We’ve all said things like, “Hey, can we bring that down a dB or 2?” or, “Bring that up about 3dB,” but what do we really mean? Or, even more to the point, what does that really mean? I mean what is a decibel, really?

You see, the word decibel simply means one-tenth of a Bel. A Bel is a unit of measurement that measures the ratio of a source against a known reference level. It was named after Alexander Graham Bell (scientists and engineers like to name things after their heroes). Since the decibel is one-tenth of the Bel, it’s a simple way to measure smaller increments without all those nasty decimal places.

So the reality is, when talking about decibels, we need to know what reference we’re dealing with, and what we’re actually measuring. Fortunately for us, those that have come before us have done all the hard work of figuring out those references and how they all relate. We’ll get to all of that in a moment. Before we do, we need to understand something about scaling, and how it relates to decibel measurements.

Logarithms

So the first point to make is that decibels are not measured on a linear scale. That is to say that the difference from 1dB to 2dB is not equal to the difference between 10dB to 11dB, even though they are both represented by a 1 decibel change. Decibels are measured on a logarithmic scale, which is a way to express large data ranges in a compact way. The logarithmic scales also change as you move away from your reference point. It’s a bit confusing, but if you think of it like a ruler it might help.

On a ruler the distance between markings is consistent all the way up and down the ruler. But what if your ruler’s marking got closer together as you moved to the higher numbers? That’s what a logarithmic scale is doing.

Looking closely you will see that the distance from 1 to 2 is the same distance from 2 to 4, which is then equal to the distance from 4 to 8.

The distance between numbers (or the scale, if you will) is compressing. This is how a logarithmic scale can cover a much wider set of values with smaller numbers. In fact, I mentioned this in a previous article about gain staging, pointing out that faders are logarithmic, and have much finer control closer to unity than they do as you move farther away from unity.

This graph is another visual representation of how a logarithmic scale is different from a linear scale. In this case I put a linear scale (the blue line) right next to a logarithmic scale, showing dBu (the red line). The X-axis (horizontal/bottom) would be decibels, while the Y-axis (vertical/left) would represent volts. Take a look:

As you can see they are not the same. The blue line is very much a 1 to 1 representation, which is the definition of linear (where 1 in = 1 out). The red line starts off slow and ramps up over time, and at no point is constant.

On the chart above the red line shows that 10dBu = 2.45 volts, and 20dBu actually equals 7.75 volts. And, in case you’re wondering, 30dBu = 24.5 volts. This is the magic of logarithms. You cover more ground with the same amount of change. Our first 10dB only increased the voltage by about 1.6 volts (because 0dBu = 0.775 volts...which we’ll cover more about a little later). The second 10dB change increased the voltage by 5.3 volts, and the next 10dB change increased the voltage by 16.75 volts. This also happens with smaller increments, such as with single decibel changes. Take a look.

Even just understanding this much will help you realize how much variation there is within the decibel scale. The change between any one decibel and the next is never the same as the change between another, different, two decibels.

Now that we have a better understanding of how decibels work, let’s look at the different things we measure with decibels.

dBspl, The Sounds Around Us

The world around us is full of sounds. Our ears pick up sound through the vibration of the air molecules bouncing into our tympanic membranes (that’s a fancy name for ear drums). The force that a specific sound enacts on said air molecules is called Sound Pressure Level, and we measure that force in Pascals (named after Blaise Pascal)

This is what dBspl is measuring; sound pressure level referenced to pascals, where 0dBspl = 0.00002 pascals. In comparison, the threshold of pain is 120dBspl, and that is equivalent to 20 pascals of pressure. That’s 1,000,000 times more pressure, represented as a change of 120 decibels.

dBu, Our Gear

When we pass signal through our studio gear it’s all done by bothering electrons. We like to call that “signal”, as in “Do you see any signal on that channel?” We typically measure this signal in volts. The reference point for the dBu measurement was chosen so that 0dBu = 0.775 volts.

There’s a story as to why this number was chosen over an integer, or even a cleaner decimal. You see, a 0.775 volt reference made a 0dBu measurement the same as a 0dBm measurement. By the way, dBm is a measurement of milliwatts, and used mainly for electrical power. We aren’t going to do more than mention them here, since we rarely have to deal with them in the studio. Just know that while all the decibel scales we use daily are 20Log scales, the dBm is a 10Log scale, making for messy cross referencing, and the 0.775 volt dBu reference level is evidence of that.

Most of the gear in our studios uses the dBu reference, and will be labeled “+4dBu”, meaning that it’s expected unity line level voltage is 1.228 volts.

dBV, Because Decimals Are Messy

Even knowing the reasoning behind it, 0.775 is a decidedly messy choice for a reference level. It’s not an integer, or even a clean decimal like 0.5 (½) or even 0.75 (¾). If you’re thinking, “Hey, wouldn’t it make life easier if we just made 0dB = 1 volt?”, you’re not alone. Others have thought that and created a second decibel reference for voltage, and called it dBV (always with a capital V, please). And, while that makes the math easier, it adds complication by introducing a second reference, giving us 2 decibel measurements that reference volts to keep track of. Two references that are very easy to mis-label.

Luckily, the dBV measurement was relegated to “consumer” electronic equipment, where you usually see a nominal output level label of -10 dBV, which makes the expected unity line level voltage a mere 0.317 volts.

The lesson here is: There is no mildly messy measurement we can’t further obfuscate by creating an alternate reference and measurement method.

dBfs, We Are Living In A Digital World

dBfs was a way of expressing digital headroom in a digital recording, and directly relates to bit depth. The “fs” stands for Full Scale, and the reference is 0dBfs = full bit depth.

This one is a little bit of an oddball because the reference can change based on the bit depth of the audio. At 24-bits you have 16,777,216 (2^24) bits per sample. 0dBfs would be filling all those bits with data, so in the case of 24-bits, 0dBfs = 16,777,216. At 16-bits you have 65,536 (2^16) bits per sample, making 0dBfs = 65,536.

Another odd thing about dBfs is that it is the only decibel measurement where we stay consistently in the negatives, since anything over 0dB, no matter how small the over is, is digital distortion.

A common confusion point for dBfs is how it relates the analogue gear that feeds it. Somewhere along the line we have to convert our analogue signal, in volts, to a digital equivalent. There are 2 accepted standards for referencing a dBfs meter to a dBu meter. The first standard is that -20dBfs = 0dBu. The other accepted standard is -18dBfs = 0dBu. It doesn’t matter that much which you choose, but you should choose one of the standards, and make sure your gear is all calibrated so that 0dBu through the gear is hitting your dBfs reference of either -20 dBfs or -18 dBfs.

Decibel Quick Reference

HINT: Are you more of a visual learner? Do you want to see what these formulas look like on a graph? Head over to Desmos and you can copy these into the formula bar to graph the formula. Just precede each formula with ‘x=’, and replace the reference with ‘y’. So, for dBspl you’d get: x = 20 • log ( y / .00002 ).

Conclusion

I hope this article has helped you better understand one of the more prevalent measurements in the life of an audio professional. We are surrounded by the language of decibels, and we don’t always ponder the complex system behind those everyday parts of our working lives.