

Watts in a Decibel
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Question:
How many watts are in a decibel? I read heard this terminology in a
song.
Replies:
The decibel is dimensionless. It is the logarithm of a ratio.
In terms of power, dB = 10 log(base10) P/Po, where Po is the
reference power. It often is referenced to 1 milliwatt (.001
watt). Thus, a power of 1 watt referenced to 1 mw would be
10 X log(1W/.001W) = 10 X log(1000) = 30 dB. Anything that
can be expressed as a ratio to a reference can be expressed in
dB. As a whimsical example, a dollar is 10 X log(100/1) = 20 DB
over a penny! So, there are no watts in a dB. The dB has no
dimensions. You can use watts to determine dB. If you have a
1 mW signal and send it through an amplifier that boosts that
signal to 5 watts, then we say the amplifier has
10 X log(5W/.001W) = 37 dB gain. If you want to relate dB to
watts, you must know the reference power.
gary e myers
Well, the question was probably arising from the tendency
to rate speakers in watts, and the fact that there is
a "unitfull" decibell  the decibell used to measure sound
levels. However, the dB level you will feel from a speaker
of a given wattage depends on how close you are to the
speaker! And I do not know if there is any real standard
relation between the dB level 1 foot from a speaker and
the power level, though there could be...
Arthur Smith
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Update: June 2012

