Notes / Frequency Units


The basic frequency unit is 1 Hertz (Hz). If the frequency of some event is n Hz, it means that the event occurs n times per second (see Time Units). Thus, $1~\textrm{Hz} = 1 / \textrm{second} = 1~\textrm{second}^{-1}$. Each frequency value corresponds to a time period. For example, 20 Hz corresponds to 50 ms because

$$ 20~\textrm{Hz}= \frac{20}{1~\textrm{s}}= \frac{20}{1000~\textrm{ms}}= \frac{1}{50~\textrm{ms}}. $$

Some additional useful frequency units (with corresponding time periods) are presented in the below table:

UnitSymbolValue in HzTime period
TerahertzTHz$10^{12}$1ps
GigahertzGHz$10^{9}$1ns
MegahertzMHz$10^{6}$1us
KilohertzkHz$10^{3}$1ms
HertzHz11s
MillihertzmHz$10^{-3}$$10^{3}$s
MicrohertzuHz ($\mu$Hz)$10^{-6}$$10^{6}$s
NanohertznHz$10^{-9}$$10^{9}$s

The common symbol for frequency is f. If we want to calculate the frequency of an event, we should divide the number of events by a time interval that contains all these events. For example, if something happens 42 times per day, it means that the frequency of the event is:

$$ f=\frac{42}{1d}=\frac{42}{86400s}\approx 0.000486s^{-1}=486\mu \textrm{Hz} $$

The frequency term is widely used in many physics and engineering disciplines. Here are some famous examples:

If we are talking about waves and we want to draw these waves on a plot, the frequency can be easily compared by a glance. Let us consider the following figure:


In this figure, we can observe three waves with different frequencies:


References (1)