The decibel scale: why 3 dB and 6 dB matter
How the logarithmic decibel scale works, why 3 dB doubles power and 6 dB doubles amplitude, and how to combine noise sources.
A ratio, not an absolute value
A decibel is not a fixed amount of anything; it describes a ratio between two quantities on a logarithmic scale. For power quantities the level is 10 times the base-ten logarithm of the ratio, and for amplitude quantities it is 20 times that logarithm. Because logarithms turn multiplication into addition, big spans compress into a manageable range, which is why sound, signal strength and gain are all quoted in dB. A level always implies a reference, such as the threshold of hearing for sound pressure.
Why 3 dB doubles power
Double the power and the ratio is 2, so the change is 10 times log10 of 2, which is 3.0103 dB. That is the origin of the familiar rule that a 3 dB rise means twice the power and a 3 dB drop means half. It also explains why two equal sources combine to about 3 dB above one of them: their powers add to double, and doubling is 3 dB. The tool prints 83.0103 dB for two 80 dB sources for exactly this reason.
Why 6 dB doubles amplitude
Amplitude quantities such as voltage or sound pressure use the factor 20 instead of 10, because power rises with the square of amplitude. Doubling amplitude is therefore 20 times log10 of 2, which is 6.0206 dB, and it quadruples power at the same time. This is why a 6 dB gain on a mixer doubles the signal voltage, while a 20 dB change corresponds to a tenfold amplitude ratio. Choosing Power or Amplitude in the tool selects between the 10 and 20 factors.
Combining sources correctly
To add levels you cannot sum the decibels directly. Each level is converted back to a linear power, the powers are summed, and the total is converted back with 10 times log10. When two sources are equal the total is 3 dB higher; when one is much weaker it barely registers, so a source 10 dB down adds only about 0.4 dB. This logarithmic behaviour is why silencing the quietest machine in a noisy room changes almost nothing, while removing one of two equal sources drops the level by 3 dB.