In the last example, if you used the formula 20 x Log (7.75/15.5), your answer would be -6.02 dB. It simply depends whether a larger number is divided by a smaller one (answer is always +dB) or a smaller one is divided by a larger one (answer is always -dB). The basic number will be the same no matter which way you divide. Try reversing the 7.75 and 15.5 in the last example. You should get -6.02 as the answer. Also, if you calculated the dB difference between the 71.30V and the 70.16V for the amplifier outputs, you would have gotten 0.139 dB or -0.139 dB, depending on which number you divided by which. This is why the difference was not significant: you can not hear a 0.139 dB difference.

The main reason for dividing a smaller by a larger number when calculating dB is to figure out the LOSS in dB. You will see this in the SPL and amplifier calculations below.

VOLTS TO dBu or dBv

You have a device that puts out 8.8 volts. What is that in dBu?
Formula: dBu = 20 x Log (volts1/volts2) or 20 x Log (8.8/0.775)
Enter 8.8 (volts1)
Hit the divide key
Enter 0.775 (volts2)
Hit the = key
Your answer should be 11.35
Hit the Log key
Your answer should be 1.05
Hit the multiply key
Enter 20
Hit the = key
Your answer should be 21.10 dBu

To find dBv simply substitute “1” for “0.775” in the calculation. Your answer should be 18.88 dBv.

SPL CALCULATIONS

You do SPL calculations using exactly the same formulas as for voltages. Both SPL and voltages are “pressures” and the factor “20” is used for both.
Your loudspeaker puts out a maximum of 120 dB SPL at 3.3 feet = 1 meter. What is the SPL at 60 feet?

First, you must understand that SPL drops 6 dB for each doubling of distance. Why is this? Calculate the multiplier for a pressure change of 6 dB.
Formula: Multiplier = 10^(SPL/20) or 10^(6/20)
Enter 6 (dB SPL)
Hit the divide key
Enter 20
Hit the = key
Your answer should be 0.3
Hit the 10x key
Your answer should be 1.99 = about 2

So the multiplier for a 6 dB SPL change is 2. This means if you move twice as close to the loudspeaker, it will be 6 dB louder.

Now recalculate this using another function on your calculator called the change sign key. This changes a number in the display from a plus to a minus number.
Formula: Multiplier = 10^(-SPL/20) or 10^(-6/20)
Enter 6 (dB SPL)
Hit the “+/-“
Your display should change to -6 (dB SPL)
Hit the divide key
Enter 20
Hit the = key
Your answer should be 0.3
Hit the 10x key
Your answer should be 0.50 = 1/2

So the multiplier for a -6 dB SPL change is 1/2. This means if you move so you are only 1/2 as close (meaning twice as far) to the loudspeaker, the SPL is 6 dB less.

Back to the problem. Your are 60 feet away and you know what the SPL is at 3.3 feet = 1 meter. You already know this should be a -dB number so you are going to divide the small number by the big one. Distances are equivalent to voltages so you simply divide the two distances. You can do this for any two distances and substitute the SPL at one of the distances for the Max SPL in this example. If this SPL is for the further distance, you must divide the further by the nearer distance. Always divide the distance you are finding the SPL for into the distance for which you know the SPL. Otherwise, you will find your answer will not make sense, such as having more SPL at a further distance. Sound just doesn’t seem to work this way.

Formula: dB SPL = Max SPL + (20 x Log (distance1/distance2)) or 120 + (20 x Log (3.3/60)
Enter 3.3 (distance1)
Hit the divide key
Enter 60 (distance2)
Hit the = key
Your answer should be 0.055
Hit the Log key
Hit the multiply key
Enter 20
Hit the = key
Your answer should be -25.19
Hit the + key
Enter 120
Hit the = key
Your answer should be 94.80 dB SPL

Note: the SPL formula is only valid outdoors and for the direct sound from the loudspeaker indoors. Indoors the reverberation of the room will take over at some distance from the loudspeaker and the sound level will remain more or less constant the further you move away. This is a subject beyond the scope of this article, but it will at least give you a rough idea of what to expect indoors.

AMPLIFIERS

There are really only two dB calculations you generally need for amplifier outputs. One is how many dB SPL is there between two wattage levels. The other is what is the difference in watts you need to achieve a given change in dB SPL. Because amplifier watts are power, that number 20 you’ve been using thus far in the calculations changes to 10 for doing the “log” calculations. Otherwise, the formulas are the same. Through a quirk in mathematics, you can use the dB answers you get when calculating differences in wattages as representing the change in SPL from the loudspeaker. While this is not mathematically correct, it is a perfectly practical thing to do. Substitue some other numbers in the following example, such as 2 watt and 4 watts. Then use 2000 watts and 4000 watts. You will find the answer is exactly the same (but the price tags are definately not!!).

WATTS TO dB (or Watts to SPL)

You have a 100W amplifier and want to change to a 350W amplifier. How many more dB will you get out of your loudspeaker?
Formula: dB = 10 x Log (watts1/watts2) or 10 x Log (350/100).
Note the larger number is divided by smaller will give you +dB. You DO expect higher SPL, don’t you?
Enter 350 (watts1)
Hit the divide key
Enter 100 (watts2)
Hit the = key
Your answer should be 3
Hit the Log key
Your answer should be 0.54
Hit the multiply key
Enter 10
Hit the = key
Your answer should be 5.4 dB

This is the power difference in dB between these amplifiers. If you were going from a 350W to a 100W, the answer would be -5.4 dB as the smaller number would be divided by the larger. Try it.

You could go through correct mathematical conversions, but because we are being practical, the SPL from your loudspeaker will be 5.4 dB greater with the 350W amplifier than the 100W amplifier. Or, it will be -5.4 dB less using a 100W amplifier instead of a 350W amplifier.

dB TO WATTS (or SPL to Watts)

Suppose you want to increase your SPL by 8 dB and you have 100 watts to start with. How many more watts would this take?
Formula: Multiplier = 10^(dB/10) or 10^(8/10)
Enter 8 (dB)
Hit the divide key
Enter 10
Hit the = key
Your answer should be 0.8
Hit the 10x key
Your answer should be 6.30
So you need 6.30 times as many watts to get an 8 dB SPL increase. How many watts is that?
Formula: New Watts = Multiplier x watts or 6.3 x 100
Enter 6.3 (multiplier)
Hit the multiply key
Enter 100 (watts)
Hit the = key
Your answer should be 630W
Thus, if you start with 100W, you need 630W to incerase your SPL by 8 dB.

SUMMARY

The above examples should give you valuable tools you need to calculate dB in the most of the ways you need for audio signals. Use them wisely.