# Frequency to Wavelength Calculator

Frequency (f):

Wavelength (λ):

## Wavelength Formula

Given frequency, f, and velocity, c, (speed of light = 299,792,458 m/s), determine the wavelength, λ, of the signal.  ## Why Convert Frequency to Wavelength?

Depending on your application, it may make more sense to speak about electromagnetic waves in terms of frequency or wavelength. And sometimes knowing both is useful. For example, when designing an antenna element for a given frequency, the wavelength plays a critical role in determining the physical size of the element. The calculator provided here is helpful if you need to know how to find the wavelength for a given frequency. Wavelength is typically denoted by the lowercase Greek letter lambda, λ, while the lowercase English letter f is used for frequency.

## Frequency Basics

Frequency refers to how often the signal, or waveform, is repeated during a period of time. The basic unit for specifying frequency is a cycle per second (1/s), which has been given the name of hertz (abbreviated Hz). This is so named in honor of Heinrich Hertz, who is credited with proving the existence of electromagnetic waves. Given that a Hz is a single cycle per second, a 1 Hz signal repeats once every second, and a 3 MHz signal repeats 3 million times per second.

## Wavelength Basics

When a signal is traveling through a medium, the physical distance that the waveform travels in one cycle is known as the wavelength. Wavelength is a function of the speed at which the waveform is traveling and the frequency of the waveform. The properties of the medium affect the velocity of the waveform. For example, a signal will travel faster in air than it will through ice, or dirt. In the above wavelength calculation, it is assumed that the signal is traveling in a vacuum, where the velocity is equivalent to the speed of light. This is a generally accepted assumption when estimating the waveform behavior in air, since the refractive index of air is very near to that of a vacuum. A more general version of the wavelength formula would include a refractive index term to account for the variation in the propogation properties of the medium.

## Relationship Between Frequency and Wavelength

Frequency and wavelength are inversely proportional: as frequency increases, the wavelength decreases (and vice versa). Why is that? The speed at which a signal travels is not dependent on the frequency of the signal, so the wavelength must be changing in order to fit more (or fewer, in the case of a lower frequency signal) cycles into the same distance traveled.