A PRACTICAL GUIDE TO dB CALCULATIONS
This is a practical guide to doing dB (decibel) calculations, covering most common audio situations. You
see dB numbers all the time in audio. You may understand that 3 dB is considered a just noticeable
change in volume level. But, you haven't a clue how to figure out how to figure out what 24 dBm from your
mixing console means to your amplifier rated for 1.4V input sensitivity. You may be aware that dB
calculations involve "logs" (logarithms). Thanks to a little technology, you can do dB calculations without
knowing a thing about the mathematics of logs, anti-logs, ratios, exponents, or even much about math.
Unfortunately, there is no real substitute for doing these calculations, but there is a substitute for having to
figure out how to do the calculations. This article figures most of that out for you. Along the way the math
is explained to some extent so that you might understand what you are doing. Some of the whys about
audio calculations are also explained.
This guide is necessarily long in order to cover many situations where you might need to use dB. But, if
you understand the calculations, you will find that most of them repeat the same things in different ways.
If you begin to see this, it means you are beginning to understand how to calculate dB.
First, if you don't have one, you need to buy yourself a cheap scientific calculator. This should cost
around $20 (US). It MUST have several specific functions on it. One is a "Log" function. There are two
common Log functions. One is "Log base e" or "natural Log" which you DON'T want. The other is "Log
base 10" which is what you need. You can check if it is "Log base 10" by simply entering 10 and hitting
the "Log" key. The display should read 1. If it doesn't, don't buy it. Another function you need is a 10
function (also called 10 to the
function or the anti-log function). You can check if this is the proper
function by entering 2 then hitting the 10
key. The display should read 100. You also need a +/- (change
sign) key. It must also have plus, minus, divide, multiply, and equal (=) keys. You can basically ignore the
other functions on it to do dB calculations.
Once armed with this tool, you can now learn to do dB calculations. Actually, you don't really have to
learn much except to push the right buttons on the calculator. In each example, you will be told exactly
what calculator key to hit and what your answer should be. Once you get the right answers as shown, you
can substitute your own numbers in the various examples to figure out your own things. Remember, a
calculator is a DUMB device. It will only do what you tell it to do. So you MUST use your brain a bit to see
if your answers make sense. This means if you come up with a number like 23841 dB or 20,000,000
watts, it is wrong. Nothing in audio has 23841 dB of anything and 20,000,000 watts is out of the question,
unless you are providing sound reinforcement for Space Shuttle launches.
All the answers given in this article only show the first two digits (numbers) to the right of the decimal