The decibel is a rather confusing concept to fully comprehend in the world of audio. It seems just as we begin to understand decibels, we learn sometimes else about them that confuses us even more than we were previously. Fear not, this article has all the details you’ll need to fully understand decibels.

What are decibels? **A decibel (dB) is a tenth of a Bel (“deci-Bel”). It is a relative unit of measurement used to express the ratio of one quantity to another on a logarithmic scale. Decibels are commonly used in audio to define gain, sound pressure level (dB SPL), signal level (dBv, dBu, dBFS), and even power (dBm).**

In this article, I will break down the decibel and define it in such a way that should be perfectly clear. My hope is that once you’ve read this article, you’ll have a full understanding of the decibel and its role in audio. I also hope this becomes a reference for you to re-read for specifics about decibels in the future. Let’s get into it.

## Table Of Contents

**The Decibel Is A Logarithmic Ratio****Power, Root-Power & Perceived Quantities****Common Decibel Reference Points****The Use Of Decibels In Audio****Related Questions**

## The Decibel Is A Logarithmic Ratio

First and foremost, we must understand that the decibel is not a linear ratio. Rather, it is logarithmic.

For instance, the signal gain (voltage gain) of an audio amplifier can be calculated as the ratio of the output voltage/signal level to the input voltage/signal level.

So if the amplifiers output signal is 100 times as strong as the input signal (its voltage amplitude is 10x that of input), then we could say that the gain of the amplifier is 10:1 (or simply “10”). That’s linear.

However, a gain of 10:1 would be considered, when speaking of the signal/voltage level, only 20 dB of gain.

The decibel ratio of two voltage ratings is defined as follows:

**Gain (in dB) = 20 • log _{10} (V_{out} / V_{in})**

We’ll get into the explanation of the above formula and other formulae regarding decibels in the next section Power, Root-Power & Perceived Quantities.

For now, let’s stick with the fact that the decibel is a relative unit of measurement (ratio) on a logarithmic scale.

### What Is A Ratio?

A ratio, in mathematics, is a unitless relative measurement that indicates how many times one number contains another number.

A ratio always compares one value to another value.

In audio and sound, we use ratios for lots of things, including but not limited to:

**Gain (as previously mentioned):**the ratio between output signal voltage/strength to input signal/voltage strength.**Noise:**the ratio between the intended signal strength/voltage and the unintentional noise signal strength/voltage.**Sound pressure level:**the ratio between the peak pressure variation caused by a sound wave and the point at which we register pressure variation as sound.

**Related article: What Is The Difference Between Sound And Audio?**

### What Is A Logarithm?

A logarithm, in mathematics, is the inverse function of an exponential.

In other words, the logarithm of a given number *x *is the exponent to which the base number *b* must be raised to produce the number *x*.

In notation, this would look like:

**log _{b} (x) = y** hold true when

*b*=^{y}*x*Other factors that must hold true are:

*x*> 0*b*> 0*b*≠ 1

For most of our decibel calculations in audio, we use the “common logarithm” where *b* = 10.

### What Is A Logarithmic Scale?

A logarithmic scale is a method of displaying numerical data over a wide range of values in a compact way. Logarithmics scales are very useful when the values in the data range in several orders of magnitude. For example, a logarithmic scale would be suitable for a set of values where the largest numbers are hundreds, thousands, tens of thousands, and etcetera larger thatn the smallest numbers.

So what ranges in audio and sound exhibit this kind of variation? Well, let’s re-list our examples from the section What Is A Ratio?

**Gain:**a weak microphone signal can be around 1 mV in strength (1 x 10^{-3}volts) while a large loudspeaker could require 100 V (1 x 10^{2}).**Noise:**The signal-to-noise ratios of “clean” audio equipment can be 100 dB or greater. This means that the intended signal strength (measured in volts) is 100,000 times stronger than the unintentional noise “signal” strength.**Sound pressure level:**SPL also has a wide range. As an example, the hearing threshold of healthy human hearing is universally accepted to be 0.000,02 Pa (2 x 10^{-5}Pa) and the threshold of pain (where hearing damage is immediate) is commonly accepted to 200 Pa. That’s a 10^{7}or 10,000,000x difference! More commonly, we say it’s a 140 dB difference.

Once again, the equations we use to find the decibel ratings will be discussed shortly!

### Recap

So to recap with our new knowledge, a decibel is a relative unit of measurement used to express the ratio of one value to another on a logarithmic scale.

So, then, the decibel expressed the ratio of one value to another and is particularly useful when the range of said values is very large.

### What Decibels Are Not

Now that we have an idea of what decibels are, let’s consider what decibels are not. Decibels are not any of the following:

- A measurement of sound pressure level
- A measurement of perceived loudness
- A measurement of audio signal voltage/amplitude
- A measurement of electrical or acoustic power

That is to say that decibels are not absolute measurements. They do not inherently tell us anything about sound pressure level, perceived loudness, voltage, power, or any other quantities related to audio and sound.

Rather, decibels tell us how much of a given quantity there is *relative* to another amount of the same quantity. There are several universally-agreed-upon reference points that help up use decibels effectively in our measurements of audio and sound quantities.

### Decibel Vs. Bel

A decibel, as we’ve discuss, is one tenth (unit prefix “deci”) of a Bel.

**For more information on the units and prefixes used in audio and sound technology, check out my article Units Of Measurement & Prefixes In Sound & Audio Electronics.**

The Bel, like the decibel, expresses the logarithmic ratio between two levels of signal power, voltage, or current. The Bel compares values to a ratio of 10 to 1.

This unit was named after Alexander Graham Bell, the inventor of the telephone (and the liquid transmitter “microphone”).

**Alexander Graham Bell is featured in My New Microphone’s article Mic History: Who Invented Each Type Of Microphone And When?**

From an ease-of-use standpoint, the Bel is a bit less practical than the decibel and has fallen out of favour because of it.

Most definitions will state that the Bel is equal to ten decibels while defining the decibel perfectly well, rather than the other way around, which would be expected. This is because decibels are used in practical measurements and Bels are [typically] not.

So in the next section, when we discuss the equations of decibels and see that factors of 10 in the equations, know that it is because we’re talking about decibels and not Bels!

Back to the Table of Contents.

## Power, Root-Power & Perceived Quantities

Alright, here’s the section where we’ll begin to understand the various equations of decibels in audio and sound technology.

First, let’s define power, root-power and perceived quantities:

### Power Quantities

Power quantities are directly proportional to power and energy.

**Power quantities include:**

**Electrical power****Energy density****Acoustic intensity****Luminous intensity**

**Related article: Complete Guide To Speaker Power Handling & Wattage Ratings**

### Root-Power Quantities

Root power quantities are quantities that have square root values proportional to power. The term “root power quantity” has replaced the term “field quantity”.

**Root-power quantities include:**

**Sound pressure****Voltage****Current****Electric field strength****Speed****Charge density**

### Perceived Quantities

Perceived quantities are defined by how we perceive power and root power quantities. We nearly always perceive less than the level of the power or root power quantity.

Perceived loudness is the psychoacoustic perceived quantity we’re concerned with in audio technology.

To really appreciate decibels when it comes to audio and sound, we must understand that a single decibel rating will, in a way, unify various quantity types into a single decibel ratio.

This becomes important when keeping track of levels when dealing with transducers of energy.

Transducers effectively convert one form of energy into another form of energy. In sound and audio, the most common transducers are:

**Microphone:**converts sound waves (mechanical wave energy) into audio signals (electrical energy).**Headphones & speakers:**convert audio signals (electrical energy) into sound waves (mechanical wave energy).**Ear:**converts sound waves (mechanical wave energy) into electrical impulses (electrical energy).

The amplitude of an audio signal (electrical energy) is most often measured as a voltage (root-power quantity) in volts but may also be measured as electrical power (power quantity) in watts.

Sound waves can be measured in acoustic power/intensity (power quantity) but in the vast majority of cases they are measured in sound pressure level (root-power quantity).

The way we perceive sound waves, however, is not quite in direct proportionality to the SPL. Rather, we hear sound as a “perceived quanitity”.

But when it comes to decibels, something interesting happens.

Let’s say we have a listening environment with an audio source, amplifier, loudspeaker and listener.

If no positions are to change and the audio signal waveform is at a consistent level, a 10 dB increase in amplifier power will cause a 10 dB increase in SPL at the listener’s ears and, therefore, a 10 dB increase in perceived loudness.

So the 10 dB increase is the same across the board. However, this 10 dB increase will yield the following increases in the actual absolute values of the different quantities:

- The 10 dB power increase will mean that 10 times as much power is sent from the amplifier to the loudspeaker.
- The 10 dB SPL increase will that the actual sound pressure at the listener’s ears will increase by √10 = 3.16 times.
- The 10 dB increase in perceived loudness will make the sound seem like it’s twice (2 times) as loud.

So increasing the power by 10x will increase the SPL by 3.16x and the perceived loudness by 2x. All quantities are increased by 3 dB.

Let’s get into the explanation behind this.

### Power Quantities & Decibel Measurements

Power quantities are directly proportional to power and energy.

To calculate power ratio in decibels, let’s begin with the basic logarithm of the Bel (remember than the Bel compares values to a ratio of 10 to 1).

So then we have a function with log_{10}. As we’ve discussed before, this is known as a “common logarithm”.

Now, because we work with decibels, we should have a factor of 10 included in the equation (1 Bel = 10 decibels).

Next, we know that the decibel is a ratio so we must have two distinct power quantity values represented as a fraction in the equation.

So then, we have the following:

**∆ Power Quantity (in dB) = 10 • log _{10} (P / P_{0})**

**Where:****P** = new power value**P _{0}** = reference power value

Once again, power quantities include:

- Electrical power
- Energy density
- Acoustic intensity
- Luminous intensity

### Root-Power Quantities & Decibel Measurements

Root power quantities are quantities that have square root values proportional to power. The term “root power quantity” has replaced the term “field quantity”.

So then, we have:

**(P / P _{0}) = (F / F_{0})^{2}**

**Where:P** = new power quantity value

**P**= power quantity value at the reference point

_{0}**F**= new root-power/field quantity value

**F**= root-power/field quantity value at the reference point

_{0}Now that we understand the equation for decibel ratings of power quantities, we can work to substitue root-power power quantities and obtain a new decibels equation for root-power quantities.

Remember:

**∆ Power Quantity (in dB) = 10 • log _{10} (P / P_{0})**

Now substitute **(P / P _{0})** for

**(F / F**and we have:

_{0})^{2}**∆ Root-Power Quantity (in dB) = 10 • log _{10} (F / F_{0})^{2}**

An interesting rule about logarithms is that:

log* _{b}*(

*a*) =

^{c}*c*• log

*(*

_{b}*a*)

So making this substitution, we arrive at the typical root-power/field quantity decibel equation of:

**∆ Root-Power Quantity (in dB) = 20 • log _{10} (F / F_{0})**

Once again, root-power quantities include:

- Sound pressure
- Voltage
- Current
- Electric field strength
- Speed
- Charge density

### Perceived Quantities & Decibel Measurements

Perceived quantities are defined by how we perceive power and root power quantities. Our perception of a changing power/root-power quantity can nearly always be considered less than the actual change in level of the power or root power quantity.

Perception is nearly impossible to calculate effectively. Each and every person will perceive sound differently.

Hearing health plays a major role in determining our sensitivity to and perception of sound waves.

A person with healthy hearing will be much more sensitive to sound across the audible spectrum (20 Hz – 20,000 Hz) than someone with damaged hearing. That’s a fact. In other words, healthy hearing will perceive sound to be louder than unhealthy hearing.

So it’s difficult to pin point “perceived quantities”.

On top of that, humans are more sensitive to certain frequencies within the audible range and less sensitive to others. We perceive certain frequencies to be louder than others. This can be shown in the Fletcher-Munson curves which we’ll discuss in a later section (Common Decibel Reference Points: dB SPL A-weighed).

All that being said, typical hearing perception has been studied and many experts have come to an agreement that perceived loudness, measured in decibels, is defined by the following equation:

**∆ Perceived Quantity (in dB) = 10 • log _{2} (p / p_{0})**

**Where: p** = new perceived loudness

**= reference perceived loudness**

**p**_{0}By the equation above, we see that a doubling of perceived loudness means a 10 dB increase.

When dealing with perceived loudness and the naturally coloured frequency response of human hearing, we typically deal with A-weighted decibels. More on this later in the article.

So what does this all means? Let’s compare what we know of power, root-power (field) and perceived quanities and look at how decibels work between them.

### Comparing Power, Root-Power & Perceived Quantity Decibel Values

Let’s begin our comparison by looking at the equations we’ve previously derived:

**∆ Power Quantity (in dB) = 10 • log _{10} (P / P_{0})**

**∆ Root-Power Quantity (in dB) = 20 • log _{10} (F / F_{0})**

**∆ Perceived Quantity (in dB) = 10 • log _{2} (p / p_{0})**

So then, a 10 dB increase would cause the following:

- 10x increase in power quantities.
- √10x or ~3.16x increase in root-power quantities.
- 2x increase in perceived loudness.

Similarly, a decrease of 10 dB would mean:

- 1/10x in power quanitites.
- 1/√10x or 0.316x in root-power quantities.
- 1/2x in perceived loudness.

Here is a table relating dB ratings to power quantities, root-power quantities and perceived quantities:

dB Change(Ratio) | Power Quantity Multiplier• Acoustic Power • Electrical Power • Sound Intensity | Root Power Quantity Multiplier• Voltage • Current • Sound Pressure Level | Perceived Quantity Multiplier• Loudness/Volume |
---|---|---|---|

+60 dB | 1,000,000x | √1,000,000 1,000x | 64x |

+50 dB | 100,000x | √100,000x 316x | 32x |

+40 dB | 10,000x | √10,000x 100x | 16x |

+30 dB | 1,000x | √1,000x 31.6x | 8x |

+20 dB | 100x | √100x 10x | 4x |

+10 dB | 10x | √10x 3.16x | 2x |

+6 dB | 4x | √4x 2x | 1.52x |

+3 dB | 2x | √2x 1.414x | 1.36x |

0 dB | 1x | 1x | 1x |

-3 dB | 1/2x 0.5x | 1/√2x 0.707x | 0.816x |

-6 dB | 1/4x 0.25x | 1/√4x 0.5x | 0.660x |

-10 dB | 1/10x 0.1x | 1/√10x 0.316x | 0.5x |

-20 dB | 1/100x 0.01x | 1/√100x 0.1x | 0.25x |

-30 dB | 1/1,000x 0.001x | 1/√1,000x 0.031,6x | 0.125x |

-40 dB | 1/10,000x 0.000,1x | 1/√10,000x 0.01x | 0.0625x |

-50 dB | 1/100,000x 0.000,01x | 1/√100,000x 0.003,16x | 0.03125x |

-60 dB | 1/1,000,000x 0.000,001x | 1/√1,000,000x 0.001x | 0.015625x |

Another, less common way of looking at decibels is relative to the true linear ratio of power, root power and perceived quantities:

The ratios are defined by the following formulae:

**Change in power quantity:**

*x* = 10^{∆P /10}

where ∆P = change in power quantity in decibels

**Change in root power quantity:**

*x* = 10^{∆F/20}

where ∆F = change in root-power quantity in decibels

**Change in loudness (psychoacoustics):**

*x* = 2^{∆p/10}

where ∆p = change in perceived quantity in decibels

Ratio (X:1)(Linear) | dB Change in Power Quantity• Acoustic Power • Electrical Power • Sound Intensity | dB Change in Root Power Quantity• Voltage • Current • Sound Pressure Level | dB Change in Perceived Quantity• Loudness/Volume |
---|---|---|---|

40 | +16.02 dB | +32.04 dB | +53.22 dB |

30 | +14.77 dB | +29.54 dB | +49.07 dB |

20 | +13.01 dB | +26.02 dB | +43.22 dB |

15 | +11.76 dB | +23.52 dB | +39.07 dB |

10 | +10 dB | +20 dB | +33.22 dB |

5 | +6.99 dB | +13.98 dB | +23.22 dB |

4 | +6.02 dB | +12.04 dB | +20 dB |

3 | +4.77 dB | +9.54 dB | +15.58 dB |

2 | +3.01 dB | +6.02 dB | +10 dB |

1 | ± 0 dB | ± 0 dB | ± 0 dB |

1/2 | -3.01 dB | -6.02 dB | -10 dB |

1/3 | -4.77 dB | -9.54 dB | -15.58 dB |

1/4 | -6.02 dB | -12.04 dB | -20 dB |

1/5 | -6.99 dB | -13.98 dB | -23.22 dB |

1/10 | -10 dB | -20 dB | -33.22 dB |

1/15 | -11.76 dB | -23.52 dB | -39.07 dB |

1/20 | -13.01 dB | -26.02 dB | -43.22 dB |

1/30 | -14.77 dB | -29.54 dB | -49.07 dB |

1/40 | -16.02 dB | -32.04 dB | -53.22 dB |

So then, let’s revisit our example scenario for earlier in this article.

We have a listening environment with an audio source, amplifier, loudspeaker and listener.

If no positions are changed and the audio signal waveform is at a consistent level, a 10 dB increase in amplifier power will cause a 10 dB increase in SPL at the listener’s ears and, therefore, a 10 dB increase in perceived loudness.

In this case, again, we have the following:

- The 10 dB power increase will mean that 10 times as much power is sent from the amplifier to the loudspeaker.
- The 10 dB SPL increase will that the actual sound pressure at the listener’s ears will increase by √10 = 3.16 times.
- The 10 dB increase in perceived loudness will make the sound seem like it’s twice (2 times) as loud.

What if we wanted the sound 3 times as loud? Using our equations (and the tables for some help), we would need a 15.58 dB increase. This requires an increase of ~6x in sound pressure level and a ~36.1x increase in power.

Okay, now for an example where we turn things down. Let’s say we wanted to listen at a quarter of the volume. In other words, we want a perceived linear ratio of 1/4.

Listening at a quarter of the perceived volume requires a descrease of 20 dB. This -20 dB means we have 0.1x (1/10 x) the sound pressure level and 0.01x (1/100 x) the power.

The beauty of decibels is that they allow us to understand and calculate the differences between power, root-power and perceived quanitities in sound and audio.

Remember, when reading the above examples, that:

- Electrical power and acoustic intensity are power quantites.
- Voltage, current and sound pressure level are root-power (field) quantities.
- Perceived loudness is a perceived quantity.

Electrical power (in watts), voltage (in volts) and current (in amperes) define the strength of the audio signal.

Acoustic intensity (in watts per square meter) defines the power carried by sound waves per unit area in a direction perpendicular to that area.

Sound pressure level (in Pascals) defines the pressure variation due to a sound waves at a given point within a medium.

Perceived loudness is how loud we perceive the acoustic intensity and resulting sound pressure levels at our ears.

Back to the Table of Contents.

## Common Decibel Reference Points

It’s worth reiterating that decibels are not measurements of sound pressure level; perceived loudness; audio signal voltage/amplitude; electrical power; acoustic intensity, or any other quantity having to do with sound and audio.

The decibel is simply a ratio set on a logarithmic scale.

So in order to use decibels to convey measurements of the above-listed quantities, we must have a reference point to compare them to. We need a second number in order to have a ratio!

Though any reference point is worthy of being part of a decibel measurement, there are several reference points that are commonly used in sound and audio. These references help all of us to comprehend sound and audio better by ensuring everyone’s on the same page when it comes to understanding the various decibel ratings.

**The common decibel ratings found in the study of sound and audio are as follows:**

Let’s describe each of these decibel “types” in more detail.

### dBV

dBV is shorthand for decibels with reference to 1 volt.

We know that voltage is a root-power quantity, so the dBV equation is:

**dBV value = 20 • log _{10} (V / V_{0})**

**Where:V** is the voltage level (in volts)

**V**is the reference point of 1 volt

_{0}So then 0 dBV = 1 V. Any positive dBV value represents a voltage above 1V and any negative dBV value represents a voltage below 1 V.

Voltage is often used to define the strength of an audio signal.

The voltages used are generally root-mean-square (RMS) rather than peak-to-peak (P-P) ratings. RMS effectively tells us the “average” of a signal that has both negative and positive amplitudes along its waveform. Such is the case of audio signals.

For instance, mic level audio signals are typically between 1 mV to 100 mV (0.001 V to 0.1 V). A line level signal is typically around 1 volt. Speaker level signal can be upwards of 100 V.

Nominal consumer line level is set to -10 dBV. This means that in consumer (typically unbalanced) line equipment, the nominal strength of the audio signal should be about -10 dBV or ~0.316 V (~316 mV) AC.

### dBu

dBu is shorthand for decibels with reference to 0.7746 volts with an open or unloaded circuit.

The “u” originate from the term “unloaded”. The 0.7746 V figure represents the voltage level that delivers 1 mW in a 600Ω resistor, which is the standard reference impedance in a telephone audio circuit.

We know that voltage is a root-power quantity, so the dBu equation is:

**dBu value = 20 • log _{10} (V / V_{0})**

**Where:V** is the voltage level (in volts)

**V**is the reference point of 0.7746 volts

_{0}So then 0 dBu = 0.7746 volts. Note, again, that the voltages are RMS and not P-P.

Nominal professional line level (which is typically balanced) is accepted to be +4 dBu. This translates to 1.228 volts RMS.

Comparing dBu to dBV, we have the following:

- 0 dBV = 2.218 dBu = 1 V
_{RMS} - -10 dBV = -7.782 dBu = 0.316 V
_{RMS} - 0 dBu = -2.218 dBV = 0.7746 V
_{RMS} - +4 dBu = 1.782 dBV = 1.228 V
_{RMS}

Note, too, that +4 dBu is equal to 0 VU (volume units), which is an old measuring system devised to help engineers aim for a certain signal level.

### dBm

dBm is shorthand for decibels with reference to one milliwatt.

dBm is not used too often in audio equipment. Though power is often the quantity we’re concerned with when amplifying signals for loudspeakers, we tend to use watts rather than dBm.

Like dBu, dBm is typically referenced relative to a 600-ohm impedance.

We know that electrical power is a power quantity, so the dBm equation is:

**dBm value = 10 • log _{10} (P / P_{0})**

**Where:P** is the power level (in milliwatts)

**is the reference point of 1 milliwatt**

**P**_{0}dBm is sometimes used to defined Bluetooth classes and Bluetooth technology is becoming more and more intertwined with audio technology. For example:

- Bluetooth Class 1 (30m range): 20 dBm = 100 mW
- Bluetooth Class 2 (10m range): 4 dBm = 2.5 mW
- Bluetooth Class 3 (1m range): 0 dBm = 1 mW

### dBFS

dBFS is shorthand for decibels relative to full scale.

dBFS is used in digital audio systems and references the maximum peak level of the audio signal.

The maximum peak level is reached at the end of the binary bit-depth resolution (all 1s in, typically speaking, a 16-bit or 24-bit system). All 0s, then, would represent no digital signal.

So then anything above 0 dBFS leads to digital clipping/distortion where the waveform is cleanly cut. Unlike analog distortion/saturation which sounds pleasing in appropraite amounts, we generally want to avoid digital clipping at all costs.

Therefore, we’d want dBFS values to be negative.

Though there’s no specific formula for dBFS, we know that for every -6 dBFS, we effectively halve the amplitude of the digital signal.

dBFS is not permitted alongside SI units (like volts, watts, Pascals, etc.). To make things easier to conceptualize, digital audio can be thought of as a representation of analog audio and dBFS can be thought of as a representation of “real” decibels.

Unfortunately, there is variation in dynamic range and oversampling between digital audio devices. There is no standard in place between dBFS and analog levels.

Instead, we have various specifications and suggestions around the world.

The European Broadcasting Union (EBU) has the following specs/suggestions:

- +18 dBu at 0 dBFS.
- −18 dBFS as the alignment level.
- Post & Film
^{ }is −18 dBFS = 0 VU.

UK broadcasters have alignment level set to 0 dBu (PPM 4 or -4 VU)

US broadcasters specify +24 dBu at 0 dBFS

American SMPTE (Society of Motion Picture and Television Engineers) standard defines:

- −20 dBFS = 0 VU = +4 dBu
- −20 dBFS as the alignment level.

There are many other standards in the world. When working with digital mastering levels, ensure you’re using whatever standard is set for the project.

dBTP (decibels relative to true peak) uses the dBFS but is measured with a true peak meter. True peak represents the maximum absolute level of the digital signal waveform. It gets very detailed to measure the peak levels of samples and the intersamples of the sigital audio.

LUFS (Loudness units relative to Full Scale) is often used instead of dBFS to better represent the perceived loudness of the digital audio.

### dB SPL

dB SPL is shorthand for decibels relative to the sound pressure threshold of human hearing.

We know that sound pressure level is a root-power quantity and so we have the following equation:

**dBV value = 20 • log _{10} (P / P_{0})**

**Where:P** is the sound pressure level (in Pascals)

**P**is the reference point of 2 x 10

_{0}^{-5}Pa or 0.0002 Pa

In the following table, we have dB SPL ratings along with their respective pressure measurements (in Pascals). Common examples of sources that produce these sound levels are also shown.

dB SPL | Pascal | Sound Source Example |
---|---|---|

0 dB SPL | 0.00002 Pa | Threshold of hearing |

10 dB SPL | 0.000063 Pa | Leaves rustling in the distance |

20 dB SPL | 0.0002 Pa | Background of a soundproof studio |

30 dB SPL | 0.00063 Pa | Quiet bedroom at night |

40 dB SPL | 0.002 Pa | Quiet library |

50 dB SPL | 0.0063 Pa | Average household with no talking |

60 dB SPL | 0.02 Pa | Normal conversational level (1 meter distance) |

70 dB SPL | 0.063 Pa | Vacuum cleaner (1 meter distance) |

80 dB SPL | 0.2 Pa | Average city traffic |

90 dB SPL | 0.63 Pa | Transport truck (10 meters) |

100 dB SPL | 2 Pa | Jackhammer |

110 dB SPL | 6.3 Pa | Threshold of discomfort |

120 dB SPL | 20 Pa | Ambulance siren |

130 dB SPL | 63 Pa | Jet engine taking off |

140 dB SPL | 200 Pa | Threshold of pain |

The varying sound pressure is generally refered to in a root-mean-square fashion (like the voltage of the audio signal) rather than as peak-to-peak.

RMS, again is a measurement of the “average” SPL. Averaging doesn’t work the case of SPL because it produces both positive and negative pressures relative to the ambient pressure of the medium.

Like in audio equipment, there is a limited amount of headroom for sound pressure level.

Headroom is defined as available (but ideally unused) dynamic‑range in audio and sound.

Headroom in digital audio is capped at 0 dBFS; headroom in audio equipment is capped at certain dBu or power limitations where distortion begins.

For sound pressure, the theoretical cap for headroom is the amount of atmospheric pressure. Standard atmospheric pressure for air is 101,325 Pa, though the actual pressure of air is certainly variable.

A common misconception is that the maximum sound pressure level before “clipping” is 194 dB SPL. This is shown in the formula:

**dB = 20 • log _{10} (P / P_{0})**

**Where: F** = 101,325 Pa

**= 0.00002 Pa**

**F**_{0}This gives us a dB SPL value just above 194 dB.

However, dB SPL is RMS not peak and so the actual max SPL should be lower than this. Of course, levels of this magnitude are not commonplace and have the potential to destroy life.

Now, sound is made of many different frequencies, all of which have a different way of reacting with the natural environment. There’s no simple way of testing for the maximum SPL possible without massive destruction.

At a single frequency and ideal conditions, we would require a peak amplitude of 101,325 Pa and, therefore, an rms value of 1√2 • 101,325 Pa = 71,648 Pa.

Plugging this value into our equation gives us a “max dB SPL” of 191 dB SPL (still ridiculously high!).

Above the theoretical limit, a “sound wave” will cause a vacuum (zero pressure) at its waveform troughs.

The instances in which this clipping occurs are rare.

Some historic moments where 191 dB SPL was exceeded include:

**1961:**Testing of the Soviet RDS-202 hydrogen bomb (estimated 224 dB SPL).**1908:**Tunguska meteor explosion (estimated 300 dB SPL)**1883:**Krakatoa volcano eruption (estimated 310 dB SPL)

As you can imagine, exceeding this limit is deadly.

### dBA (A-weighted)

dBA (A-weighted) are weighted to account for the variation in hearing perception across the audible range of frequencies.

dBA gives us a better representation of what we hear as opposed to dB SPL which is independent of frequency-specific sensitivities in human hearing.

Human hearing responds differently to different frequencies within the audible range of 20 Hz – 20,000Hz.

Generally speaking, we as humans are more sensitive to frequencies in the band between 400 Hz and 8,000 Hz than we are to low-end and high-end frequencies.

In other words, given the same sound pressure levels, we will perceive mid-range sounds as being louder than low-end or high-end frequencies.

This can be shown in the Fletcher-Munson Curves below:

We see the audible frequencies from 20 Hz to 20 kHz along the X-axis and the sound pressure level in dB SPL along the Y-axis.

The curves (lines) drawn on the diagram represent phons.

A phon is a unit of perceived loudness for pure sinewave tones (single frequencies).

The phon is psychophysically matched to a reference frequency of 1 kHz so that X dB SPL is equal to X phon at 1 kHz. At a given sound pressure level, the sine wave is then swept across other frequencies while perceived loudness is measured. Some frequencies a reperceived as being louder than the 1 kHz tone while others are perceived as being quieter. The phone gives us such information.

Again, hearing health plays a major factor in actual hearing sensitivity. The phone and Fletcher-Munson curves simply generalize for average human hearing.

As we can see from the curves, we’re most sensitivite to mid-range frequencies and particularly around 4 kHz where much of speech intelligibity resides.

As an example, let’s look at the 80 phon line and what it tells us. We can infer the following from the Fletcher-Munson curve and its 80-phon line:

- A 1 kHz tone at 80 dB SPL will sound equally as loud as a 4 kHz tone at 70 dB SPL.
- A 4 kHz tone at 70 dB SPL will sound equally as loud as a 70 Hz tone at 90 dB SPL.
- A 70 Hz tone at 90 dB SPL will sound equally as loud as a 10 kHz tone at 85 dB SPL.

There is great variation in the way we hear frequencies without the audible range and A-weighted decibels factor for this by reducing the effect of high and low-end frequencies on its measurements.

The NIOSH (National Institute for Occupational Safety and Health) and the OSHA (Occupational Safety and Health Administration) have published safe listening time limits at various decibel SPL levels (A-weighted). Their findings can be found in the following table:

NIOSH Standard (dBA) | Equivalent Sound Pressure Level (at 1 kHz) | Maximum Exposure Time Limit | OSHA Standard (dBA) | Equivalent Sound Pressure Level (at 1 kHz) |
---|---|---|---|---|

127 dBA | 127 dB SPL 44.8 Pa | 1 second | 160 dBA | 160 dB SPL 2.00 kPa |

124 dBA | 124 dB SPL 31.7 Pa | 3 seconds | 155 dBA | 155 dB SPL 1.12 kPa |

121 dBA | 121 dB SPL 22.4 Pa | 7 seconds | 150 dBA | 150 dB SPL 632 Pa |

118 dBA | 118 dB SPL 12.6 Pa | 14 seconds | 145 dBA | 145 dB SPL 356 Pa |

115 dBA | 115 dB SPL 11.2 Pa | 28 seconds | 140 dBA | 140 dB SPL 200 Pa |

112 dBA | 112 dB SPL 7.96 Pa | 56 seconds | 135 dBA | 135 dB SPL 112 Pa |

109 dBA | 109 dB SPL 5.64 Pa | 1 minute 52 seconds | 130 dBA | 130 dB SPL 63.2 Pa |

106 dBA | 106 dB SPL 3.99 Pa | 3 minutes 45 seconds | 125 dBA | 125 dB SPL 35.6 Pa |

103 dBA | 103 dB SPL 2.83 Pa | 7 minutes 30 seconds | 120 dBA | 120 dB SPL 20.0 Pa |

100 dBA | 100 dB SPL 2.00 Pa | 15 minutes | 115 dBA | 115 dB SPL 11.2 Pa |

97 dBA | 97 dB SPL 1.42 Pa | 30 minutes | 110 dBA | 110 dB SPL 6.32 Pa |

94 dBA | 94 dB SPL 1.00 Pa | 1 hour | 105 dBA | 105 dB SPL 3.56 Pa |

91 dBA | 91 dB SPL 0.71 Pa | 2 hours | 100 dBA | 100 dB SPL 2.00 Pa |

88 dBA | 88 dB SPL 0.50 Pa | 4 hours | 95 dBA | 95 dB SPL 1.12 Pa |

85 dBA | 85 dB SPL 0.36 Pa | 8 hours | 90 dBA | 90 dB SPL 0.63 Pa |

82 dBA | 82 dB SPL 0.25 Pa | 16 hours | 85 dBA | 85 dB SPL 0.36 Pa |

Hearing safety is important! I always advise following the protocols of one of the regulartors mentioned above.

### dBC (C-weighted)

Looking closer at the Fletcher-Munson curves, we see that human hearing flattens out (relatively) above 100 dB SPL.

C-weighting is reserved for measurements in the higher dB SPL ratings (<100 dB SPL). As mentioned earlier, these levels are in the territory of loud rock concerts and jackhammers and are not recommended for prolonged listening exposure.

So while the more popular A-weighted reduces the high and low-end frequencies rather significantly, the C-weighted scale does this filtering to a lesser extent to account for the “flattening” of the human hearing above 100 dB.

C-weighting is typically used for Peak measurements in audio equipment and some noise measurements where the transmission of bass noise can be an issue.

As we can imagine, the dBC is less common than the dBA.

### dBZ (Z-weighted)

Z-weighting maintain a flat frequency response between 10 Hz and 20 kHz with a tolerance of ±1.5dB.

dBZ aims to replace the older “Linear” or “Unweighted” dB SPL responses by defining a specific frequency range.

You’ll rarely, if ever, see dBZ ratings.

Back to the Table of Contents.

## The Use Of Decibels In Audio

**Decibels are regularly used to purvey audio equipment data. Let’s look at the ways in which decibels are used in audio:**

**Gain****Signal level****Maximum input level****Dynamic range****Transformer insertion loss**

**Noise****Common-mode rejection ratio****Crosstalk/channel separation****Self-noise (equivalent noise)****Signal-to-noise ratio**

**Power transfer****Sound pressure level****Sensitivity****Maximum sound pressure level**

**Passive attenuation device (pad)****Tolerance****Frequency response****Power bandwidth****Driver matching****Polar response****Coverage angle**

**EQ****Boosts/cuts****Filters/crossovers (dB/octave)**

**Noise cancellation****Passive noise cancellation****Active noise cancellation**

### Gain

Decibels are perhaps most commonly used to define gain. Gain is technically the ratio of an amplified output signal to the input signal (pre-amplification).

Gain is a unitless measurement that is technically defined as a ratio linear. Decibels provide a logarithmic scale for this ratio.

Amplification of audio signals is standard and gain is, too. Decibels are the conventional way to measure and state gain in audio amplifiers.

**Related articles:• What Is Microphone Gain And How Does It Affect Mic Signals?**

### Signal Level

Decibels are very common in defining the level of an audio signal.

**The two most common audio signal level decibel measurements are:**

**dBV:**decibels relative to a voltage of 1 volt.- 1 volt = 0 dBV

**dBu:**decibels relative to a voltage of 0.7746 volts.- 0.7746 volt = 0 dBu

**dBFS:**decibels relative to the digital ceiling of 0 dBFS.

**To put these two ratings into further perspective:**

- Consumer nominal line level = -10 dBV (0.3162 volts)
- Professional line level = +4 dBu (1.228 volts)
- Digital audio clipping happens above 0 dBFS

Here are some formulae for defining the analog audio signal levels (voltage):

**Level (in dB) = 20 • log (V / V _{0})**

**Voltage (in volts) = V _{0} • 10^{L (in dB) / 20}**

Where V_{0} = 1 V to measure dBV and V_{0} = 0.7746 to measure dBu.

These decibel units are used extensively to measure signal level.

**dBV, dBu and dBFS can be found in the following audio specifications:**

**Maximum Input Level:**the maximum signal strength that can drive an input without significant distortion and overload.**Dynamic Range:**the range between the quietest possible signal (noise floor) and the loudest possible signal.**Transformer Insertion Loss:**any loss of signal when connecting distributed speakers into a distributed system.

### Noise

Decibel values are also often used to specify noise in a signal.

**Common noise specifications for audio equipment include:**

**Common-Mode Rejection Ratio:**the amount of noise/interference rejection that happens as a result of the differential amplifier in a balanced input.**Crosstalk/Channel Separation:**the amount of signal that will spill from the right channel into the left channel and vice versa.**Self-Noise (Equivalent Noise):**the inherent noise produced by the electronics of an active audio device.**Signal-To-Noise Ratio:**the ratio of the intended signal to the unintended noise in an overall audio signal.

**Related articles:• What Is Microphone Self-Noise? (Equivalent Noise Level)• What Is A Good Signal-To-Noise Ratio For A Microphone?**

### Power Transfer

Power transfer refers to the amount of power that is transferred between audio devices (how much power is dissipated at the load). It is another way to tell us the strength of an audio signal.

Audio power is often measured in watts when it applied to power amplifiers and loudspeakers.

In other audio devices, it is often defined in dBm (decibels as referenced to 1 milliwatt).

0 dBm = 1 mW.

Technically speaking, this is a reference to power only and does not consider voltage, current or resistance/impedance.

That being said, conventions allow us to assume dBm to be referenced to 1 milliwatt dissipated into a 600Ω load.

With a 600Ω load, 0.775 V (0 dBu) will produce 1 mW (0 dBm).

dBm is not overly used anymore because of this assumption.

**The equation to calculate dBm is as follows:**

**dBm = 10 • log (P / P _{0})**

Where P_{0} = 1 mW

### Sound Pressure Level

Sound pressure level (SPL) measurements will tell us a lot about the strength of the sound waves. SPL can be measured linearly in Pascal (SI unit) or in pounds-per-square-inch (imperial unit).

However, SPL is more often measured in dB SPL. That is decibels of sound pressure relative to the threshold of human hearing (20 x 10^{-6} Pa or 20 µPa).

The equation to calculate dB SPL from typical Pascal pressure measurements is as follows:

**dB SPL = 20 • log (P / P _{0})**

Where P_{0} = 20 x 10^{-6} Pa

Audio transducers include microphones, headphones, loudspeakers and more.

Of these devices, dB SPL values are used to describe a few things, mainly:

- Sensitivity
- Maximum Sound Pressure Level

#### Sensitivity

Microphone sensitivity tells us how much signal level the microphone will output for a given sound pressure level at its diaphragm.

Headphone sensitivity tells us how much sound pressure the headphone will produce (at the ear of the listen when the headphone is worn as intended) when a given signal level (typically measured as 1 mW) is applied to it.

Loudspeaker sensitivity tells us how much sound pressure level, at a given distance (typically 1 meter), a loudspeaker will produce when a certain signal level (generally measured at 1 watt or 2.83 volts) is applied to it.

**Related articles:• Full Guide To Loudspeaker Sensitivity & Efficiency Ratings• The Complete Guide To Headphones Sensitivity Ratings• What Is Microphone Sensitivity? An In-Depth Description**

#### Maximum Sound Pressure Level

The maximum sound pressure level of a microphones tells us how much SPL the microphone can effectively convert into an audio signal without distorting.

The maximum sound pressure level (often referred to as maximum output level) for headphones and loudspeakers refers to the maximum SPL (measured at a given distance) the device will produce without significant distortion.

**Related article:What Does A Microphone’s Maximum Sound Pressure Level Actually Mean?**

### Passive Attenuation Device (Pad)

A pad is a passive switchable circuit that is featured in some audio equipment that works to drop the level of the signal by a defined amount. The amount of attenuation is predetermined in the pad design and is generally measured in decibels.

More specifically, pad values are defined in negative dB values (as they compare to the attenuated output signal level to the input signal level).

**Related article:****• What Is A Microphone Attenuation Pad And What Does It Do?**

### Tolerance

Tolerance is the “margin or error” or “margin of fluctuation” that helps give other specifications meaning.

The tolerance is typically measured in decibels (as a comparison to the average value or the on-point value). It is the measurements after the “+/-” or “±” signs.

Having a tolerance gives us a much better idea of any ranges in audio. It can commonly be seen in the following audio device specifications:

#### Frequency Response

Frequency response refers to the frequency-specific sensitivity of an audio device.

In other words, how well (and evenly) will an audio device produce, reproduce, or process the audio signal. Will the audio device colour the signal by cutting out certain frequencies while reducing or boosting some others?

Note that the range of human hearing is 20 Hz to 20,000 Hz.

**Frequency response is best shown with a graph:**

**Frequency (in Hertz) along the X-axis****Sensitivity (in decibels) along the Y-axis**

Here is the Shure SM57 (link to compare prices at select retailers) frequency response graph as an example. We can see that:

- The SM57 is incapable of producing 20 Hz to 20,000 Hz.
- Not all frequencies that the microphone will output will be equally represented in the output signal.

Frequency response, however, is generally only defined as a range between the lowest frequency the unit is capable of handling and the highest frequency the unit is capable of handling.

The ranges are fairly useless without some sort of tolerance value that will tell us the points at which the unit’s frequency-dependent processing/sensitivity will fall off.

As an example, 20 Hz – 20,000 Hz is much less descriptive as 20 Hz – 20,000 Hz ± 3 dB.

**Related articles:• What Is Headphone Frequency Response & What Is A Good Range?• Complete Guide To Microphone Frequency Response (With Mic Examples)**

#### Power Bandwidth

This specification is pretty much the same as frequency response. It refer to the bandwidth (frequency range) than an amplifier can effectively output.

Though a graph would best for comprehension, a tolerance value (measured in dB) is very useful to understand power bandwidth.

#### Driver Matching

This is a headphone specification that tells us the maximum room for error for the relative output levels of the two drivers (left and right).

#### Polar Response

The polar response (also known as the polar pattern) of a microphone refers to the directionality of that microphone.

In other words, it tells us, relative to the on-axis direction of the microphone, how the microphone will pick up sound from all other directions.

This microphone specification is best defined with a graph, like that of the aforementioned Shure SM57 cardioid microphone. We can see from the graphs below that:

- Polar pattern varies with frequency (becoming more directional at higher frequencies).
- The most sensitive point is on-axis (0º) and is set at 0 dB. All other angles are relative to that 0 dB reference.

Aside (or instead of) a graph, a microphone may have a qualitative polar pattern title (such as the cardioid pattern mentioned above). It may also have an angle of acceptance with a “tolerance” or cutoff frequency.

For example, the Shure SM57 could have a pickup pattern acceptance angle of 60º ± 3 dB

**Related articles:• The Complete Guide To Microphone Polar Patterns• What Is An Omnidirectional Microphone? (Polar Pattern + Mic Examples)• What Is A Supercardioid Microphone? (Polar Pattern + Mic Examples)• What Is A Hypercardioid Microphone? (Polar Pattern + Mic Examples)• The Lobar/Shotgun Microphone Polar Pattern (With Mic Examples)• The Hemispherical Boundary Microphone/PZM Polar Pattern• What Is A Cardioid Microphone? (Polar Pattern + Mic Examples)**

#### Coverage Angle

Coverage angle refer to the output of a loudspeaker. Most speakers are at least somewhat directional (especially at mid and upper frequencies) due to their relatively large drivers and enclosures.

Decibels relative to the on-axis response are useful for determining a set cutoff point/threshold at which the speaker’s directionality can be defined by.

### EQ

Decibels are used to define the frequency-dependent cutting and boosting that happens with audio equalization.

Filters (including those used in speaker crossovers) can also be defined using decibels. More specifically, filters are largely defined by the roll-off (decibels/octave) in which they reduce the level of the audio.

### Noise Cancellation

Noise cancellation is a headphone specification that tells us how much the headphone will block out external noise. This is typically measured in decibels relative to the “noise” we would otherwise hear had we not worn the headphones.

This is true of passive and active noise cancellation.

Passive noise cancellation is the simple mechanical blockage of sound waves from entering the ear canal.

Active noise cancellation refers to the use of complex circuits complete with microphones; feed-forward and feedback circuitry; phase and volume adjustments, and speakers to inject the anti-noise sound waves into the headphone output.

**Related articles:• Passive Vs. Active Noise-Cancelling Headphones• How Do Noise-Cancelling Headphones Work? (PNC & ANC)• Do Noise-Cancelling Headphones Work With Or Without Music?**

Back to the Table of Contents.

## Related Questions

How loud can a human yell? **The loudest human scream to be measured was 129 dB performed by Jill Drake. A typical human with healthy lungs and vocal chords can be expected to produce a yell in the range of 110 dB – 120 dB.**

Can you hear a 1 dB difference? **A 1 dB difference in the SPL of a sound wave will cause a change of about 7% in the perceived loudness of that sound wave. Many would consider a 1 dB difference to be the threshold of perceived difference in a sound though most people would not be able to perceive this difference.**