DEFINITIONS

Some definitions you need to know:

Any dB value is a RATIO, meaning it represents one number divided by another. If you simply state something in dB then you are only stating the ratio in between one thing and another. So you might say the difference in two voltages is 6 dB but that only means one voltage is twice the other (6 dB = 2 times voltage). It doesn’t tell you anything about the actual voltages.

If you want to state the actual value of something in dB, most common audio calculations have a 0 dB reference value that is indicated by suffix (a letter or letters following dB). The 0 dB reference value is always used as one of the numers for the ratio. You should always use a suffix when stating the dB of something as an actual value so that anyone else will know what 0 dB reference is. So when you say your mixer is putting out + 6 dB, you really need to say + 6 dBu or whatever the 0 dB reference is. Thus +6dB means you have twice as much voltage while +6 dBu means you have 0.775 volts or 1.55 volts.

For electronic calculations (voltage and wattage) the 0 dB references are: 0 dBu (or dBv) = 0.775 volts
0 dBV = 1 volt
0 dBm = 1 milliwatt (0.001 watts). The standard reference value for 0dBm is 0.775 volts into a load of 600 Ohms. For most audio calculations, simply assume you are NOT using a 600 Ohm load and thus dBm can equal dBu. For example, a +24 dBm output specification on a mixing console can be used as +24 dBu to calculate voltages. The reason for this is that modern audio equipment will put out the same voltage whether there is a “load” on it or not. Thus knowing the power in a line level audio circuit is of little value and simply complicates what you need to know.

Example: 6 dBu is the ratio of some voltage divided by 0.775 volts. That voltage is 1.55 volts.
For SPL (Sound Pressure Level) calculations the 0 dB reference is:
0 dB SPL = 0.00002 pascals (a pascal is a measure of pressure, in this case air pressure, just like a meter is for distance).
Example: 100 dB SPL is the ratio of some sound pressure to 0.00002 Pascals. That pressure is 2 Pascals
These are the symbols used in the formulas:
”x” means multiply
”/” means divide
”^” This symbol indicates what follows is an exponent of the number preceding it. An exponent means “raised to the power of”, as in 10^2 is 10 raised to the power of 2 or more simply stated as “10 squared”. With dB calculations you get “funny” powers like 10^(34/20). Spelled out this is “ten to the power of thirty four divided by twenty”. Don’t be afraid of this. The instructions and your trusty calculator will get you through it without having to fully understand it.

”( )” in the formulas means that everything inside the parenthesis is calculated first to come up with a single number. In the first example below, (24/20) is calculated first to come up with 1.2. Then 10 is raised to the power of 1.2.

dBu TO VOLTAGE

How many volts does a mixing console put out with a maximum rating of +24 dBm? Although rated in dBm you can “change” this, as stated above, to dBu for this calculation. Using you new calculator you need to find out how many volts +24 dBu is above 0 dBu.
Formula: Volts = 10^(dB/20) x volts @ 0 dBu or 10^(24/20) x 0.775
Enter 24 (dBu)
Hit the divide key
Enter 20
Hit the = key
Your answer should be 1.2
Hit the 10x key.
Your answer should be 15.84
Multiply this by 0.775
Your final answer should be 12.28 volts
The reason you multiply by 0.775 is that any dB number is always a RATIO (one number divided by another). So 15.84 is the numerical ratio of +24 dBu to 0 dBu. Put another way the voltage at +24 dBu is 15.84 times bigger than 0.775 volts so you must multiply 0.775 by 15.84. The 15.84 is used as a multiplier and will be called this from now on. However, to be mathematically correct, this multiplier is actually a ratio representing one number divided by another.