above c & f values in the above equation.

λ = 3 x 10^{8} m/sec / (5.38 x 1014 Hz) = 5.576 x 10-7 m

1 nm = 10^{-9} m

λ = 557.6 nm (or) 5.576 x 10-7 m (or) 557.6 nm.

### Convert Wavelength to Frequency

In Northern latitudes, the night display like “Aurora Borealis” is caused due to ionizing radiation which interacts with the magnetic field of the earth as well as the higher atmosphere. The individual green color can be caused because of the interaction between radiation and oxygen. So the wavelength of this is 5577 Å. Calculate the frequency of this light?

We know that, Speed of light = frequency x wavelength

Thus,

**f = c/λ**

f = 3 x 10^{8} m/sec / (5577 Å x 10^{-10} m/1 Å)

ν = 3 x 10^{8} m/sec / 5.577 x 10^{-7} = 5.38 x 10^{14} Hz

The frequency of the light is f = 5.38 x 10^{14} Hz.

Thus, this is all about and overview of wavelength & frequency, how they are related and wavelength to frequency & frequency to wavelength calculations with examples. Here is a question for you, how to calculate wavelength from frequency?