# Decibel

dB | Power ratio | Amplitude ratio | ||
---|---|---|---|---|

100 | 10000000000 | 100000 | ||

90 | 1000000000 | 31623 | ||

80 | 100000000 | 10000 | ||

70 | 10000000 | 3162 | ||

60 | 1000000 | 1000 | ||

50 | 100000 | 316 | .2 | |

40 | 10000 | 100 | ||

30 | 1000 | 31 | .62 | |

20 | 100 | 10 | ||

10 | 10 | 3 | .162 | |

6 | 3 | .981 ≈ 4 | 1 | .995 ≈ 2 |

3 | 1 | .995 ≈ 2 | 1 | .413 ≈ √2 |

1 | 1 | .259 | 1 | .122 |

0 | 1 | 1 | ||

−1 | 0 | .794 | 0 | .891 |

−3 | 0 | .501 ≈ ^{1}⁄_{2} |
0 | .708 ≈ √^{1}⁄_{2} |

−6 | 0 | .251 ≈ ^{1}⁄_{4} |
0 | .501 ≈ ^{1}⁄_{2} |

−10 | 0 | .1 | 0 | .3162 |

−20 | 0 | .01 | 0 | .1 |

−30 | 0 | .001 | 0 | .03162 |

−40 | 0 | .0001 | 0 | .01 |

−50 | 0 | .00001 | 0 | .003162 |

−60 | 0 | .000001 | 0 | .001 |

−70 | 0 | .0000001 | 0 | .0003162 |

−80 | 0 | .00000001 | 0 | .0001 |

−90 | 0 | .000000001 | 0 | .00003162 |

−100 | 0 | .0000000001 | 0 | .00001 |

An example scale showing power ratios x, amplitude ratios √x, and dB equivalents 10 log_{10} x. |

The **decibel** (symbol: dB) is a unit of measurement used to express the ratio of one value of a physical property to another on a logarithmic scale. It can be used to express a change in value (e.g., +1 dB or −1 dB) or an absolute value. In the latter case, it expresses the ratio of a value to a reference value; when used in this way, the decibel symbol should be appended with a suffix that indicates the reference value, or some other property. For example, if the reference value is 1 volt, then the suffix is "V" (e.g., "20 dBV"), and if the reference value is one milliwatt, then the suffix is "m" (e.g., "20 dBm").^{[1]}

There are two different scales used when expressing a ratio in decibels depending on the nature of the quantities: field, power, and root-power. When expressing power quantities, the number of decibels is ten times the logarithm to base 10 of the ratio of two power quantities.^{[2]} That is, a change in *power* by a factor of 10 corresponds to a 10 dB change in level. When expressing field quantities, a change in *amplitude* by a factor of 10 corresponds to a 20 dB change in level. The extra factor of two is due to the logarithm of the quadratic relationship between power and amplitude. The decibel scales differ so that direct comparisons can be made between related power and field quantities when they are expressed in decibels.

The definition of the decibel is based on the measurement of power in telephony of the early 20th century in the Bell System in the United States. One decibel is one tenth (deci-) of one **bel**, named in honor of Alexander Graham Bell; however, the bel is seldom used. Today, the decibel is used for a wide variety of measurements in science and engineering, most prominently in acoustics, electronics, and control theory. In electronics, the gains of amplifiers, attenuation of signals, and signal-to-noise ratios are often expressed in decibels.

In the International System of Quantities, the decibel is defined as a unit of measurement for quantities of type level or level difference, which are defined as the logarithm of the ratio of power- or field-type quantities.^{[3]}

## History

The decibel originates from methods used to quantify signal loss in telegraph and telephone circuits. The unit for loss was originally *Miles of Standard Cable* (MSC). 1 MSC corresponded to the loss of power over a 1 mile (approximately 1.6 km) length of standard telephone cable at a frequency of 5000 radians per second (795.8 Hz), and matched closely the smallest attenuation detectable to the average listener. The standard telephone cable implied was "a cable having uniformly distributed resistance of 88 Ohms per loop-mile and uniformly distributed shunt capacitance of 0.054 microfarads per mile" (approximately corresponding to 19 gauge wire).^{[4]}

In 1924, Bell Telephone Laboratories received favorable response to a new unit definition among members of the International Advisory Committee on Long Distance Telephony in Europe and replaced the MSC with the *Transmission Unit* (TU). 1 TU was defined such that the number of TUs was ten times the base-10 logarithm of the ratio of measured power to a reference power.^{[5]}
The definition was conveniently chosen such that 1 TU approximated 1 MSC; specifically, 1 MSC was 1.056 TU. In 1928, the Bell system renamed the TU into the decibel,^{[6]} being one tenth of a newly defined unit for the base-10 logarithm of the power ratio. It was named the *bel*, in honor of the telecommunications pioneer Alexander Graham Bell.^{[7]}
The bel is seldom used, as the decibel was the proposed working unit.^{[8]}

The naming and early definition of the decibel is described in the NBS Standard's Yearbook of 1931:^{[9]}

Since the earliest days of the telephone, the need for a unit in which to measure the transmission efficiency of telephone facilities has been recognized. The introduction of cable in 1896 afforded a stable basis for a convenient unit and the "mile of standard" cable came into general use shortly thereafter. This unit was employed up to 1923 when a new unit was adopted as being more suitable for modern telephone work. The new transmission unit is widely used among the foreign telephone organizations and recently it was termed the "decibel" at the suggestion of the International Advisory Committee on Long Distance Telephony.

The decibel may be defined by the statement that two amounts of power differ by 1 decibel when they are in the ratio of 10

^{0.1}and any two amounts of power differ byNdecibels when they are in the ratio of 10^{N(0.1)}. The number of transmission units expressing the ratio of any two powers is therefore ten times the common logarithm of that ratio. This method of designating the gain or loss of power in telephone circuits permits direct addition or subtraction of the units expressing the efficiency of different parts of the circuit ...

In 1954, C. W. Horton argued that the use of the decibel as a unit for quantities other than transmission loss led to confusion, and suggested the name 'logit' for "standard magnitudes which combine by addition".^{[10]}

In April 2003, the International Committee for Weights and Measures (CIPM) considered a recommendation for the inclusion of the decibel in the International System of Units (SI), but decided against the proposal.^{[11]} However, the decibel is recognized by other international bodies such as the International Electrotechnical Commission (IEC) and International Organization for Standardization (ISO).^{[12]} The IEC permits the use of the decibel with field quantities as well as power and this recommendation is followed by many national standards bodies, such as NIST, which justifies the use of the decibel for voltage ratios.^{[13]} The term *field quantity* is deprecated by ISO 80000-1, which favors root-power. In spite of their widespread use, suffixes (such as in dBA or dBV) are not recognized by the IEC or ISO.

## Definition

ISO 80000-3 describes definitions for quantities and units of space and time. The decibel for use in acoustics is defined in ISO 80000-8. The major difference from the article below is that for acoustics the decibel has no absolute value.

The ISO Standard 80000-3:2006 defines the following quantities. The decibel (dB) is one-tenth of a bel: 1 dB = 0.1 B. The bel (B) is ^{1}⁄_{2} ln(10) nepers: 1 B = ^{1}⁄_{2} ln(10) Np. The neper is the change in the level of a field quantity when the field quantity changes by a factor of *e*, that is 1 Np = ln(e) = 1, thereby relating all of the units as nondimensional natural log of field-quantity ratios, 1 dB = 0.11513… Np = 0.11513…. Finally, the level of a quantity is the logarithm of the ratio of the value of that quantity to a reference value of the same kind of quantity.

Therefore, the bel represents the logarithm of a ratio between two power quantities of 10:1, or the logarithm of a ratio between two field quantities of √10:1.^{[14]}

Two signals whose levels differ by one decibel have a power ratio of 10^{1/10}, which is approximately 1.25893, and an amplitude (field quantity) ratio of 10^{1⁄20} (1.12202).^{[15]}^{[16]}

The bel is rarely used either without a prefix or with SI unit prefixes other than *deci*; it is preferred, for example, to use *hundredths of a decibel* rather than *millibels*. Thus, five one-thousandths of a bel would normally be written '0.05 dB', and not '5 mB'.^{[17]}

The method of expressing a ratio as a level in decibels depends on whether the measured property is a *power quantity* or a *field quantity*; see Field, power, and root-power quantities for details.

### Power quantities

When referring to measurements of *power* quantities, a ratio can be expressed as a level in decibels by evaluating ten times the base-10 logarithm of the ratio of the measured quantity to reference value. Thus, the ratio of *P* (measured power) to *P*_{0} (reference power) is represented by *L*_{P}, that ratio expressed in decibels,^{[18]} which is calculated using the formula:^{[3]}

The base-10 logarithm of the ratio of the two power quantities is the number of bels. The number of decibels is ten times the number of bels (equivalently, a decibel is one-tenth of a bel). *P* and *P*_{0} must measure the same type of quantity, and have the same units before calculating the ratio. If *P* = *P*_{0} in the above equation, then *L*_{P} = 0. If *P* is greater than *P*_{0} then *L*_{P} is positive; if *P* is less than *P*_{0} then *L*_{P} is negative.

Rearranging the above equation gives the following formula for *P* in terms of *P*_{0} and *L*_{P}:

### Field quantities and root-power quantities

When referring to measurements of field quantities, it is usual to consider the ratio of the squares of *F* (measured field) and *F*_{0} (reference field). This is because in most applications power is proportional to the square of field, and it is desirable for the two decibel formulations to give the same result in such typical cases. Thus, the following definition is used:

The formula may be rearranged to give

Similarly, in electrical circuits, dissipated power is typically proportional to the square of voltage or current when the impedance is held constant. Taking voltage as an example, this leads to the equation:

where *V* is the voltage being measured, *V*_{0} is a specified reference voltage, and *G*_{dB} is the power gain expressed in decibels. A similar formula holds for current.

The term *root-power quantity* is introduced by ISO Standard 80000-1:2009 as a substitute of *field quantity*. The term *field quantity* is deprecated by that standard.

### Conversions

Since logarithm differences measured in these units are used to represent power ratios and field ratios, the values of the ratios represented by each unit are also included in the table.

Unit | In decibels | In bels | In nepers | Power ratio | Field ratio |
---|---|---|---|---|---|

1 dB | 1 dB | 0.1 B | 0.11513 Np | 10^{1⁄10} ≈ 1.25893 | 10^{1⁄20} ≈ 1.12202 |

1 Np | 8.68589 dB | 0.868589 B | 1 Np | e^{2} ≈ 7.38906 | e ≈ 2.71828 |

1 B | 10 dB | 1 B | 1.1513 Np | 10 | 10^{1⁄2} ≈ 3.16228 |

### Examples

All of these examples yield dimensionless answers in dB because they are relative ratios expressed in decibels. The unit dBW is often used to denote a ratio for which the reference is 1 W, and similarly dBm for a 1 mW reference point.

- Calculating the ratio of 1 kW (one kilowatt, or 1000 watts) to 1 W in decibels yields:

- The ratio of √1000 V ≈ 31.62 V to 1 V in decibels is

(31.62 V/1 V)^{2} ≈ 1 kW/1 W, illustrating the consequence from the definitions above that *G*_{dB} has the same value, 30, regardless of whether it is obtained from powers or from amplitudes, provided that in the specific system being considered power ratios are equal to amplitude ratios squared.

- The ratio of 1 mW (one milliwatt) to 10 W in decibels is obtained with the formula

- The power ratio corresponding to a 3 dB change in level is given by

A change in power ratio by a factor of 10 corresponds to a change in level of 10 dB. A change in power ratio by a factor of 2 or ^{1}⁄_{2} is approximately a change of 3 dB. More precisely, the change is ±3.0103 dB, but this is almost universally rounded to "3 dB" in technical writing. This implies an increase in voltage by a factor of √2 ≈ 1.4142. Likewise, a doubling or halving of the voltage, and quadrupling or quartering of the power, is commonly described as "6 dB" rather than ±6.0206 dB.

Should it be necessary to make the distinction, the number of decibels is written with additional significant figures. 3.00 dB is a power ratio of 10^{3⁄10}, or 1.9953, about 0.24% different from exactly 2, and a voltage ratio of 1.4125, 0.12% different from exactly √2. Similarly, an increase of 6.00 dB is the power ratio is 10^{6⁄10} ≈ 3.9811, about 0.5% different from 4.

## Properties

The decibel is useful for representing large ratios and for simplifying representation of multiplied effects such as attenuation from multiple sources along a signal chain. Its application in systems with additive effects is less intuitive.

### Reporting large ratios

The logarithmic scale nature of the decibel means that a very large range of ratios can be represented by a convenient number, in a similar manner to scientific notation. This allows one to clearly visualize huge changes of some quantity. See Bode plot and semi-log plot. For example, 120 dB SPL may be clearer than "a trillion times more intense than the threshold of hearing".

### Representation of multiplication operations

Level values in decibels can be added instead of multiplying the underlying power values, which means that the overall gain of a multi-component system, such as a series of amplifier stages, can be calculated by summing the gains in decibels of the individual components, rather than multiply the amplification factors; that is, log(*A* × *B* × *C*) = log(*A*) + log(*B*) + log(*C*). Practically, this means that, armed only with the knowledge that 1 dB is approximately 26% power gain, 3 dB is approximately 2× power gain, and 10 dB is 10× power gain, it is possible to determine the power ratio of a system from the gain in dB with only simple addition and multiplication. For example:

- A system consists of 3 amplifiers in series, with gains (ratio of power out to in) of 10 dB, 8 dB, and 7 dB respectively, for a total gain of 25 dB. Broken into combinations of 10, 3, and 1 dB, this is:
- 25 dB = 10 dB + 10 dB + 3 dB + 1 dB + 1 dB

- With an input of 1 watt, the output is approximately
- 1 W × 10 × 10 × 2 × 1.26 × 1.26 ≈ 317.5 W

- Calculated exactly, the output is 1 W × 10
^{25⁄10}= 316.2 W. The approximate value has an error of only +0.4% with respect to the actual value which is negligible given the precision of the values supplied and the accuracy of most measurement instrumentation.

- A system consists of 3 amplifiers in series, with gains (ratio of power out to in) of 10 dB, 8 dB, and 7 dB respectively, for a total gain of 25 dB. Broken into combinations of 10, 3, and 1 dB, this is:

However, according to its critics, the decibel creates confusion, obscures reasoning, is more related to the era of slide rules than to modern digital processing, and is cumbersome and difficult to interpret.^{[19]}

### Representation of addition operations

According to Mitschke,^{[20]} "The advantage of using a logarithmic measure is that in a transmission chain, there are many elements concatenated, and each has its own gain or attenuation. To obtain the total, addition of decibel values is much more convenient than multiplication of the individual factors." However, for the same reason that humans excel at additive operation over multiplication, decibels are awkward in inherently additive operations:^{[21]} "if two machines each individually produce a [sound pressure] level of, say, 90 dB at a certain point, then when both are operating together we should expect the combined sound pressure level to increase to 93 dB, but certainly not to 180 dB!" "suppose that the noise from a machine is measured (including the contribution of background noise) and found to be 87 dBA but when the machine is switched off the background noise alone is measured as 83 dBA. ... the machine noise [level (alone)] may be obtained by 'subtracting' the 83 dBA background noise from the combined level of 87 dBA; i.e., 84.8 dBA." "in order to find a representative value of the sound level in a room a number of measurements are taken at different positions within the room, and an average value is calculated. (...) Compare the logarithmic and arithmetic averages of ... 70 dB and 90 dB: logarithmic average = 87 dB; arithmetic average = 80 dB."

Quantities in decibels are not necessarily additive,^{[22]}^{[23]} thus being "of unacceptable form for use in dimensional analysis".^{[24]}

## Uses

### Perception

The human perception of the intensity of sound and light approximates the logarithm of intensity rather than a linear relationship (Weber–Fechner law), making the dB scale a useful measure.^{[25]}^{[26]}^{[27]}^{[28]}^{[29]}^{[30]}

### Acoustics

The decibel is commonly used in acoustics as a unit of sound pressure level. The reference pressure for sound in air is set at the typical threshold of perception of an average human and there are common comparisons used to illustrate different levels of sound pressure. Sound pressure is a field quantity, therefore the field version of the unit definition is used:

where *p*_{rms} is the root mean square of the measured sound pressure in pascals and *p*_{ref} is the standard reference sound pressure of 20 micropascals in air or 1 micropascal in water.^{[31]}

Use of the decibel in underwater acoustics leads to confusion, in part because of this difference in reference value.^{[32]}

The human ear has a large dynamic range in sound reception. The ratio of the sound intensity that causes permanent damage during short exposure to that of the quietest sound that the ear can hear is greater than or equal to 1 trillion (10^{12}).^{[33]} Such large measurement ranges are conveniently expressed in logarithmic scale: the base-10 logarithm of 10^{12} is 12, which is expressed as a sound pressure level of 120 dB re 20 μPa.

Since the human ear is not equally sensitive to all sound frequencies, noise levels at maximum human sensitivity, somewhere between 2 and 4 kHz, are factored more heavily into some measurements using frequency weighting. (See also Stevens' power law.)

The main instrument used for measuring sound levels in the environment and in the workplace is the Sound Level Meter. Most sound level meters provide readings in A, C, and Z-weighted decibels and must meet international standards such as IEC 61672 - 2013.

According to Hickling, "Decibels are a useless affectation, which is impeding the development of noise control as an engineering discipline".^{[19]}

### Electronics

In electronics, the decibel is often used to express power or amplitude ratios (gains), in preference to arithmetic ratios or percentages. One advantage is that the total decibel gain of a series of components (such as amplifiers and attenuators) can be calculated simply by summing the decibel gains of the individual components. Similarly, in telecommunications, decibels denote signal gain or loss from a transmitter to a receiver through some medium (free space, waveguide, coaxial cable, fiber optics, etc.) using a link budget.

The decibel unit can also be combined with a suffix to create an absolute unit of electric power. For example, it can be combined with "m" for "milliwatt" to produce the "dBm". A power level of 0 dBm corresponds to one milliwatt, and 1 dBm is one decibel greater (about 1.259 mW).

In professional audio specifications, a popular unit is the dBu. This is relative to the root mean square voltage which delivers 1 mW (0 dBm) into a 600-ohm resistor, or √1 mW×600 Ω ≈ 0.775 V_{RMS}. When used in a 600-ohm circuit (historically, the standard reference impedance in telephone circuits), dBu and dBm are identical.

### Optics

In an optical link, if a known amount of optical power, in dBm (referenced to 1 mW), is launched into a fiber, and the losses, in dB (decibels), of each component (e.g., connectors, splices, and lengths of fiber) are known, the overall link loss may be quickly calculated by addition and subtraction of decibel quantities.^{[34]}

In spectrometry and optics, the blocking unit used to measure optical density is equivalent to −1 B.

### Video and digital imaging

In connection with video and digital image sensors, decibels generally represent ratios of video voltages or digitized light intensities, using 20 log of the ratio, even when the represented optical power is directly proportional to the voltage, not to its square, as in a CCD imager where response voltage is linear in intensity.^{[35]}
Thus, a camera signal-to-noise ratio or dynamic range quoted as 40 dB represents a power ratio of 100:1 between signal power and noise power, not 10,000:1.^{[36]}
Sometimes the 20 log ratio definition is applied to electron counts or photon counts directly, which are proportional to intensity without the need to consider whether the voltage response is linear.^{[37]}

However, as mentioned above, the 10 log intensity convention prevails more generally in physical optics, including fiber optics, so the terminology can become murky between the conventions of digital photographic technology and physics. Most commonly, quantities called "dynamic range" or "signal-to-noise" (of the camera) would be specified in 20 log dB, but in related contexts (e.g. attenuation, gain, intensifier SNR, or rejection ratio) the term should be interpreted cautiously, as confusion of the two units can result in very large misunderstandings of the value.

Photographers typically use an alternative base-2 log unit, the stop, to describe light intensity ratios or dynamic range.

## Suffixes and reference values

Suffixes are commonly attached to the basic dB unit in order to indicate the reference value by which the ratio is calculated. For example, dBm indicates power measurement relative to 1 milliwatt.

In cases where the unit value of the reference is stated, the decibel value is known as "absolute". If the unit value of the reference is not explicitly stated, as in the dB gain of an amplifier, then the decibel value is considered relative.

The SI does not permit attaching qualifiers to units, whether as suffix or prefix, other than standard SI prefixes. Therefore, even though the decibel is accepted for use alongside SI units, the practice of attaching a suffix to the basic dB unit, forming compound units such as dBm, dBu, dBA, etc., is not.^{[13]} The proper way, according to the IEC 60027-3,^{[12]} is either as *L*_{x} (re *x*_{ref}) or as *L*_{x/xref}, where *x* is the quantity symbol and *x*_{ref} is the value of the reference quantity, e.g., *L*_{E} (re 1 μV/m) = *L*_{E/(1 μV/m)} for the electric field strength *E* relative to 1 μV/m reference value.

Outside of documents adhering to SI units, the practice is very common as illustrated by the following examples. There is no general rule, with various discipline-specific practices. Sometimes the suffix is a unit symbol ("W","K","m"), sometimes it is a transliteration of a unit symbol ("uV" instead of μV for microvolt), sometimes it is an acronym for the unit's name ("sm" for square meter, "m" for milliwatt), other times it is a mnemonic for the type of quantity being calculated ("i" for antenna gain with respect to an isotropic antenna, "λ" for anything normalized by the EM wavelength), or otherwise a general attribute or identifier about the nature of the quantity ("A" for A-weighted sound pressure level). The suffix is often connected with a dash (dB-Hz), with a space (dB HL), with no intervening character (dBm), or enclosed in parentheses, dB(sm).

### Voltage

Since the decibel is defined with respect to power, not amplitude, conversions of voltage ratios to decibels must square the amplitude, or use the factor of 20 instead of 10, as discussed above.

- dBV
- dB(V
_{RMS}) – voltage relative to 1 volt, regardless of impedance.^{[1]}This is used to measure microphone sensitivity, and also to specify the consumer line-level of −10 dBV, in order to reduce manufacturing costs relative to equipment using a +4 dBu line-level signal.^{[38]}

- dBu or dBv
- RMS voltage relative to
. An RMS voltage of 1 V is therefore corresponds to
^{[1]}Originally dBv, it was changed to dBu to avoid confusion with dBV.^{[39]}The "v" comes from "volt", while "u" comes from the volume*unit*used in the VU meter.^{[40]}dBu can be used as a measure of voltage, regardless of impedance, but is derived from a 600 Ω load dissipating 0 dBm (1 mW). The reference voltage comes from the computation . In professional audio, equipment may be calibrated to indicate a "0" on the VU meters some finite time after a signal has been applied at an amplitude of +4 dBu. Consumer equipment typically uses a lower "nominal" signal level of −10 dBV.^{[41]}Therefore, many devices offer dual voltage operation (with different gain or "trim" settings) for interoperability reasons. A switch or adjustment that covers at least the range between +4 dBu and −10 dBV is common in professional equipment.

- dBu0s
- Defined by Recommendation ITU-R V.574.

- dBm0s
- Defined by Recommendation ITU-R V.574.;dBmV: dB(mV
_{RMS}) – voltage relative to 1 millivolt across 75 Ω.^{[42]}Widely used in cable television networks, where the nominal strength of a single TV signal at the receiver terminals is about 0 dBmV. Cable TV uses 75 Ω coaxial cable, so 0 dBmV corresponds to −78.75 dBW (−48.75 dBm) or approx. 13 nW.

- dBμV or dBuV
- dB(μV
_{RMS}) – voltage relative to 1 microvolt. Widely used in television and aerial amplifier specifications. 60 dBμV = 0 dBmV.

### Acoustics

Probably the most common usage of "decibels" in reference to sound level is dB SPL, sound pressure level referenced to the nominal threshold of human hearing:^{[43]} The measures of pressure (a field quantity) use the factor of 20, and the measures of power (e.g. dB SIL and dB SWL) use the factor of 10.

- dB SPL
- dB SPL (sound pressure level) – for sound in air and other gases, relative to 20 micropascals (μPa) = 2×10
^{−5}Pa, approximately the quietest sound a human can hear. For sound in water and other liquids, a reference pressure of 1 μPa is used.^{[44]}An RMS sound pressure of one pascal corresponds to a level of 94 dB SPL. - dB SIL
- dB sound intensity level – relative to 10
^{−12}W/m^{2}, which is roughly the threshold of human hearing in air. - dB SWL
- dB sound power level – relative to 10
^{−12}W. - dBA, dBB, and dBC
- These symbols are often used to denote the use of different weighting filters, used to approximate the human ear's response to sound, although the measurement is still in dB (SPL). These measurements usually refer to noise and its effects on humans and other animals, and they are widely used in industry while discussing noise control issues, regulations and environmental standards. Other variations that may be seen are dB
_{A}or dB(A). According to ANSI standards,^{[45]}the preferred usage is to write L_{A}= x dB. Nevertheless, the units dBA and dB(A) are still commonly used as a shorthand for A-weighted measurements. Compare dBc, used in telecommunications. - dB HL
- dB hearing level is used in audiograms as a measure of hearing loss. The reference level varies with frequency according to a minimum audibility curve as defined in ANSI and other standards, such that the resulting audiogram shows deviation from what is regarded as 'normal' hearing.
- dB Q
- sometimes used to denote weighted noise level, commonly using the ITU-R 468 noise weighting
- dBpp
- relative to the peak to peak sound pressure.
^{[46]} - dBG
- G-weighted spectrum
^{[47]}

### Audio electronics

See also dBV and dBu above.

- dBm
- dB(mW) – power relative to 1 milliwatt. In audio and telephony, dBm is typically referenced relative to a 600 ohm impedance,
^{[48]}which corresponds to a voltage level of 0.775 volts or 775 millivolts. - dBFS
- dB(full scale) – the amplitude of a signal compared with the maximum which a device can handle before clipping occurs. Full-scale may be defined as the power level of a full-scale sinusoid or alternatively a full-scale square wave. A signal measured with reference to a full-scale sine-wave will appear 3 dB weaker when referenced to a full-scale square wave, thus: 0 dBFS(fullscale sine wave) = −3 dBFS(fullscale square wave).
- dBVU
- dB volume unit
^{[49]} - dBTP
- dB(true peak) – peak amplitude of a signal compared with the maximum which a device can handle before clipping occurs.
^{[50]}In digital systems, 0 dBTP would equal the highest level (number) the processor is capable of representing. Measured values are always negative or zero, since they are less than or equal to full-scale. - dBm0
- Power in dBm measured at a zero transmission level point.

### Radar

- dBZ
- dB(Z) – decibel relative to Z = 1 mm
^{6}·m^{−3}:^{[51]}energy of reflectivity (weather radar), related to the amount of transmitted power returned to the radar receiver. Values above 15–20 dBZ usually indicate falling precipitation.^{[52]} - dBsm
- dB(m
^{2}) – decibel relative to one square meter: measure of the radar cross section (RCS) of a target. The power reflected by the target is proportional to its RCS. "Stealth" aircraft and insects have negative RCS measured in dBsm, large flat plates or non-stealthy aircraft have positive values.^{[53]}

### Radio power, energy, and field strength

- dBc
- relative to carrier—in telecommunications, this indicates the relative levels of noise or sideband power, compared with the carrier power. Compare dBC, used in acoustics.
- dBpp
- relative to the maximum value of the peak power.
- dBJ
- energy relative to 1 joule. 1 joule = 1 watt second = 1 watt per hertz, so power spectral density can be expressed in dBJ.
- dBm
- dB(mW) – power relative to 1 milliwatt. In the radio field, dBm is usually referenced to a 50 ohm load, with the resultant voltage being 0.224 volts.
^{[54]} - dBμV/m, dBuV/m, or dBμ
^{[55]}dB(μV/m) – electric field strength relative to 1 microvolt per meter. Often used to specify the signal strength from a television broadcast at a receiving site (the signal measured*at the antenna output*will be in dBμV).- dBf
- dB(fW) – power relative to 1 femtowatt.
- dBW
- dB(W) – power relative to 1 watt.
- dBk
- dB(kW) – power relative to 1 kilowatt.
- dBe
- dB electrical.
- dBo
- dB optical. A change of 1 dBo in optical power can result in a change of up to 2 dBe in electrical signal power in system that is thermal noise limited.
^{[56]}

### Antenna measurements

- dBi
- dB(isotropic) – the forward gain of an antenna compared with the hypothetical isotropic antenna, which uniformly distributes energy in all directions. Linear polarization of the EM field is assumed unless noted otherwise.
- dBd
- dB(dipole) – the forward gain of an antenna compared with a half-wave dipole antenna. 0 dBd = 2.15 dBi
- dBiC
- dB(isotropic circular) – the forward gain of an antenna compared to a circularly polarized isotropic antenna. There is no fixed conversion rule between dBiC and dBi, as it depends on the receiving antenna and the field polarization.
- dBq
- dB(quarterwave) – the forward gain of an antenna compared to a quarter wavelength whip. Rarely used, except in some marketing material. 0 dBq = −0.85 dBi
- dBsm
- dB(m
^{2}) – decibel relative to one square meter: measure of the antenna effective area.^{[57]} - dBm
^{−1} - dB(m
^{−1}) – decibel relative to reciprocal of meter: measure of the antenna factor.

### Other measurements

- dB-Hz
- dB(Hz) – bandwidth relative to one hertz. E.g., 20 dB-Hz corresponds to a bandwidth of 100 Hz. Commonly used in link budget calculations. Also used in carrier-to-noise-density ratio (not to be confused with carrier-to-noise ratio, in dB).
- dBov or dBO
- dB(overload) – the amplitude of a signal (usually audio) compared with the maximum which a device can handle before clipping occurs. Similar to dBFS, but also applicable to analog systems. According to ITU-T Rec. G.100.1 the Level in dBov of a digital system is defined as::
, with the maximum signal power
, for a rectangular signal with the maximum amplitude
. The level of a tone with a digital amplitude (peak value) of
is therefore
.
^{[58]} - dBr
- dB(relative) – simply a relative difference from something else, which is made apparent in context. The difference of a filter's response to nominal levels, for instance.
- dBrn
- dB above reference noise. See also
**dBrnC** - dBrnC
**dBrnC**represents an audio level measurement, typically in a telephone circuit, relative to the circuit noise level, with the measurement of this level frequency-weighted by a standard C-message weighting filter. The C-message weighting filter was chiefly used in North America. The Psophometric filter is used for this purpose on international circuits. See Psophometric weighting to see a comparison of frequency response curves for the C-message weighting and Psophometric weighting filters.^{[59]}- dBK
**dB(K)**– decibels relative to 1 K: Used to express noise temperature.^{[60]}- dB/K
- dB(K
^{−1}) – decibels relative to 1 K^{-1}.^{[61]}—*not*decibels per kelvin: Used for the*G/T*factor, a figure of merit utilized in satellite communications, relating the antenna gain*G*to the receiver system noise equivalent temperature*T*.^{[62]}^{[63]}

### List of suffixes in alphabetical order

#### Unpunctuated suffixes

- dBA
- see dB(A).

- dBB
- see dB(B).
- dBc
- relative to carrier—in telecommunications, this indicates the relative levels of noise or sideband power, compared with the carrier power.
- dBC
- see dB(C).
- dBd
- dB(dipole) – the forward gain of an antenna compared with a half-wave dipole antenna. 0 dBd = 2.15 dBi
- dBe
- dB electrical.
- dBf
- dB(fW) – power relative to 1 femtowatt.
- dBFS
- dB(full scale) – the amplitude of a signal compared with the maximum which a device can handle before clipping occurs. Full-scale may be defined as the power level of a full-scale sinusoid or alternatively a full-scale square wave. A signal measured with reference to a full-scale sine-wave will appear 3 dB weaker when referenced to a full-scale square wave, thus: 0 dBFS(fullscale sine wave) = −3 dBFS(fullscale square wave).
- dBG
- G-weighted spectrum
- dBi
- dB(isotropic) – the forward gain of an antenna compared with the hypothetical isotropic antenna, which uniformly distributes energy in all directions. Linear polarization of the EM field is assumed unless noted otherwise.
- dBiC
- dB(isotropic circular) – the forward gain of an antenna compared to a circularly polarized isotropic antenna. There is no fixed conversion rule between dBiC and dBi, as it depends on the receiving antenna and the field polarization.
- dBJ
- energy relative to 1 joule. 1 joule = 1 watt second = 1 watt per hertz, so power spectral density can be expressed in dBJ.
- dBk
- dB(kW) – power relative to 1 kilowatt.
- dBK
**dB(K)**– decibels relative to kelvin: Used to express noise temperature.- dBm
- dB(mW) – power relative to 1 milliwatt.
- dBm0
- Power in dBm measured at a zero transmission level point.
- dBm0s
- Defined by Recommendation ITU-R V.574.
- dBmV
- dB(mV
_{RMS}) – voltage relative to 1 millivolt across 75 Ω. - dBo
- dB optical. A change of 1 dBo in optical power can result in a change of up to 2 dBe in electrical signal power in system that is thermal noise limited.
- dBO
- see dBov
- dBov or dBO
- dB(overload) – the amplitude of a signal (usually audio) compared with the maximum which a device can handle before clipping occurs.
- dBpp
- relative to the peak to peak sound pressure.
- dBpp
- relative to the maximum value of the peak power.
- dBq
- dB(quarterwave) – the forward gain of an antenna compared to a quarter wavelength whip. Rarely used, except in some marketing material. 0 dBq = −0.85 dBi
- dBr
- dB(relative) – simply a relative difference from something else, which is made apparent in context. The difference of a filter's response to nominal levels, for instance.
- dBrn
- dB above reference noise. See also
**dBrnC** - dBrnC
**dBrnC**represents an audio level measurement, typically in a telephone circuit, relative to the circuit noise level, with the measurement of this level frequency-weighted by a standard C-message weighting filter. The C-message weighting filter was chiefly used in North America.- dBsm
- dB(m
^{2}) – decibel relative to one square meter - dBTP
- dB(true peak) – peak amplitude of a signal compared with the maximum which a device can handle before clipping occurs.
- dBu or dBv
- RMS voltage relative to .
- dBu0s
- Defined by Recommendation ITU-R V.574.
- dBuV
- see dBμV
- dBuV/m
- see dBμV/m
- dBv
- see dBu
- dBV
- dB(V
_{RMS}) – voltage relative to 1 volt, regardless of impedance. - dBVU
- dB volume unit
- dBW
- dB(W) – power relative to 1 watt.
- dBZ
- dB(Z) – decibel relative to Z = 1 mm
^{6}·m^{−3} - dBμ
- see dBμV/m
- dBμV or dBuV
- dB(μV
_{RMS}) – voltage relative to 1 microvolt. - dBμV/m, dBuV/m, or dBμ
- dB(μV/m) – electric field strength relative to 1 microvolt per meter.

#### Suffixes preceded by a space

- dB HL
- dB hearing level is used in audiograms as a measure of hearing loss.
- dB Q
- sometimes used to denote weighted noise level
- dB SIL
- dB sound intensity level – relative to 10
^{−12}W/m^{2} - dB SPL
- dB SPL (sound pressure level) – for sound in air and other gases, relative to 20 μPa in air or μPa in water
- dB SWL
- dB sound power level – relative to 10
^{−12}W.

#### Suffixes within parentheses

- dB(A), dB(B), and dB(C)
- These symbols are often used to denote the use of different weighting filters, used to approximate the human ear's response to sound, although the measurement is still in dB (SPL). These measurements usually refer to noise and its effects on humans and other animals, and they are widely used in industry while discussing noise control issues, regulations and environmental standards. Other variations that may be seen are dB
_{A}or dBA.

#### Other suffixes

- dB-Hz
- dB(Hz) – bandwidth relative to one hertz.
- dB/K
- dB(K
^{−1}) – decibels relative to reciprocal of kelvin - dBm
^{−1} - dB(m
^{−1}) – decibel relative to reciprocal of meter: measure of the antenna factor.

## Related units

- mBm
- mB(mW) – power relative to 1 milliwatt, in millibels (one hundredth of a decibel). 100 mBm = 1 dBm. This unit is in the Wi-Fi drivers of the Linux kernel
^{[64]}and the regulatory domain sections.^{[65]}

**Np** or **cNp**

- Another closely related unit is the neper (Np) or centineper (cNp). Like the decibel, the neper is a unit of level.
^{[3]}The linear approximation of 1 cNp being equivalent to 1% for small percentage differences is widely used in financial mathematics, specifically the Fisher equation.

## Fractions

Attenuation constants, in fields such as optical fiber communication and radio propagation path loss, are often expressed as a fraction or ratio to distance of transmission. *dB/m* means decibels per meter, *dB/mi* is decibels per mile, for example. These quantities are to be manipulated obeying the rules of dimensional analysis, e.g., a 100-meter run with a 3.5 dB/km fiber yields a loss of 0.35 dB = 3.5 dB/km × 0.1 km.

## See also

- Apparent magnitude
- Cent (music)
- dB drag racing
- Decade (log scale)
- Loudness
- One-third octave § Base 10
- Phon
- Richter magnitude scale
- Sone
- pH

## Notes

## References

- 1 2 3
*Utilities : V*, Analog Devices, retrieved 2016-09-16_{RMS}/ dBm / dBu / dBV calculator - ↑
*IEEE Standard 100: a dictionary of IEEE standards and terms*(7th ed.). New York: The Institute of Electrical and Electronics Engineering. 2000. p. 288. ISBN 0-7381-2601-2. - 1 2 3 "ISO 80000-3:2006". International Organization for Standardization. Retrieved 20 July 2013.
- ↑ Johnson, Kenneth Simonds (1944).
*Transmission Circuits for Telephonic Communication: Methods of analysis and design*. New York: D. Van Nostrand Co. p. 10. - ↑ Davis, Don; Davis, Carolyn (1997).
*Sound system engineering*(2nd ed.). Focal Press. p. 35. ISBN 978-0-240-80305-0. - ↑ Hartley, R. V. L. (December 1928). "'TU' becomes 'Decibel'".
*Bell Laboratories Record*. AT&T.**7**(4): 137–139. - ↑ Martin, W. H. (January 1929). "DeciBel—The New Name for the Transmission Unit".
*Bell System Technical Journal*.**8**(1). - ↑
*100 Years of Telephone Switching*, p. 276, at Google Books, Robert J. Chapuis, Amos E. Joel, 2003 - ↑ Harrison, William H. (1931). "Standards for Transmission of Speech".
*Standards Yearbook*. National Bureau of Standards, U. S. Govt. Printing Office.**119**. - ↑ Horton, C. W. (1954). "The bewildering decibel".
*Electrical Engineering*.**73**: 550–555. - ↑ "Meeting minutes" (PDF). Consultative Committee for Units. Section 3.
- 1 2 "Letter symbols to be used in electrical technology". International Electrotechnical Commission. 19 July 2002. Part 3: Logarithmic and related quantities, and their units. IEC 60027-3, Ed. 3.0.
- 1 2 Thompson, A. and Taylor, B. N. sec 8.7, "Logarithmic quantities and units: level, neper, bel",
*Guide for the Use of the International System of Units (SI) 2008 Edition*, NIST Special Publication 811, 2nd printing (November 2008), SP811 PDF - ↑ "Letter symbols to be used in electrical technology".
*International Standard CEI-IEC 27-3*. International Electrotechnical Commission. Part 3: Logarithmic quantities and units. - ↑ Mark, James E. (2007).
*Physical Properties of Polymers Handbook*. Springer. p. 1025.[…] the decibel represents a reduction in power of 1.258 times […]

- ↑ Yost, William (1985).
*Fundamentals of Hearing: An Introduction*(Second ed.). Holt, Rinehart and Winston. p. 206. ISBN 0-12-772690-X.[…] a pressure ratio of 1.122 equals + 1.0 dB […]

- ↑ Fedor Mitschke,
*Fiber Optics: Physics and Technology*, Springer, 2010 ISBN 3642037038. - ↑ Pozar, David M. (2005).
*Microwave Engineering*(3rd ed.). Wiley. p. 63. ISBN 978-0-471-44878-5. - 1 2 R. Hickling (1999), Noise Control and SI Units, J Acoust Soc Am 106, 3048
- ↑
*Fiber Optics*. Springer. 2010. - ↑ R. J. Peters,
*Acoustics and Noise Control*, Routledge, November 12, 2013, 400 pages, p.13 - ↑ Nicholas P. Cheremisinoff (1996) Noise Control in Industry: A Practical Guide, Elsevier, 203 pp, p. 7
- ↑ Andrew Clennel Palmer (2008), Dimensional Analysis and Intelligent Experimentation, World Scientific, 154 pp, p.13
- ↑ J. C. Gibbings,
*Dimensional Analysis*, p.37, Springer, 2011 ISBN 1849963177. - ↑
*Sensation and Perception*, p. 268, at Google Books - ↑
*Introduction to Understandable Physics, Volume 2*, p. SA19-PA9, at Google Books - ↑
*Visual Perception: Physiology, Psychology, and Ecology*, p. 356, at Google Books - ↑
*Exercise Psychology*, p. 407, at Google Books - ↑
*Foundations of Perception*, p. 83, at Google Books - ↑
*Fitting The Task To The Human*, p. 304, at Google Books - ↑ ISO 1683:2015
- ↑ C. S. Clay (1999), Underwater sound transmission and SI units, J Acoust Soc Am 106, 3047
- ↑
*Noise-Induced Hearing Loss*, National Institute on Deafness and Other Communications Disorders, 2008, archived from the original on 9 May 2016 - ↑
Chomycz, Bob (2000).
*Fiber optic installer's field manual*. McGraw-Hill Professional. pp. 123–126. ISBN 978-0-07-135604-6. - ↑
Stephen J. Sangwine and Robin E. N. Horne (1998).
*The Colour Image Processing Handbook*. Springer. pp. 127–130. ISBN 978-0-412-80620-9. - ↑
Francis T. S. Yu and Xiangyang Yang (1997).
*Introduction to optical engineering*. Cambridge University Press. pp. 102–103. ISBN 978-0-521-57493-8. - ↑
Junichi Nakamura (2006). "Basics of Image Sensors". In Junichi Nakamura.
*Image sensors and signal processing for digital still cameras*. CRC Press. pp. 79–83. ISBN 978-0-8493-3545-7. - ↑ Winer, Ethan (2013).
*The Audio Expert: Everything You Need to Know About Audio*. Focal Press. p. 107. ISBN 978-0-240-82100-9. - ↑ stason.org, Stas Bekman: stas (at). "3.3 - What is the difference between dBv, dBu, dBV, dBm, dB SPL, and plain old dB? Why not just use regular voltage and power measurements?".
*stason.org*. - ↑ Rupert Neve,
*Creation of the dBu standard level reference* - ↑ deltamedia.com. "DB or Not DB". Deltamedia.com. Retrieved 2013-09-16.
- ↑
*The IEEE Standard Dictionary of Electrical and Electronics terms*(6th ed.). IEEE. 1996 [1941]. ISBN 1-55937-833-6. - ↑ Jay Rose (2002).
*Audio postproduction for digital video*. Focal Press,. p. 25. ISBN 978-1-57820-116-7. - ↑ Morfey, C. L. (2001). Dictionary of Acoustics. Academic Press, San Diego.
- ↑ ANSI, S1.4-19823 Specification for Sound Level Meters, 2.3 Sound Level, p. 2-3.
- ↑ Zimmer, Walter MX, Mark P. Johnson, Peter T. Madsen, and Peter L. Tyack. "Echolocation clicks of free-ranging Cuvier’s beaked whales (Ziphius cavirostris)." The Journal of the Acoustical Society of America 117, no. 6 (2005): 3919–3927.
- ↑ http://oto2.wustl.edu/cochlea/wt4.html
- ↑ Bigelow, Stephen.
*Understanding Telephone Electronics*. Newnes. p. 16. ISBN 978-0750671750. - ↑ Tharr, D. (1998). Case Studies: Transient Sounds Through Communication Headsets. Applied Occupational and Environmental Hygiene, 13(10), 691–697.
- ↑ ITU-R BS.1770
- ↑ "Glossary: D's". National Weather Service. Retrieved 2013-04-25.
- ↑ "Radar FAQ from WSI". Archived from the original on 18 May 2008. Retrieved 2008-03-18.
- ↑ "Definition at Everything2". Retrieved 2008-08-06.
- ↑ Carr, Joseph (2002).
*RF Components and Circuits*. Newnes. pp. 45–46. ISBN 978-0750648448. - ↑ "The dBµ vs. dBu Mystery: Signal Strength vs. Field Strength?".
*radio-timetraveller.blogspot.com*. Retrieved 13 October 2016. - ↑ Chand, N., Magill, P. D., Swaminathan, S. V., & Daugherty, T. H. (1999). Delivery of digital video and other multimedia services (> 1 Gb/s bandwidth) in passband above the 155 Mb/s baseband services on a FTTx full service access network. Journal of lightwave technology, 17(12), 2449–2460.
- ↑ David Adamy.
*EW 102: A Second Course in Electronic Warfare*. Retrieved 2013-09-16. - ↑ ITU-T Rec. G.100.1 The use of the decibel and of relative levels in speechband telecommunications https://www.itu.int/rec/dologin_pub.asp?lang=e&id=T-REC-G.100.1-201506-I!!PDF-E&type=items
- ↑ dBrnC is defined on page 230 in "Engineering and Operations in the Bell System," (2ed), R.F. Rey (technical editor), copyright 1983, AT&T Bell Laboratories, Murray Hill, NJ, ISBN 0-932764-04-5
- ↑ K. N. Raja Rao (2013-01-31).
*Satellite Communication: Concepts And Applications*. Retrieved 2013-09-16. - ↑ Ali Akbar Arabi.
*Comprehensive Glossary of Telecom Abbreviations and Acronyms*. Retrieved 2013-09-16. - ↑ Mark E. Long.
*The Digital Satellite TV Handbook*. Retrieved 2013-09-16. - ↑ Mac E. Van Valkenburg (2001-10-19).
*Reference Data for Engineers: Radio, Electronics, Computers and Communications*. Retrieved 2013-09-16. - ↑ "en:users:documentation:iw [Linux Wireless]".
*wireless.kernel.org*. - ↑ "Is your WiFi AP Missing Channels 12 & 13?".
*wordpress.com*. 16 May 2013.

## Further reading

- Tuffentsammer, Karl (1956). "Das Dezilog, eine Brücke zwischen Logarithmen, Dezibel, Neper und Normzahlen" [The decilog, a bridge between logarithms, decibel, neper and preferred numbers].
*VDI-Zeitschrift*(in German).**98**: 267–274. - Paulin, Eugen (2007-09-01).
*Logarithmen, Normzahlen, Dezibel, Neper, Phon - natürlich verwandt!*[*Logarithms, preferred numbers, decibel, neper, phon - naturally related!*] (PDF) (in German). Archived (PDF) from the original on 2016-12-18. Retrieved 2016-12-18.