Decibels (dB)

The decibel is a logarithmic ratio commonly used to express amplitudes, voltages, sound pressure, gain and attenuation and no doubt other things as well. The word literally means one tenth of a Bel. The Bel is named for Alexander Graham Bell, inventor of the telephone (or one of the inventors anyway). Why they called it a “Bel” instead of a “Bell” is a question that someone else would have to answer, but that probably explains why the abbreviation for decibels is written as dB (with a capital B). Although no one seems to use Bels for much of anything – most people would just say 10 dB instead – the formulas for converting to and from decibels may seem less arbitrary if you consider that one Bel represents the logarithm of a power ratio of 10:1 and a decibel is 1/10th of that. 

With that thought in mind:

Because decibels express a ratio, decibel values must be referenced to something. If no reference is explicitly given, as in the equations on the previous page, the reference is assumed to be one, however, it could potentially be any number. To reference dB to a number other than one, you simply divide the value that you want to convert to dB by the reference value before taking the log.

In that case: