# What is the reason for using decibels to measure sound?

If the decibel represents a gain ratio, why do we use it in sound measurements?

Yes, since we have an input signal in audio amplifier circuits, we can understand the behavior of this system according to how much the signal grows or shrinks. It makes sense to express this in decibels or gain, but why do noise meters that measure sound level in a normal environment use decibels? On Wikipedia, Sound pressure level is expressed as the reference (input) value used when measuring the signal.

... threshold of human hearing (roughly the sound of a mosquito flying 3 m away).

Why is it necessary to calculate such a thing and give the ratio of it? Why didn't they measure the sound level of the environment to be measured directly and express it with a unit suitable for it?

The other answers focus on the large range in pressure which corresponds to sound, and suggest that this is the reason we use a logarithmic measure. This isn't really right: it's true the range is large, but this isn't the reason. Consider: We have a large range of distances we deal with, but only rarely use logarithmic distances; or at most, we use a small choice of logarithmic scalings (the SI prefixes).

The reason we use a logarithmic scale is because our senses are mostly logarithmic, a property called the "Weber-Fechner Law" in the field of psychophysics.

From Varshney and Sun cited below:

Nonlinear scalings that give greater perceptual resolution to less intense stimuli are ubiquitous across animal species and across sensory modalities: heaviness, pain, warmth, taste, loudness, pitch, brightness, distance, time delay, and colour saturation, among others, are all perceived this way. Moreover, these mappings between observable stimulus and our internal perception-space – these psychophysical scales and laws – are approximately logarithmic.

What this means for sound is that, over much of the hearing range, a given multiplicative increase in pressure has the same sensation at lower volume and higher volume (as an approximation, with limits). This is the same as how a doubling of frequency is perceived the same whether it's 500 to 1,000 Hz or 5,000 to 10,000 Hz. In western music we normally use semitones, which are the 12th root of 2 (12√2 = 1.0595), as the multiplier for measuring frequency ratios.

And if you want to measure a pressure logarithmically, decibels are an excellent and established system to use for it; especially since a lot of the sounds we want to measure are coming out of electronic amplifiers. And because dB are really just a ratio, we measure as a logarithm of multipliers from an arbitrary and convenient "standard quiet" reference point, typically 20 μPa (link).

Indeed, it's possible to argue that we use ratiometric measurements for power in electronics because we want ratiometric measurements for sound power.

If the decibel represents a gain ratio, why do we use it in sound measurements?

Let me correct you; the decibel represents a ratio, and when used to talk about amplifiers, it represents a gain ratio. But in other cases (such as sound) it represents a ratio to the threshold of sound (20 μPa): -

Image from here.

Why is it necessary to calculate such a thing and give the ratio of it? Why didn't they measure the sound level of the environment to be measured directly and express it with a unit suitable for it?

Well, if we said that the human ear can detect sound from 20 μPa to 20 Pa, that's a scale of 1,000,000:1 and, it's more meaningful to rescale it to something from zero to 120 dB SPL.

• "that's a scale of 1,000,000:1, it's more meaningful to rescale it". That doesn't seem obvious to me at all. The human eye can detect features of about 10um to a few km, a scale of 1.000.000.000:1, yet we have no problem using normal linear distance units instead of a logarithmic ratio.
– BrtH
Commented Jul 5 at 12:33
• @BrtH you are not comparing apples with apples. Sound level is an intensity whereas distance is distance; the equivalent in eyes would be light intensity and, we readily measure optical power in decibels. Commented Jul 5 at 13:12
• @BrtH Visual resolution is measured in terms of solid angles, not distance. Commented Jul 5 at 13:29
• To add to that answer, a lot of human perception is actually logarithmic. So it makes even more sense to use dB SPL, even if the base of the logarithm is different. Commented Jul 6 at 3:07
• "Why is it necessary to calculate such a thing and give the ratio of it" I think can be answered more obviously - all units are ratios of things. When you measure something in meters it's actually the ratio of the measured length to the length of 1 meter ie. 1km is 1000 times larger than 1 meter. Similarly, 30dB is 1000 times larger than 0dB, and 0dB is our base unit of value just like how 1 meter is our base unit of value for linear units. So what is 0dB? For power we use dBW which defines 0 dBW = 1 * 1 Watt, and for audio we might use dBA which defines 0 dBA = 1 * (some super quiet sound). Commented Jul 7 at 20:25

If you're trying to measure what a human being hears, dB make more sense than some system such as SI unit Pascals. Each 10dB increase in sound level appears to be roughly twice as loud. Since dB are a ratio, you need to pick a reference level and the approximate threshold of human hearing is a sensible one.

If you're trying to calculate how far from ground zero windows will be blown out of buildings, then maybe Pascals would be appropriate (or PSI for the non-SI crowd).

• "Each 10dB increase in sound level appears to be roughly twice as loud." This isn't correct: each 10db appears to our senses to be the same amount louder, not twice. (Although this is an approximation: see wikipedia Web-Flechner law section on sound) Commented Jul 7 at 18:55

What is the reason for using decibels to measure sound?

The point to understand is that we do not measure sound level as decibel (I will use dB as the short form).

Decibel as such is, as correctly noted, a way to describe a ratio between two values. We might say that one signal or sound is 10dB stronger than another signal. We can say that an amplifier increases a signal by 20dB. Or that a sound insulation decreases the sound by 15 dB. But there is a need for describing the frequency response as well. A certain sound isolation might decrease sound by 15dB at 1000 Hertz but only 5dB at 50 Herz of frequency.

Now for sound levels. These are as said not measured in dB but most commonly in dB (SPL). The addition of (SPL) shows that we have selected a reference point for the dB scale at 2.00×10−5 Pascal and that we are measuring sound pressure. All of these are conventions adopted over time, 0dB (SPL) is supposed to indicate the auditory threshold. The (SPL) notation is often left out and simply assumed.

Another very common variation of measuring sound is to take into consideration how we as humans perceive sounds. Most of us cannot hear sounds outside the range of 20Hz to 20kHz. But even in this range our ears are not equally sensitive. The version most commonly seen is A-weighted, shortened as dB A. (there are other weithings in use).

dB SPL is computed by first measuring the actual sound pressure (e.g. in pascals) and then taking the logarithm, so people do measure the pressure, it is how you get the dB value. Typically though a log scale is more useful since the range of human hearing spans ~6 orders of magnitude and most people have no intuition for what 0.0004 Pa sounds like whereas "X times the quietest thing you can hear" is more intuitive, especially when there are a lot of leading zeros in the number.

• But this is incorrect. You don't get SPL that way in decibels. You measure the sound in Pascals, yes, but divide it by reference of 20 micropascals and then take the logarithm and multiply by 20, and only then you have dB SPL. Commented Jul 5 at 8:17
• @Justme yes, what you and he said is exactly the same thing: you compute the db from the measured 'actual sound pressure (eg in pascals). That's what you said. That's what he said. That's what you both said. Commented Jul 5 at 12:21
• @Justme it is not incorrect, you're just being excessively pedantic. The person linked to the equation and asked why it is used. It is not necessary or even helpful to reiterate the equation to explain what it's purpose is. Commented Jul 5 at 12:36

There are a few main reasons.

Sound pressure spans so large range that it makes sense to use a logarithmic unit to begin with, like for many other things like Richter magnitude scale for earthquakes, f-stops in photography, pH for acidity and the pitch intervals like semitones and octaves for sound.

Also, why decibels? Well, 1 bel is inconveniently large, and 1 centibel would be inconveniently small, so for many things expressed in 1 or 2 digits, decibels fit just conveniently in between. And why notes are expressed in cents where 100 cents is one semitone and 1200 cents is one octave.

And the decibel isn't an unit, it is simply a ratio between two things, whatever they are. You just conveniently used it as amplifier gain example. The gain of an ampmifier is the ratio between output and input amplitudes, if in volts, the volts cancel out, and you get simply a gain factor, like 20, and can convert it to decibels, megabels, microbels or whatever measure you like.

So having a sound measurement and expressing it as decibels requires that there is a reference value to compare it with. It could be any reference. It could be pressure of some known sound level, or something like maximum possible sound level in air on planet Earth which has atmospheric pressure of about 1000mbar. In order to avoid negative numbers, and have an understandable reference, also the smallest sound pressure most people can hear could be used, and if done so, most of everyday life sounds are above 0dB and maybe below 120dB. Even the sound of a volcano which cannot exceed the 1 Atm pressure without clipping fits nicely to around 200dB. And smaller sounds you can hear can be expressed with negative numbers, and it simply tells you how much you need to amplify something to get to 0dB so you can barely hear it.

I also used the dB very liberally in my above context and like I said, the dB always needs a unit where you reference it to - hence it would be more correct to say that a lawnmower measures 80 dB SPL, as saying just 80 dB makes you think it measures 80 dB compared to what, grams in weight or milliliters in volume.

Another distinction I haven't seen made between sounds and distances is that distances add linearly, but sound levels don't. If two devices that would produce sounds at a certain pressure level are placed near each other, the resulting sound pressure level will generally be greater than for either device in isolation, but less than the sum of the sound pressure levels produced by the individual devices. Trying to calculate such things precisely is apt to be difficult, but depending upon the nature of the noise sources, decibels may be convenient for estimation purposes, especially if one applies a simple principle: for purposes of estimating sound pressure levels, anything that isn't within 10dB of the loudest sound can generally be ignored.

To see why this is so, it may be helpful to imagine sounds as being walks in random directions from a starting point, and sound pressure level as being the distance from the starting point, someone who walks 1km in a random direction will be 1km from the starting point. If the person walks 1km in another random direction that's not within 120 degrees of the first direction, they'll end up less than 1km away from where they started, but if all directions are equally likely, the probability of that happening would only be 1/3. More likely, the second direction will be within 120 degrees of the first one, causing them to end up more than 1km away from the starting point.

If one were e.g. 10km away from the starting point and one were to walk 1km in some random direction, the range of angles that would put one further away from the starting point is greater than +/- 90 degrees, but not by much. A 1km random movement would be almost as likely to leave one less than 10km away from the start as to leave one more than 10km away. If, starting 10km away from a reference point, one makes a bunch of random 1km moves, the ones that would bring one closer the reference are likely to almost cancel out the ones that would take one further away, leaving one somewhere very close to a 10km circle around the reference point.

Using decibels for sound pressure levels rather than absolute units helps emphasize the fact that the normal sorts of arithmetic reasoning that would be useful for things like linear distances are simply not applicable.