# Are there any formulae that involve decibels?

47
Thanks.

2. ### HallsofIvy

40,241
Staff Emeritus
Any formula that deals with "loudness" can be put in terms of decibels. The simplest, of course, is that one decibel is one tenth of a bel!

3. ### Bobbywhy

1,908
Ralphonsicus, Google and Wikipedia are your friends...learn to use them to find answers to your questions plus references for where to look for more detailed research. I found this in about one minute! Here are two paragraphs from the Wiki page on “decibel”:

“The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities.[1] A decibel is one tenth of a bel, a seldom-used unit.

The decibel is used for a wide variety of measurements in science and engineering, most prominently in acoustics, electronics, and control theory. In electronics, the gains of amplifiers, attenuation of signals, and signal-to-noise ratios are often expressed in decibels. The decibel confers a number of advantages, such as the ability to conveniently represent very large or small numbers, and the ability to carry out multiplication of ratios by simple addition and subtraction.”

http://en.wikipedia.org/wiki/Decibel

### Staff: Mentor

Please try to give more context and detail in questions like this. You do not say why you are asking the question, you do not specify which areas of science you are asking about, etc.

It makes it a lot easier for folks who want to help you if you post what you know and what research you have done on the question so far, and what *specifically* you are looking for.

5. ### sophiecentaur

13,286
Beware the huge amount of rubbish that it talked about the dreaded dB.
In my experience, many people tend to struggle with Logarithms until they get familiar with them from extended use - I mean lots of example problems.
Likewise with dB. You will eventually get a feel for them and you find 30dB will automatically mean a Power ratio of 1000 to you, without thinking about it.

You can reduce the risk of going wrong if you always remember that dB is defined as a ratio of POWERS. It so happens that, when you are operating at the same impedance, you can relate Voltage or Current ratios to power ratios but it really is a nonsense just to say that a multiplication of volts implies a 'gain in dB'. A 1:10 transformer will have a (power) gain of less than 0dB, despite producing ten times as many volts and a 'voltage follower' circuit may have a gain of 60dB, although the voltage gain is 1.

Anyone who you hear using the term " Volts dB" is on shifty ground unless they specify a constant impedance. 60dBμV is OK as long as, somewhere, there is a 50Ω specified.

6. ### Nehmo

8
Last edited: Jan 27, 2012
7. ### sophiecentaur

13,286
Shame he breaks the first rule at the start. dB is a ratio of powers so he isn't helping by starting off with Voltage ratios. I am not nitpicking here and his approach can lead to serious misconceptions. Too glib and chatty to be safe, imo.

8. ### Kholdstare

390
Well power = voltage^2 / resistance , isnt it? So even if dB is actually a rule which applies for power, we can use it for voltage also given the load remains same (which is most of the case).

9. ### sophiecentaur

13,286
Is it the same for a transformer or an amplifier? Like I said, it's dangerous.

I seem to remember someone trying 'decilogs' as a possible way out.