View source for Decibel

{{Short description|Logarithmic unit expressing the ratio of physical quantities}}
{{About|the logarithmic unit|use of this unit in sound measurements|Sound pressure level|other uses}}
{{Use dmy dates|date=February 2014}}
{{Infobox unit
| name         = decibel
| image        = 
| caption      = 
| standard     = [[Non-SI units mentioned in the SI|Non-SI accepted unit]]
| quantity     = 
| symbol       = dB
| symbol2      = 
| namedafter   = [[Alexander Graham Bell]]
| units1 = bel
| inunits1 = {{sfrac|10}} bel
}}

The '''decibel''' (symbol: '''dB''') is a relative [[unit of measurement]] equal to one tenth of a '''bel''' ('''B'''). It expresses the [[ratio]] of two values of a [[Power, root-power, and field quantities|power or root-power quantity]] on a [[logarithmic scale]]. Two [[signals]] whose [[level (logarithmic quantity)|levels]] differ by one decibel have a power ratio of 10<sup>1/10</sup> (approximately {{val|1.26}}) or root-power ratio of 10<sup>1/20</sup> (approximately {{val|1.12}}).<ref name="auto">{{cite book |author-last=Mark |author-first=James E. |title=Physical Properties of Polymers Handbook |publisher=Springer |date=2007 |page=1025 |bibcode=2007ppph.book.....M |quote=[…] the decibel represents a reduction in power of 1.258 times […]}}</ref><ref name="auto1">{{cite book |author-last=Yost |author-first=William |title=Fundamentals of Hearing: An Introduction |url=https://archive.org/details/fundamentalsofhe00yost |url-access=registration |publisher=Holt, Rinehart and Winston |edition=Second |date=1985 |page=[https://archive.org/details/fundamentalsofhe00yost/page/206 206] |isbn=978-0-12-772690-8 |quote=[...] a pressure ratio of 1.122 equals +1.0&nbsp;dB [...]}}</ref> 

The strict original usage above only expresses a relative change. However, the word decibel has since also been used for expressing an [[Absolute scale|absolute]] value that is relative to some fixed reference value, in which case the dB symbol is often suffixed with letter codes that indicate the reference value. For example, for the reference value of 1&nbsp;[[volt]], a common suffix is "[[#Voltage|V]]" (e.g., "20&nbsp;dBV").<ref name="clqgmk"/><ref name="NIST">{{cite web |last1=Thompson |first1=Ambler |last2=Taylor |first2=Barry N. |title=Guide for the Use of the International System of Units (SI) |url=http://physics.nist.gov/cuu/pdf/sp811.pdf |website=nist.gov |publisher=NIST |access-date=6 June 2025 |archive-url=https://web.archive.org/web/20160603203340/http://physics.nist.gov/cuu/pdf/sp811.pdf |archive-date=3 June 2016 |date=2008 |url-status=live}}</ref>

As it originated from a need to express power ratios, two principal types of scaling of the decibel are used to provide consistency depending on whether the scaling refers to ratios of power quantities or root-power quantities. When expressing a power ratio, it{{what|date=May 2025}} is defined as ten times the [[Common logarithm|logarithm with base 10]].<ref>{{cite book |title=IEEE Standard 100: a dictionary of IEEE standards and terms |edition=7th |publisher=The Institute of Electrical and Electronics Engineering |location=New York |year=2000 |isbn=978-0-7381-2601-2 |page=288}}</ref> That is, a change in ''power'' by a factor of 10 corresponds to a 10&nbsp;dB change in level. When expressing root-power ratios, a change in [[amplitude]] by a factor of 10 corresponds to a 20&nbsp;dB change in level. The decibel scales differ by a factor of two, so that the related power and root-power levels change by the same value in linear systems, where power is proportional to the square of amplitude.

The definition of the decibel originated in the measurement of transmission loss and power in [[telephony]] of the early 20th century in the [[Bell System]] in the United States. The bel was named in honor of [[Alexander Graham Bell]], but the bel is seldom used. Instead, the decibel is used for a wide variety of measurements in science and [[engineering]], most prominently for [[sound power]] in [[acoustics]], in [[electronics]] and [[control theory]]. In electronics, the [[Gain (electronics)|gain]]s of [[amplifier]]s, [[attenuation]] of signals, and [[signal-to-noise ratio]]s are often expressed in decibels.

== History ==
The decibel originates from methods used to quantify signal loss in telegraph and telephone circuits. Until the mid-1920s, the unit for loss was ''miles of standard cable'' (MSC). 1&nbsp;MSC corresponded to the loss of power over one [[mile]] (approximately 1.6&nbsp;km) of standard telephone cable at a frequency of {{val|5000}}&nbsp;[[radian]]s per second (795.8&nbsp;Hz), and matched closely the smallest attenuation detectable to a listener. A standard telephone cable was "a cable having uniformly distributed resistance of 88&nbsp;ohms per loop-mile and uniformly distributed [[shunt (electrical)|shunt]] [[capacitance]] of 0.054&nbsp;[[microfarad]]s per mile" (approximately corresponding to 19&nbsp;[[wire gauge|gauge]] wire).<ref>{{cite book |last=Johnson |first=Kenneth Simonds |title=Transmission Circuits for Telephonic Communication: Methods of analysis and design |date=1944 |publisher=[[D. Van Nostrand Co.]] |location=New York |page=10}}</ref>

In 1924, [[Bell Labs|Bell Telephone Laboratories]] received a 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&nbsp;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.<ref>{{cite book |title=Sound system engineering |edition=2nd |author-first1=Don |author-last1=Davis |author-first2=Carolyn |author-last2=Davis |publisher=[[Focal Press]] |date=1997 |isbn=978-0-240-80305-0 |page=35 |url={{Google books|plainurl=yes|id=9mAUp5IC5AMC|page=35}}}}</ref> The definition was conveniently chosen such that 1&nbsp;TU approximated 1&nbsp;MSC; specifically, 1&nbsp;MSC was 1.056&nbsp;TU. In 1928, the Bell system renamed the TU into the decibel,<ref>{{cite journal |journal=Bell Laboratories Record |title='TU' becomes 'Decibel' |author-first=R. V. L. |author-last=Hartley |author-link=R. V. L. Hartley |volume=7 |issue=4 |publisher=AT&T |pages=137–139 |date=December 1928 |url={{Google books|plainurl=yes|id=h1ciAQAAIAAJ}}}}</ref> 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]].<ref>{{Cite journal |author-last=Martin |author-first=W. H. |date=January 1929 |title=DeciBel—The New Name for the Transmission Unit |journal=[[Bell System Technical Journal]] |volume=8 |issue=1}}</ref> The bel is seldom used, as the decibel was the proposed working unit.<ref>{{Google books |id=EaVSbjsaBfMC |page=276 |title=100 Years of Telephone Switching}}, Robert J. Chapuis, Amos E. Joel, 2003</ref>

The naming and early definition of the decibel is described in the [[National Institute of Standards and Technology|NBS]] Standard's Yearbook of 1931:<ref>{{Cite journal |title=Standards for Transmission of Speech |journal=Standards Yearbook |volume=119 |author-first=William H. |author-last=Harrison |date=1931 |publisher=National Bureau of Standards, U. S. Govt. Printing Office}}</ref>

{{blockquote |
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<sup>0.1</sup> and any two amounts of power differ by ''N'' decibels when they are in the ratio of 10<sup>''N''(0.1)</sup>. 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&nbsp;...}}

{{anchor|Logit|Decilog}}The word decibel was soon misused to refer to absolute quantities and to ratios other than power. Some proposals attempted to address the resulting confusion. In 1954, J. W. Horton considered that 10{{Superscript|0.1}} be treated as an elementary ratio and proposed the word ''logit'' as "a standard ratio which has the numerical value 10{{Superscript|0.1}} and which combines by multiplication with similar ratios of the same value", so one would describe a 10{{Superscript|0.1}} ratio of units of mass as "a mass logit". This contrasts with the word ''unit'' which would be reserved for magnitudes which combine by addition and reserves the word ''decibel'' specifically for unit transmission loss.<ref>{{cite journal |first=J. W. |last=Horton |title=The bewildering decibel |journal=Electrical Engineering |volume=73 |issue=6 |pages=550–555 |year=1954|doi=10.1109/EE.1954.6438830 |s2cid=51654766 }}
</ref> The ''decilog'' was another proposal (by N. B. Saunders in 1943, A. G. Fox in 1951, and E. I. Green in 1954) to express a division of the logarithmic scale corresponding to a ratio of 10{{Superscript|0.1}}.<ref name=":0">{{Cite journal |last=Green |first=E. I. |date=July 1954 |title=The decilog: A unit for logarithmic measurement |url=https://ieeexplore.ieee.org/document/6438862 |journal=Electrical Engineering |volume=73 |issue=7 |pages=597–599 |doi=10.1109/EE.1954.6438862 |issn=2376-7804}}</ref>

In April&nbsp;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.<ref>{{cite web |url=http://www.bipm.org/utils/common/pdf/CC/CCU/CCU16.pdf |archive-url=https://web.archive.org/web/20141006105908/http://www.bipm.org/utils/common/pdf/CC/CCU/CCU16.pdf |archive-date=2014-10-06 |url-status=live |publisher=Consultative Committee for Units |title=Meeting minutes |at=Section 3}}</ref> However, the decibel is recognized by other international bodies such as the [[International Electrotechnical Commission]] (IEC) and [[International Organization for Standardization]]  (ISO).<ref name="IEC60027-3">{{cite web |url=http://webstore.iec.ch/webstore/webstore.nsf/artnum/028981 |title=Letter symbols to be used in electrical technology |at=Part 3: Logarithmic and related quantities, and their units |id=IEC&nbsp;60027-3, Ed.&nbsp;3.0 |publisher=International Electrotechnical Commission |date=19 July 2002}}</ref> The IEC permits the use of the decibel with root-power 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.<ref name="NIST2008"/> In spite of their widespread use, [[#Suffixes and reference values|suffixes]] (such as in [[A-weighting|dBA]] or dBV) are not recognized by the IEC or ISO.<ref name="NIST"/>

== Definition ==
{| class="wikitable floatright" style="width:0; font-size:85%; margin-left:1em"
|-
! scope="col" style="text-align:right;" |  dB
! scope="col" colspan="2" | Power ratio
! scope="col" colspan="2" | Amplitude ratio
|-
| style="text-align:right; border:none;" | 100
| style="text-align:right; border:none; padding-right:0" | {{gaps|10|000|000|000}} || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |        {{gaps|100|000}} || style="border:none;" |
|-
| style="text-align:right; border:none;" |  90
| style="text-align:right; border:none; padding-right:0" |  {{gaps|1|000|000|000}} || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |         {{gaps|31|623}} || style="border:none;" |
|-
| style="text-align:right; border:none;" |  80
| style="text-align:right; border:none; padding-right:0" |    {{gaps|100|000|000}} || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |         {{gaps|10|000}} || style="border:none;" |
|-
| style="text-align:right; border:none;" |  70
| style="text-align:right; border:none; padding-right:0" |     {{gaps|10|000|000}} || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |          {{gaps|3|162}} || style="border:none;" |
|-
| style="text-align:right; border:none;" |  60
| style="text-align:right; border:none; padding-right:0" |      {{gaps|1|000|000}} || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |          {{gaps|1|000}} || style="border:none;" |
|-
| style="text-align:right; border:none;" |  50
| style="text-align:right; border:none; padding-right:0" |        {{gaps|100|000}} || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |                     316 || style="border:none; padding-left:0;" | .2
|-
| style="text-align:right; border:none;" |  40
| style="text-align:right; border:none; padding-right:0" |         {{gaps|10|000}} || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |                     100 || style="border:none;" |
|-
| style="text-align:right; border:none;" |  30
| style="text-align:right; border:none; padding-right:0" |          {{gaps|1|000}} || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |                      31 || style="border:none; padding-left:0;" | .62
|-
| style="text-align:right; border:none;" |  20
| style="text-align:right; border:none; padding-right:0" |                     100 || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |                      10 || style="border:none;" |
|-
| style="text-align:right; border:none;" |  10
| style="text-align:right; border:none; padding-right:0" |                      10 || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |                       3 || style="border:none; padding-left:0;" | .162
|-
| style="text-align:right; border:none;" |   6
| style="text-align:right; border:none; padding-right:0" |                       3 || style="border:none; padding-left:0;" | .981 ≈ 4
| style="text-align:right; border:none; padding-right:0" |                       1 || style="border:none; padding-left:0;" | .995 ≈ 2
|-
| style="text-align:right; border:none;" |   3
| style="text-align:right; border:none; padding-right:0" |                       1 || style="border:none; padding-left:0;" | .995 ≈ 2
| style="text-align:right; border:none; padding-right:0" |                       1 || style="border:none; padding-left:0;" | .413 ≈ {{sqrt|2}}
|-
| style="text-align:right; border:none;" |   1
| style="text-align:right; border:none; padding-right:0" |                       1 || style="border:none; padding-left:0;" | .259
| style="text-align:right; border:none; padding-right:0" |                       1 || style="border:none; padding-left:0;" | .122
|-
| style="text-align:right; border:none;" |   0
| style="text-align:right; border:none; padding-right:0" |                       1 || style="border:none;" |
| style="text-align:right; border:none; padding-right:0" |                       1 || style="border:none;" |
|-
| style="text-align:right; border:none;" |  −1
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .794
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .891
|-
| style="text-align:right; border:none;" |  −3
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .501 ≈ {{sfrac|2}}
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .708 ≈ {{sqrt|{{sfrac|2}}}}
|-
| style="text-align:right; border:none;" |  −6
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .251 ≈ {{sfrac|4}}
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .501 ≈ {{sfrac|2}}
|-
| style="text-align:right; border:none;" | −10
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .1
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.316|2}}
|-
| style="text-align:right; border:none;" | −20
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .01
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .1
|-
| style="text-align:right; border:none;" | −30
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .001
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.031|62}}
|-
| style="text-align:right; border:none;" | −40
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|1}}
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .01
|-
| style="text-align:right; border:none;" | −50
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|01}}
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.003|162}}
|-
| style="text-align:right; border:none;" | −60
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|001}}
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | .001
|-
| style="text-align:right; border:none;" | −70
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|000|1}}
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|316|2}}
|-
| style="text-align:right; border:none;" | −80
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|000|01}}
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|1}}
|-
| style="text-align:right; border:none;" | −90
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|000|001}}
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|031|62}}
|-
| style="text-align:right; border:none;" | −100
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|000|000|1}}
| style="text-align:right; border:none; padding-right:0" |                       0 || style="border:none; padding-left:0;" | {{gaps|.000|01}}
|-
| colspan="5" style="text-align:left; background:#f8f8ff;" | An example scale showing power ratios ''x'', amplitude ratios {{sqrt|''x''}}, and dB equivalents 10&nbsp;log<sub>10</sub>&nbsp;''x''
|}

The IEC Standard [[IEC 60027|60027-3:2002]] defines the following quantities. The decibel (dB) is one-tenth of a bel: 1&nbsp;dB&nbsp;= 0.1&nbsp;B. The bel (B) is {{1/2}}&nbsp;ln(10) [[neper]]s: 1&nbsp;B&nbsp;= {{1/2}}&nbsp;ln(10)&nbsp;Np. The neper is the change in the [[level (logarithmic quantity)|level]] of a [[root-power quantity]] when the root-power quantity changes by a factor of [[e (mathematical constant)|''e'']], that is {{nowrap|1=1 Np = ln(e) = 1}}, thereby relating all of the units as nondimensional [[Natural logarithm|natural ''log'']] of root-power-quantity ratios, {{val|1|u=dB}}&nbsp;= {{val|0.11513|end=...|u=Np}}&nbsp;= {{val|0.11513|end=...}}.  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 root-power quantities of {{radic|10}}:1.<ref>{{cite book |title=International Standard CEI-IEC 27-3 |chapter=Letter symbols to be used in electrical technology |at=Part 3: Logarithmic quantities and units |publisher=International Electrotechnical Commission}}</ref>

Two signals whose levels differ by one decibel have a power ratio of 10<sup>1/10</sup>, which is approximately {{val|1.25893}}, and an amplitude (root-power quantity) ratio of 10<sup>1/20</sup> ({{val|1.12202}}).<ref name="auto"/><ref name="auto1"/>

The bel is rarely used either without a prefix or with [[metric prefix|SI unit prefixes]] other than ''[[deci-|deci]]''; it is customary, for example, to use ''hundredths of a decibel'' rather than ''millibels''.  Thus, five one-thousandths of a bel would normally be written 0.05&nbsp;dB, and not 5&nbsp;mB.<ref>Fedor Mitschke, ''Fiber Optics: Physics and Technology'', Springer, 2010 {{ISBN|3642037038}}.</ref>

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

=== Power quantities ===
When referring to measurements of ''[[Power (physics)|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''<sub>0</sub> (reference power) is represented by ''L''<sub>''P''</sub>, that ratio expressed in decibels,<ref>{{Cite book |title=Microwave Engineering |author-first=David M. |author-last=Pozar |edition=3rd |publisher=Wiley |date=2005 |author-link=David M. Pozar |isbn=978-0-471-44878-5 |page=63}}</ref> which is calculated using the formula:<ref>IEC 60027-3:2002</ref>
: <math>
L_P = \frac{1}{2} \ln\!\left(\frac{P}{P_0}\right)\,\text{Np} = 10 \log_{10}\!\left(\frac{P}{P_0}\right)\,\text{dB}
</math>

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''<sub>0</sub> must measure the same type of quantity, and have the same units before calculating the ratio. If {{nowrap|1=''P'' =}} ''P''<sub>0</sub> in the above equation, then ''L''<sub>''P''</sub>&nbsp;= 0. If ''P'' is greater than ''P''<sub>0</sub> then ''L''<sub>''P''</sub> is positive; if ''P'' is less than ''P''<sub>0</sub> then ''L''<sub>''P''</sub> is negative.

Rearranging the above equation gives the following formula for ''P'' in terms of ''P''<sub>0</sub> and ''L''<sub>''P''</sub> :
: <math>
P = 10^\frac{L_P}{10\,\text{dB}} P_0
</math>

=== Root-power (field) quantities ===
{{main|Power, root-power, and field quantities}}

When referring to measurements of root-power quantities, it is usual to consider the ratio of the squares of ''F'' (measured) and ''F''<sub>0</sub> (reference). This is because the definitions were originally formulated to give the same value for relative ratios for both power and root-power quantities. Thus, the following definition is used:
: <math>
L_F = \ln\!\left(\frac{F}{F_0}\right)\,\text{Np} = 10 \log_{10}\!\left(\frac{F^2}{F_0^2}\right)\,\text{dB} = 20 \log_{10} \left(\frac{F}{F_0}\right)\,\text{dB}
</math>

The formula may be rearranged to give
: <math>
F = 10^\frac{L_F}{20\,\text{dB}} F_0
</math>

Similarly, in [[Electronic circuit|electrical circuits]], dissipated power is typically proportional to the square of voltage or current when the [[Electrical impedance|impedance]] is constant. Taking voltage as an example, this leads to the equation for power gain level ''L''<sub>''G''</sub>:
: <math>
L_G = 20 \log_{10}\!\left (\frac{V_\text{out}}{V_\text{in}}\right)\,\text{dB}
</math>
where ''V''<sub>out</sub> is the [[root-mean-square]] (rms) output voltage, ''V''<sub>in</sub> is the rms input voltage. A similar formula holds for current.

The term ''root-power quantity'' is introduced by ISO Standard [[ISO/IEC 80000|80000-1:2009]] as a substitute of ''field quantity''.  The term ''field quantity'' is deprecated by that standard and ''root-power'' is used throughout this article.

=== Relationship between power and root-power levels ===
Although power and root-power quantities are different quantities, their respective levels are historically measured in the same units, typically decibels.  A factor of 2 is introduced to make ''changes'' in the respective levels match under restricted conditions such as when the medium is linear and the ''same'' waveform is under consideration with changes in amplitude, or the medium impedance is linear and independent of both frequency and time.  This relies on the relationship
:<math> \frac{P(t)}{P_0} = \left(\frac{F(t)}{F_0}\right)^2 </math>
holding.<ref>{{citation |author=I M Mills |author2=B N Taylor |author3=A J Thor |title=Definitions of the units radian, neper, bel and decibel |year=2001 |journal=Metrologia |volume=38 |page=353 |number=4 |doi=10.1088/0026-1394/38/4/8|bibcode=2001Metro..38..353M |s2cid=250827251 }}</ref>  In a nonlinear system, this relationship does not hold by the definition of linearity.  However, even in a [[linear system]] in which the power quantity is the product of two linearly related quantities (e.g. voltage and current), if the impedance is frequency- or time-dependent, this relationship does not hold in general, for example if the energy spectrum of the waveform changes.

For differences in level, the required relationship is relaxed from that above to one of proportionality (i.e., the reference quantities ''P''{{sub|0}} and ''F''{{sub|0}} need not be related), or equivalently,
: <math> \frac{P_2}{P_1} = \left(\frac{F_2}{F_1}\right)^2 </math>
must hold to allow the power level difference to be equal to the root-power level difference from power ''P''{{sub|1}} and ''F''{{sub|1}} to ''P''{{sub|2}} and ''F''{{sub|2}}.  An example might be an [[amplifier]] with unity voltage gain independent of load and frequency driving a load with a frequency-dependent impedance: the relative voltage gain of the amplifier is always 0&nbsp;dB, but the power gain depends on the changing spectral composition of the waveform being amplified.  Frequency-dependent impedances may be analyzed by considering the quantities [[power spectral density]] and the associated root-power quantities via the [[Fourier transform]], which allows elimination of the frequency dependence in the analysis by analyzing the system at each frequency independently.

=== Conversions ===
Since logarithm differences measured in these units often represent power ratios and root-power ratios, values for both are shown below. The bel is traditionally used as a unit of logarithmic power ratio, while the neper is used for logarithmic root-power (amplitude) ratio.

{| class="wikitable"
|+ Conversion between units of level and a list of corresponding ratios
!Unit !! In decibels !! In bels !! In [[neper]]s !! Power ratio !! Root-power ratio
|-
| 1&nbsp;dB || 1&nbsp;dB || 0.1 B || {{val|0.11513}}&nbsp;Np || 10<sup>1/10</sup> ≈ {{val|1.25893}} || 10<sup>1/20</sup> ≈ {{val|1.12202}}
|-
| 1 Np || {{val|8.68589}}&nbsp;dB || {{val|0.868589}}&nbsp;B || 1 Np || e<sup>2</sup> ≈ {{val|7.38906}} || [[e (mathematical constant)|e]] ≈ {{val|2.71828}}
|-
| 1 B || 10&nbsp;dB || 1 B || 1.151&nbsp;3 Np || 10 || 10<sup>1/2</sup> ≈ 3.162&nbsp;28
|}

=== Examples ===
* Calculating the ratio in decibels of {{nowrap|1 kW}} (one kilowatt, or {{val|1000}} watts) to {{nowrap|1 W}} yields: <math display="block">
L_G = 10 \log_{10} \left(\frac{1\,000\,\text{W}}{1\,\text{W}}\right)\,\text{dB} = 30\,\text{dB}
</math>
* The ratio in decibels of {{nowrap|1={{radic|1000}} V ≈ 31.62 V}} to {{nowrap|1 V}} is: <math display="block">
L_G = 20 \log_{10} \left(\frac{31.62\,\text{V}}{1\,\text{V}}\right)\,\text{dB} = 30\,\text{dB}
</math>
{{nowrap|1=(31.62 V / 1 V)<sup>2</sup> ≈ 1 kW / 1 W}}, illustrating the consequence from the definitions above that ''L''<sub>''G''</sub> has the same value, 30&nbsp;dB, 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 in decibels of {{nowrap|10 W}} to {{nowrap|1 mW}} (one milliwatt) is obtained with the formula: <math display="block">
L_G = 10 \log_{10} \left(\frac{10\text{W}}{0.001\text{W}}\right)\,\text{dB} = 40\,\text{dB}
</math>
* The power ratio corresponding to a {{nowrap|3 dB}} change in level is given by: <math display="block">
G = 10^\frac{3}{10} \times 1 = 1.995\,26\ldots \approx 2
</math>

A change in power ratio by a factor of 10 corresponds to a change in level of {{nowrap|10 dB}}. A change in power ratio by a factor of 2 or {{sfrac|2}} is approximately a [[Half-power point|change of 3&nbsp;dB]]. More precisely, the change is ±{{val|3.0103}}&nbsp;dB, but this is almost universally rounded to 3&nbsp;dB in technical writing.{{Citation needed|date=January 2025}}  This implies an increase in voltage by a factor of {{nowrap|{{sqrt|2}} ≈}} {{val|1.4142}}.  Likewise, a doubling or halving of the voltage, corresponding to a quadrupling or quartering of the power, is commonly described as 6&nbsp;dB rather than ±{{val|6.0206}}&nbsp;dB.

Should it be necessary to make the distinction, the number of decibels is written with additional [[significant figures]].  3.000&nbsp;dB corresponds to a power ratio of 10<sup>3/10</sup>, or {{val|1.9953}}, about 0.24% different from exactly 2, and a voltage ratio of {{val|1.4125}}, about 0.12% different from exactly {{sqrt|2}}.  Similarly, an increase of 6.000&nbsp;dB corresponds to a power ratio of {{nowrap|10<sup>6/10</sup> ≈}} {{val|3.9811}}, about 0.5% different from 4.

== Properties ==
The decibel is useful for representing large ratios and for simplifying representation of multiplicative effects, such as attenuation from multiple sources along a signal chain. Its application in systems with additive effects is less intuitive, such as in the combined [[sound pressure level]] of two machines operating together. Care is also necessary with decibels directly in fractions and with the units of multiplicative operations.

=== Reporting large ratios ===
[[File:Bode Low Pass Magnitude Plot.PNG|thumb|A [[Bode plot]] labels its magnitude axis in decibel, to help express a large logarithmic scale with 0&nbsp;dB for [[unity gain]] and simple notches typically every 10&nbsp;dB.]]
The [[logarithmic scale]] nature of the decibel means that a very large range of ratios can be represented by a convenient number. For example, 50&nbsp;dB is easier to say than "the two powers bear a 100,000 to 1 ratio" or that "one power is 10{{Superscript|5}} the other".<ref name=":0" /> Decibels express huge changes of a quantity with few digits of dB.

=== 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, {{nowrap|log(''A'' × ''B'' × ''C'') }}= log(''A'') + log(''B'') + log(''C''). Practically, this means that, armed only with the knowledge that 1&nbsp;dB is a power gain of approximately 26%, 3&nbsp;dB is approximately 2× power gain, and 10&nbsp;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&nbsp;dB, 8&nbsp;dB, and 7&nbsp;dB respectively, for a total gain of 25&nbsp;dB. Broken into combinations of 10, 3, and 1&nbsp;dB, this is: {{block indent | em = 1.5 | text =
 25&nbsp;dB&nbsp;= 10&nbsp;dB&nbsp;+ 10&nbsp;dB&nbsp;+ 3&nbsp;dB&nbsp;+ 1&nbsp;dB&nbsp;+ 1&nbsp;dB
}} With an input of 1 watt, the output is approximately {{block indent | em = 1.5 | text =
 1&nbsp;W&nbsp;× 10&nbsp;× 10&nbsp;× 2&nbsp;× 1.26&nbsp;× 1.26&nbsp;≈ 317.5&nbsp;W
}} Calculated precisely, the output is 1&nbsp;W&nbsp;× 10<sup>25/10</sup>&nbsp;≈ 316.2&nbsp;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.

However, according to its critics, the decibel creates confusion, obscures reasoning, is more related to the era of [[slide rule]]s than to modern digital processing, and is cumbersome and difficult to interpret.<ref name="Hickling">R. Hickling (1999), Noise Control and SI Units, J Acoust Soc Am 106, 3048</ref><ref>Hickling, R. (2006). Decibels and octaves, who needs them?. Journal of sound and vibration, 291(3-5), 1202-1207.</ref> Quantities in decibels are not necessarily [[Dimensional homogeneity|additive]],<ref>Nicholas P. Cheremisinoff (1996) Noise Control in Industry: A Practical Guide, Elsevier, 203 pp, p. [{{Google books |plainurl=yes |id=rrpEuUOkT3UC |page=7}} 7]</ref><ref>Andrew Clennel Palmer (2008), Dimensional Analysis and Intelligent Experimentation, World Scientific, 154 pp, p.13</ref> thus being "of unacceptable form for use in [[dimensional analysis]]".<ref>J. C. Gibbings, ''Dimensional Analysis'', [{{Google books |plainurl=yes |id=Q6iflrgVaWcC |page=37}} p.37], Springer, 2011 {{ISBN|1849963177}}.</ref> Thus, units require special care in decibel operations. Take, for example, [[carrier-to-noise-density ratio]] ''C''/''N''<sub>0</sub> (in hertz), involving carrier power ''C'' (in watts) and noise power spectral density ''N''<sub>0</sub> (in W/Hz). Expressed in decibels, this ratio would be a subtraction (''C''/''N''<sub>0</sub>)<sub>dB</sub> = ''C''<sub>dB</sub> − ''N''<sub>0&nbsp;dB</sub>. However, the linear-scale units still simplify in the implied fraction, so that the results would be expressed in dB-Hz.

=== Representation of addition operations <span class="anchor" id="Addition"></span> ===
{{Further|Logarithmic addition}}
According to Mitschke,<ref>{{cite book |title=Fiber Optics |publisher=Springer |date=2010}}</ref> "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:<ref>R. J. Peters, ''Acoustics and Noise Control'', Routledge, 12 November 2013, 400 pages, p.&nbsp;13</ref><blockquote>if two machines each individually produce a sound pressure level of, say, 90&nbsp;dB at a certain point, then when both are operating together we should expect the combined sound pressure level to increase to 93&nbsp;dB, but certainly not to 180&nbsp;dB!; suppose that the noise from a machine is measured (including the contribution of background noise) and found to be 87&nbsp;dBA but when the machine is switched off the background noise alone is measured as 83&nbsp;dBA. [...] the machine noise [level (alone)] may be obtained by 'subtracting' the 83&nbsp;dBA background noise from the combined level of 87&nbsp;dBA; i.e., 84.8&nbsp;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&nbsp;dB and 90&nbsp;dB: [[logarithmic average]] = 87&nbsp;dB; [[arithmetic average]] = 80&nbsp;dB.</blockquote>

Addition on a logarithmic scale is called [[logarithmic addition]], and can be defined by taking exponentials to convert to a linear scale, adding there, and then taking logarithms to return. For example, where operations on decibels are logarithmic addition/subtraction and logarithmic multiplication/division, while operations on the linear scale are the usual operations:
:<math>87\,\text{dBA} \ominus 83\,\text{dBA} = 10 \cdot \log_{10}\bigl(10^{87/10} - 10^{83/10}\bigr)\,\text{dBA} \approx 84.8\,\text{dBA}</math>
:<math>
\begin{align}
M_\text{lm}(70, 90) &= \left(70\,\text{dBA} + 90\,\text{dBA}\right)/2 \\
&= 10 \cdot \log_{10}\left(\bigl(10^{70/10} + 10^{90/10}\bigr)/2\right)\,\text{dBA} \\
&= 10 \cdot \left(\log_{10}\bigl(10^{70/10} + 10^{90/10}\bigr) - \log_{10} 2\right)\,\text{dBA}
\approx 87\,\text{dBA}
\end{align}
</math>
The [[logarithmic mean]] is obtained from the logarithmic sum by subtracting <math>10\log_{10} 2</math>, since logarithmic division is linear subtraction.

=== Fractions ===
[[Attenuation]] constants, in topics such as [[optical fiber]] communication and [[radio propagation]] [[path loss]], are often expressed as a [[Fraction (mathematics)|fraction]] or ratio to distance of transmission. In this case, {{nowrap|dB/m}} represents decibel per meter, {{nowrap|dB/mi}} represents decibel per mile, for example. These quantities are to be manipulated obeying the rules of dimensional analysis, e.g., a 100-meter run with a {{nowrap|3.5 dB/km}} fiber yields a loss of {{nowrap|0.35 dB =}} {{nowrap|3.5 dB/km ×}} 0.1&nbsp;km.

== Uses ==

=== Perception ===
The human perception of the intensity of sound and light more nearly approximates the logarithm of intensity rather than a linear relationship (see [[Weber–Fechner law]]), making the dB scale a useful measure.<ref>{{Google books |id=1SMXAAAAQBAJ |page=268 |title=Sensation and Perception}}</ref><ref>{{Google books |id=BggrpTek5kAC |page=SA19-PA9 |title=Introduction to Understandable Physics, Volume 2}}</ref><ref>{{Google books |id=ukvei0wge_8C |page=356 |title=Visual Perception: Physiology, Psychology, and Ecology}}</ref><ref>{{Google books |id=-QIfF9q6Q_EC |page=407 |title=Exercise Psychology}}</ref><ref>{{Google books |id=oUNfSjS11ggC |page=83 |title=Foundations of Perception}}</ref><ref>{{Google books |id=w888Mw1dh_EC |page=304 |title=Fitting The Task To The Human}}</ref>

=== Acoustics ===
The decibel is commonly used in [[acoustics]] as a unit of [[sound power level]] or [[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 [[Sound pressure#Examples of sound pressure|common comparisons used to illustrate different levels of sound pressure]]. As sound pressure is a root-power quantity, the appropriate version of the unit definition is used:
: <math>
L_p = 20 \log_{10}\!\left(\frac{p_{\text{rms}}}{p_{\text{ref}}}\right)\,\text{dB},
</math>
where ''p''<sub>rms</sub> is the [[root mean square]] of the measured sound pressure and ''p''<sub>ref</sub> is the standard reference sound pressure of 20 [[micropascal]]s in air or 1 micropascal in water.<ref>ISO 1683:2015</ref>

Use of the decibel in underwater acoustics leads to confusion, in part because of this difference in reference value.<ref>Chapman, D. M., & Ellis, D. D. (1998). Elusive decibel: Thoughts on sonars and marine mammals. Canadian Acoustics, 26(2), 29-31.</ref><ref>C. S. Clay (1999), Underwater sound transmission and SI units, J Acoust Soc Am 106, 3047</ref>

[[Sound intensity#Sound intensity level|Sound intensity]] is proportional to the square of sound pressure. Therefore, the sound intensity level can also be defined as:
: <math>
L_p = 10 \log_{10}\!\left(\frac{I}{I_{\text{ref}}}\right)\,\text{dB},
</math>

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 equal to or greater than 1 trillion (10<sup>12</sup>).<ref>{{cite web |title=Loud Noise Can Cause Hearing Loss |url=https://www.cdc.gov/nceh/hearing_loss/what_noises_cause_hearing_loss.html |website=cdc.gov |date=7 October 2019 |publisher=Centers for Disease Control and Prevention |access-date=30 July 2020}}</ref> Such large measurement ranges are conveniently expressed in logarithmic scale: the base-10 logarithm of 10<sup>12</sup> is 12, which is expressed as a sound intensity level of 120&nbsp;dB re 1 pW/m<sup>2</sup>. The reference values of I and p in air have been chosen such that this corresponds approximately to a sound pressure level of 120&nbsp;dB re 20&nbsp;[[Pascal (unit)|μPa]].

Since the human ear is not equally sensitive to all sound frequencies, the acoustic power spectrum is modified by [[frequency weighting]] ([[A-weighting]] being the most common standard) to get the weighted acoustic power before converting to a sound level or noise level in decibels.<ref name=Pierre>{{citation |url= http://storeycountywindfarms.org/ref3_Impact_Sound_Pressure.pdf |archive-url=https://web.archive.org/web/20151222153918/http://storeycountywindfarms.org/ref3_Impact_Sound_Pressure.pdf |archive-date=2015-12-22 |url-status=live |author=Richard L. St. Pierre, Jr. and Daniel J. Maguire |title=The Impact of A-weighting Sound Pressure Level Measurements during the Evaluation of Noise Exposure |date=July 2004 |access-date=2011-09-13}}</ref>

=== Telephony ===
The decibel is used in [[telephony]] and [[Audio signal|audio]].  Similarly to the use in acoustics, a frequency weighted power is often used.  For audio noise measurements in electrical circuits, the weightings are called [[psophometric weighting]]s.<ref name="Reeve">{{Cite book |last=Reeve |first= William D. |year= 1992 |title= Subscriber Loop Signaling and Transmission Handbook – Analog |edition= 1st |publisher=IEEE Press |isbn= 0-87942-274-2}}</ref>

=== Electronics ===
In electronics, the decibel is often used to express power or amplitude ratios (as for [[Gain (electronics)|gains]]) in preference to [[arithmetic]] ratios or [[percent]]ages. One advantage is that the total decibel gain of a series of components (such as amplifiers and [[Attenuator (electronics)|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 optical communication|free space]], [[waveguide]], [[coaxial cable]], [[fiber optics]], etc.) using a [[link budget]].

The decibel unit can also be combined with a reference level, often indicated via a suffix, to create an absolute unit of electric power. For example, dBW uses a 1&nbsp;W reference, while [[dBm]] uses a {{nowrap|1 mW}} reference (''m'' being short for ''milliwatt''). A power level of 0&nbsp;dBm corresponds to one milliwatt, and 1&nbsp;dBm is one decibel greater (about 1.259&nbsp;mW).

In professional audio specifications, a popular unit is the [[dBu]].  This is relative to the root mean square voltage which delivers 1&nbsp;mW (0&nbsp;dBm) into a 600-ohm resistor, or {{sqrt|1&nbsp;mW &times; 600&nbsp;Ω }}≈ 0.775&nbsp;V<sub>RMS</sub>.  When used in a 600-ohm circuit (historically, the standard reference impedance in telephone circuits), dBu and dBm are [[#dBu or dBv|identical]].

=== Optics ===
In an [[optical link]], if a known amount of [[Optics|optical]] power, in [[dBm]] (referenced to 1&nbsp;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.<ref>
{{cite book
 | title = Fiber optic installer's field manual
 | author-first = Bob |author-last=Chomycz
 | publisher = McGraw-Hill Professional
 | year = 2000
 | isbn = 978-0-07-135604-6
 | pages = 123–126
 | url = {{Google books |plainurl=yes |id=B810SYIAa4IC |page=123 }}
}}</ref>

In spectrometry and optics, the [[absorbance|blocking unit]] used to measure [[optical density]] is equivalent to −1&nbsp;B.

=== Video and digital imaging ===
In connection with video and digital [[image sensor]]s, decibels generally represent ratios of video voltages or digitized light intensities, using 20&nbsp;log of the ratio, even when the represented intensity (optical power) is directly proportional to the voltage generated by the sensor, not to its square, as in a [[CCD imager]] where response voltage is linear in intensity.<ref>
{{cite book
 | title = The Colour Image Processing Handbook
 | author = Stephen J. Sangwine and Robin E. N. Horne
 | publisher = Springer
 | year = 1998
 | isbn = 978-0-412-80620-9
 | pages = 127–130
 | url = {{Google books |plainurl=yes |id=oEsZiCt5VOAC |page=127 }}
}}</ref>
Thus, a camera [[signal-to-noise ratio]] or dynamic range quoted as 40&nbsp;dB represents a ratio of 100:1 between optical signal intensity and optical-equivalent dark-noise intensity, not a 10,000:1 intensity (power) ratio as 40&nbsp;dB might suggest.<ref>
{{cite book
 | title = Introduction to optical engineering
 | author = Francis T. S. Yu and Xiangyang Yang
 | publisher = Cambridge University Press
 | year = 1997
 | isbn = 978-0-521-57493-8
 | pages = 102–103
 | url = {{Google books |plainurl=yes |id=RYm7WwjsyzkC |page=120 }}
}}</ref>
Sometimes the 20&nbsp;log ratio definition is applied to electron counts or photon counts directly, which are proportional to sensor signal amplitude without the need to consider whether the voltage response to intensity is linear.<ref>
{{cite book
 | title = Image sensors and signal processing for digital still cameras
 | chapter = Basics of Image Sensors
 | author = Junichi Nakamura
 | editor = Junichi Nakamura
 | publisher = CRC Press
 | year = 2006
 | isbn = 978-0-8493-3545-7
 | pages = 79–83
 | chapter-url = {{Google books |plainurl=yes |id=UY6QzgzgieYC |page=79 }}
}}</ref>

However, as mentioned above, the 10&nbsp;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 {{nowrap|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 [[F-number#Stops.2C f-stop conventions.2C and exposure|stop]], to describe light intensity ratios or dynamic range.

== Suffixes and reference values <span class="anchor" id="Suffixes"></span> ==
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&nbsp;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.

This form of attaching suffixes to dB is widespread in practice, albeit being against the rules promulgated by standards bodies (ISO and IEC),<ref name=NIST2008>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 [http://physics.nist.gov/cuu/pdf/sp811.pdf PDF]</ref> given the "unacceptability of attaching information to units"{{efn|"When one gives the value of a quantity, it is incorrect to attach letters or other symbols to the unit in order to provide information about the quantity or its conditions of measurement. Instead, the letters or other symbols should be attached to the quantity."{{r|NIST2008|p=16}}}} and the "unacceptability of mixing information with units".{{efn|"When one gives the value of a quantity, any information concerning the quantity or its conditions of measurement must be presented in such a way as not to be associated with the unit. This means that quantities must be defined so that they can be expressed solely in acceptable units..."{{r|NIST2008|p=17}}}} The [[IEC 60027-3]] standard recommends the following format:<ref name="IEC60027-3"/> {{nowrap|''L''<sub>''x''</sub> (re ''x''<sub>ref</sub>)}} or as {{nowrap|''L''<sub>''x''/''x''<sub>ref</sub></sub>}}, where ''x'' is the quantity symbol and ''x''<sub>ref</sub> is the value of the reference quantity, e.g., ''L''<sub>''E''</sub> (re 1&nbsp;μV/m)&nbsp;= 20&nbsp;dB or {{nowrap|''L''<sub>''E''/(1 μV/m)</sub>}}&nbsp;= 20&nbsp;dB for the [[electric field strength]] ''E'' relative to {{nowrap|1 μV/m}} reference value.
If the measurement result 20&nbsp;dB is presented separately, it can be specified using the information in parentheses, which is then part of the surrounding text and not a part of the unit: 20&nbsp;dB (re {{nowrap|1 μV/m}}) or 20&nbsp;dB {{nowrap|(1 μV/m)}}.

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 [[hyphen]], as in "dB{{nbhyph}}Hz", or with a space, as in "dB&nbsp;HL", or enclosed in parentheses, as in "dB(HL)", or with no intervening character, as in "dBm" (which is non-compliant with international standards).

== List of suffixes ==

=== 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.

; dB{{sub| V}} : dB(V<sub>[[root mean square|RMS]]</sub>)&nbsp;– voltage relative to 1&nbsp;volt, regardless of impedance.<ref name=clqgmk>{{cite web |title=V<sub>RMS</sub> / dBm / dBu / dBV calculator |department=Utilities |publisher=Analog Devices |url=http://designtools.analog.com/dt/dbconvert/dbconvert.html |via=designtools.analog.com |access-date=2016-09-16}}</ref> This is used to measure microphone sensitivity, and also to specify the consumer [[Line level|line-level]] of {{nowrap|−10 dBV}}, in order to reduce manufacturing costs relative to equipment using the much larger {{nowrap|+4 dBu}} line-level standard.<ref>{{cite book |last=Winer |first=Ethan |year=2013 |title=The Audio Expert: Everything you need to know about audio |publisher=Focal Press |isbn=978-0-240-82100-9 |page=[https://books.google.com/books?id=TIfOAwAAQBAJ&q=%22%E2%88%9210+dBV%22+%221+kHz%22 107] |url=https://books.google.com/books?id=TIfOAwAAQBAJ |via=Google }}</ref>

; [[File:Relationship between dBu and dBm.png|thumb|upright=1.25|Schematic of a 0 [[dBu|dB{{sub| u}}]] [[voltage source]] dissipating 0 dB{{sub| m}} of power as [[heat]] in a 600&nbsp;Ω [[resistor]]]]dB{{sub| u}} or dB{{sub| v}} : 0 dB{{sub| u}} is defined as the RMS voltage that would dissipate 0&nbsp;dB{{sub| m}} (1&nbsp;mW) in a 600&nbsp;Ω [[Electrical load|load]]. Per [[Ohm's law]], this voltage equals:<math display="block">\sqrt{\text{resistance} \cdot \text{power}} = \sqrt{600\ \mathsf{\Omega} \ \cdot\ 0.001\ \mathsf{W}\;} = \sqrt{.6} \ \mathsf{V_{RMS}} \approx 0.7746\ \mathsf{V_{RMS}}\, . </math>Therefore, 1&nbsp;V{{Sub|RMS}} corresponds to:<ref name=clqgmk/> <math display="block">20 \cdot \log_{10} \left( \frac{ 1\ \mathsf{V_{RMS}}}{\sqrt{0.6}\ \mathsf{V_{RMS}}} \right) \approx 2.218\ \mathsf{dB_u} ~.</math>Originally called dB{{sub| v }}, it was changed to dB{{sub| u}} to avoid confusion with dB{{sub| V}}.<ref>{{cite web |first=Stas |last=Bekman  |title=3.3 – What is the difference between dBv, dBu, dBV, dBm, dB&nbsp;SPL, and plain old dB? Why not just use regular voltage and power measurements? |website=stason.org |department=Entertainment audio |series=TULARC |url=http://stason.org/TULARC/entertainment/audio/pro/3-3-What-is-the-difference-between-dBv-dBu-dBV-dBm-dB.html }}</ref> According to [[Rupert Neve]], the ''u'' originated from the [[volume unit|volume ''unit'']] displayed on a [[VU meter]].<ref>{{cite AV media |first=Rupert |last=Neve |author-link=Rupert Neve |date=9 October 2015 |title=Creation of the dB{{sub| u}} standard level reference |medium=video |url=https://www.youtube.com/watch?v=b02P4f3CBuM | archive-url=https://ghostarchive.org/varchive/youtube/20211030/b02P4f3CBuM |archive-date=2021-10-30 }}{{cbignore}}</ref> The ''u'' has also been interpreted as ''unloaded''.<ref>{{Cite web |last=White |first=Paul |date=February 1994 |title=Decibels Explained |url=https://www.soundonsound.com/sound-advice/decibels-explained |url-status=live |archive-url=https://web.archive.org/web/20250121014734/https://www.soundonsound.com/sound-advice/decibels-explained |archive-date=2025-01-21 |access-date=2025-05-31 |website=[[Sound on Sound]]}}</ref>{{paragraphbreak}}

: 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 {{nobr|+4 dBu}}. Consumer equipment typically uses a lower "nominal" signal level of {{nobr|−10 dB{{sub| V}} .}}<ref>{{cite web |title=dB or not dB&nbsp;? |website=deltamedia.com |url=http://www.deltamedia.com/resource/db_or_not_db.html |url-status=dead |access-date=2013-09-16 |archive-url=https://web.archive.org/web/20130620064637/http://www.deltamedia.com/resource/db_or_not_db.html |archive-date=20 June 2013 }}</ref> Therefore, many devices offer dual voltage operation (with different gain or "trim" settings) for compatibility. A switch or adjustment that covers at least the range between {{nobr|+4 dB{{sub| u}}}} and {{nobr|−10 dB{{sub| V}}}} is common in professional equipment.

; dB{{sub| m0s}} : Defined by Recommendation ITU-R V.574&nbsp;; dB{{sub| mV}}: dB(mV<sub>RMS</sub>) – root mean square voltage relative to 1&nbsp;millivolt across 75&nbsp;Ω.<ref>
{{cite book
 |title=The IEEE Standard Dictionary of Electrical and Electronics terms
 |edition=6th
 |year=1996
 |orig-year=1941
 |publisher=[[Institute of Electrical and Electronics Engineers]]
 |isbn=978-1-55937-833-8
}}
</ref> Widely used in [[cable television]] networks, where the nominal strength of a single TV signal at the receiver terminals is about 0&nbsp;dB{{sub| mV}}. Cable&nbsp;TV uses 75&nbsp;Ω coaxial cable, so 0&nbsp;dB{{sub| mV}} corresponds to −78.75&nbsp;dB{{sub| W}} {{nobr|( −48.75 dB{{sub| m}} )}} or approximately 13&nbsp;nW.

; dB{{sub| μV}} or dB{{sub| uV}} : dB(μV<sub>RMS</sub>) – voltage relative to 1&nbsp;microvolt. Widely used in television and aerial amplifier specifications. 60&nbsp;dBμV&nbsp;= 0&nbsp;dB{{sub| mV}}.

=== Acoustics ===
Probably the most common usage of "decibels" in reference to sound level is dB{{sub| SPL}}, sound pressure level referenced to the nominal threshold of human hearing:<ref>
{{cite book
 | title = Audio postproduction for digital video
 | first = Jay  | last = Rose
 | publisher = Focal Press
 | year = 2002
 | isbn = 978-1-57820-116-7
 | page = 25
 | url = {{Google books |plainurl=yes |id=sUcRegHAXdkC |page=25 }}
}}</ref>  The measures of pressure (a root-power quantity) use the factor of 20, and the measures of power (e.g. dB{{sub| SIL}} and dB{{sub| SWL}}) use the factor of 10.
; dB{{sub| SPL}} : dB{{sub| SPL}} (sound pressure level) – for sound in air and other gases, relative to 20&nbsp;micropascals (μPa), or {{val|2|e=-5|u=Pa}}, a level of 0&nbsp;dB{{sub| SPL}} is approximately the quietest sound a human can hear. For [[Underwater acoustics|sound in water]] and other liquids, a reference pressure of 1&nbsp;μPa is used.<ref>Morfey, C. L. (2001). Dictionary of Acoustics. Academic Press, San Diego.</ref>{{paragraphbreak}} An RMS sound pressure of one pascal corresponds to a level of 94&nbsp;dB&nbsp;SPL.
; dB{{sub| SIL}} : dB [[sound intensity level]] – relative to 10<sup>−12</sup>&nbsp;W/m<sup>2</sup>, which is roughly the [[threshold of human hearing]] in air.
; dB{{sub| SWL}} : dB [[sound power level]] – relative to 10<sup>−12</sup>&nbsp;W.
; dB{{sub| A}}, dB{{sub| B}}, and dB{{sub| C}} : These symbols are often used to denote the use of different [[weighting filter]]s, used to approximate the human ear's [[stimulus (psychology)|response]] to sound, although the measurement is still in dB&nbsp;(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{{sub| A}} or dB(A). According to standards from the International Electro-technical Committee ([[IEC 61672|IEC 61672-2013]])<ref>{{cite book |title=IEC 61672-1:2013 Electroacoustics - Sound Level meters - Part 1: Specifications |date=2013 |publisher=International Electrotechnical Committee |location=Geneva}}</ref> and the American National Standards Institute, [[ANSI S1.4]],<ref>[[ANSI]] [https://law.resource.org/pub/us/cfr/ibr/002/ansi.s1.4.1983.pdf S1.4-19823 Specification for Sound Level Meters], 2.3 Sound Level, p. 2–3.</ref> the preferred usage is to write {{nobr| {{mvar|L}}{{sub| A}} {{=}} {{mvar|x}}&nbsp;dB .}} Nevertheless, the units dB{{sub| A}} and dB(A) are still commonly used as a shorthand for A{{nbhyph}}weighted measurements. Compare [[dBc|dB{{sub| c}}]], used in telecommunications.
; dB{{sub| HL}} : dB [[hearing level]] is used in [[audiogram]]s 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.{{Citation needed|date=March 2008}}
; dB{{sub| Q}} : sometimes used to denote weighted noise level, commonly using the [[ITU-R 468 noise weighting]]{{Citation needed|date=March 2008}}
; dB{{sub| pp}} : relative to the peak to peak sound pressure.<ref>{{cite journal |last1=Zimmer |first1=Walter M.X. |first2=Mark P. |last2=Johnson |first3=Peter T. |last3=Madsen |first4=Peter L. |last4=Tyack |year=2005 |title=Echolocation clicks of free-ranging Cuvier's beaked whales (''Ziphius cavirostris'') |journal=[[The Journal of the Acoustical Society of America]] |volume=117 |issue=6 |pages=3919–3927 |doi=10.1121/1.1910225 |pmid=16018493 |bibcode=2005ASAJ..117.3919Z |hdl=1912/2358 |hdl-access=free }}</ref>
; dB{{sub| G}} : G‑weighted spectrum<ref>{{cite web | title = Turbine sound measurements |via=wustl.edu | url = http://oto2.wustl.edu/cochlea/wt4.html | url-status = dead | archive-url = https://web.archive.org/web/20101212221829/http://oto2.wustl.edu/cochlea/wt4.html | archive-date = 12 December 2010 }}</ref>

=== Audio electronics ===
See also dB{{sub| V}} and dB{{sub| u}} above.

; [[dBm|dB{{sub| m}}]] : dB(mW) – power relative to 1&nbsp;[[milliwatt]]. In audio and telephony, dB{{sub| m}} is typically referenced relative to a 600&nbsp;Ω impedance,<ref>{{cite book|last=Bigelow |first=Stephen |year=2001 |title=Understanding Telephone Electronics |publisher=Newnes Press |place=Boston, MA |isbn=978-0750671750 |page=[https://archive.org/details/isbn_9780750671750/page/16 16] |url-access=registration |url=https://archive.org/details/isbn_9780750671750/page/16 }}</ref> which corresponds to a voltage level of 0.775&nbsp;volts or 775&nbsp;millivolts.
; [[dBm0|dB{{sub| m0}}]] : Power in dB{{sub| m}} (described above) measured at a [[zero transmission level point]].
; [[dBFS|dB{{sub| FS}}]] : dB([[full scale]]) – the amplitude of a signal compared with the maximum which a device can handle before [[Clipping (signal processing)|clipping]] occurs. Full-scale may be defined as the power level of a full-scale [[Sine wave|sinusoid]] or alternatively a full-scale [[Square wave (waveform)|square wave]]. A signal measured with reference to a full-scale sine-wave appears 3&nbsp;dB weaker when referenced to a full-scale square wave, thus: 0&nbsp;dBFS(fullscale sine wave) = −3&nbsp;dB{{sub| FS}} (fullscale square wave).
; dB{{sub| VU}} : dB [[volume unit]]<ref>{{cite journal |last=Thar |first=D. |year=1998 |title=Case Studies: Transient sounds through communication headsets |journal=Applied Occupational and Environmental Hygiene |volume=13 |issue=10 |pages=691–697 |doi=10.1080/1047322X.1998.10390142 }}</ref>
; dB{{sub| TP}} : dB(true peak) – [[peak amplitude]] of a signal compared with the maximum which a device can handle before clipping occurs.<ref>[[ITU-R BS.1770]]</ref> In digital systems, 0&nbsp;dB{{sub| TP}} 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.

=== Radar ===
; [[dBZ (meteorology)|dB{{sub| Z}}]] : dB(Z) – decibel relative to Z&nbsp;= 1&nbsp;mm{{sup|6 }}⋅m{{sup|−3 }}:<ref>{{cite web |title=Terms starting with&nbsp;'''D''' |department=Glossary |publisher=U.S. [[National Weather Service]] |website=weather.gov |url=https://www.weather.gov/jetstream/glossary_d<!-- Former URL: http://www.srh.noaa.gov/jetstream/append/glossary_d.htm --> |access-date=2013-04-25 |archive-url=https://web.archive.org/web/20190808140856/https://www.weather.gov/jetstream/glossary_d |archive-date=2019-08-08 |url-status=live}}</ref> energy of reflectivity (weather radar), related to the amount of transmitted power returned to the radar receiver. Values above 20&nbsp;dB{{sub| Z}} usually indicate falling precipitation.<ref>{{cite web |title=Frequently Asked Questions |department=RIDGE Radar |publisher=U.S. [[National Weather Service]] |website=weather.gov |url=https://www.weather.gov/jetstream/radarfaq#reflcolor |access-date=2019-08-08 |archive-url=https://web.archive.org/web/20190331123302/https://www.weather.gov/jetstream/radarfaq#reflcolor |archive-date=2019-03-31 |url-status=live }}</ref>
; dB{{sub| sm}} : dB(m²) – 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 dB{{sub| sm }}, large flat plates or non-stealthy aircraft have positive values.<ref>{{cite web |title=dBsm |department=Definition |website=Everything&nbsp;2 |url=http://everything2.com/title/dBsm |access-date=2019-08-08 |archive-url=https://web.archive.org/web/20190610170944/https://everything2.com/title/dBsm?%2F |archive-date=10 June 2019 |url-status=live }}</ref>

=== Radio power, energy, and field strength ===
; [[dBc|dB{{sub| c}}]] : relative to carrier – in [[telecommunications]], this indicates the relative levels of noise or sideband power, compared with the carrier power. Compare dB{{sub| C}}, used in acoustics.
; dB{{sub| pp}} : relative to the maximum value of the peak power.
; dB{{sub| J}} : energy relative to 1&nbsp;[[joule]]. 1&nbsp;joule&nbsp;= 1&nbsp;watt second&nbsp;= 1&nbsp;watt per hertz, so power spectral density can be expressed in dB{{sub| J }}.
; [[dBm|dB{{sub| m}}]] : dB(mW) – power relative to 1&nbsp;[[milliwatt]]. In the radio field, dB{{sub| m}} is usually referenced to a 50&nbsp;Ω load, with the resultant voltage being 0.224&nbsp;volts.<ref>{{cite book |last=Carr |first=Joseph |author-link=Joseph Carr |year=2002 |title=RF Components and Circuits |publisher=Newnes |isbn=978-0750648448 |pages=45–46 }}</ref>
; dB{{sub| μV/m }}, dB{{sub| uV/m }}, or dB{{sub| μ }} :<ref name="dBμ">{{cite web |title=The dBμ vs. dBu mystery: Signal strength vs. field strength? |date=24 February 2015 |website=Radio Time Traveller (radio-timetraveller.blogspot.com) |type=blog |via=blogspot.com |url=http://radio-timetraveller.blogspot.com/2015/02/the-db-versus-dbu-mystery-signal.html |access-date=13 October 2016 }}</ref> dB(μV/m) – [[electric field strength]] relative to 1&nbsp;[[microvolt]] per [[meter]]. The unit is often used to specify the signal strength of a [[television]] [[broadcast]] at a receiving site (the signal measured ''at the antenna output'' is reported in dBμ{{sub| V}}).
; dB{{sub| f}} : dB(fW) – power relative to 1&nbsp;[[femtowatt]].
; dB{{sub| W}} : dB(W) – power relative to 1&nbsp;[[watt]].
; dB{{sub| k}} : dB(kW) – power relative to 1&nbsp;[[kilowatt]].
; dB{{sub| e}} : dB electrical.
; dB{{sub| o}} : dB optical. A change of 1&nbsp;dB{{sub| o}} in optical power can result in a change of up to 2&nbsp;dB{{sub| e}} in electrical signal power in a system that is thermal noise limited.<ref>{{cite journal |last1=Chand |first1=N. |last2=Magill |first2=P.D. |last3=Swaminathan |first3=S.V. |last4=Daugherty |first4=T.H. |year=1999 |title=Delivery of digital video and other multimedia services {{nobr|( > 1 Gb/s}} bandwidth) in passband above the 155&nbsp;Mb/s baseband services on a FTTx full service access network |journal=Journal of Lightwave Technology |volume=17 |issue=12 |pages=2449–2460 |doi=10.1109/50.809663 }}</ref>

=== Antenna measurements ===
; dB{{sub| i}} : dB(isotropic) <span id="dBi_anchor" class="anchor"></span> – the [[antenna gain|gain]] of an antenna compared with the gain of a theoretical [[isotropic antenna]], which uniformly distributes energy in all directions. [[Linear polarization]] of the EM field is assumed unless noted otherwise.
; dB{{sub| d}} : dB(dipole) – the [[antenna gain|gain]] of an [[antenna (electronics)|antenna]] compared with the gain a half-wave [[dipole antenna]]. 0&nbsp;dBd&nbsp;= 2.15&nbsp;dBi
; dB{{sub| iC}} : dB(isotropic circular) – the gain of an antenna compared to the gain of a theoretical [[Circular polarization|circularly polarized]] isotropic antenna. There is no fixed conversion rule between dB{{sub|iC}} and dB{{sub|i}}, as it depends on the receiving antenna and the field polarization.
; dB{{sub| q}} : dB(quarterwave) – the [[antenna gain|gain]] of an antenna compared to the gain of a quarter wavelength whip. Rarely used, except in some marketing material; {{nobr|0 dB{{sub|q}}}}&nbsp;= {{nobr|−0.85 dB{{sub|i}}}}
; dB{{sub| sm}} : dB{{sub| m²}}, dB(m²) – decibels relative to one square meter: A measure of the [[antenna effective area|effective area]] for capturing signals of the antenna.<ref>{{cite book |first=David |last=Adamy |year=2004 |title=EW&nbsp;102: A second course in electronic warfare |series=Artech House Radar Library |place=Boston, MA |publisher=Artech House |isbn=9781-58053687-5 |page=[{{Google books |plainurl=yes |id=-AkfVZskc64C |page=118 }} 118] |url={{Google books |plainurl=yes |id=-AkfVZskc64C }} |via=Google |access-date=2013-09-16}}</ref>
; dB{{sub| m⁻¹}} : dB(m{{sup|−1}}) – decibels relative to reciprocal of meter: measure of the [[antenna factor]].

=== Other measurements ===
; dB{{sub| Hz}} or dB‑Hz : dB(Hz) – bandwidth relative to one hertz. E.g., 20&nbsp;dB{{nbhyph}}Hz corresponds to a bandwidth of 100&nbsp;Hz. Commonly used in [[link budget]] calculations. Also used in [[carrier-to-receiver noise density|carrier-to-noise-density ratio]] (not to be confused with [[carrier-to-noise ratio]], in dB).
; [[dBFS|dB{{sub| ov}} or dB{{sub| O}}]]: dB(overload) – the amplitude of a signal (usually audio) compared with the maximum which a device can handle before [[Clipping (signal processing)|clipping]] occurs. Similar to dB FS, but also applicable to analog systems. According to ITU-T Rec. G.100.1 the level in dB ov of a digital system is defined as: <math display = "block">\ L_\mathsf{ov} = 10 \log_{10} \left( \frac{ P }{\ P_\mathsf{max}\ } \right)\ [\mathsf{dB_{ov}}]\ ,</math> with the maximum signal power <math>\ P_\mathsf{max} = 1.0\ ,</math> for a rectangular signal with the maximum amplitude <math>\ x_\mathsf{over} ~.</math> The level of a tone with a digital amplitude (peak value) of <math>\ x_\mathsf{over}\ </math> is therefore <math>\ L_\mathsf{ov} = -3.01\ \mathsf{dB_{ov}} ~.</math><ref>{{cite report |title=The use of the decibel and of relative levels in speech band telecommunications |date=June 2015 |id=ITU-T Rec. G.100.1 |publisher=[[International Telecommunication Union]] (ITU) |place=Geneva, CH |type=tech spec |url=https://www.itu.int/rec/dologin_pub.asp?lang=e&id=T-REC-G.100.1-201506-I!!PDF-E&type=items }}</ref>
; dB{{sub| r}} : 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{{sub| rn}}]] : dB above [[reference noise]].  See also '''dB{{sub| rnC}}'''
; dB{{sub| rnC}} : '''dB(rnC)''' represents an audio level measurement, typically in a telephone circuit, relative to a −90&nbsp;dB{{sub| m}} reference 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 weighting|psophometric]] filter is used for this purpose on international circuits.{{efn|See ''[[psophometric weighting]]'' to see a comparison of frequency response curves for the C-message weighting and psophometric weighting filters.}}<ref>Definition of dB{{sub| rnC}} is given in <br/>{{cite book |editor-first=R.F. |editor-last=Rey |year=1983 |title=Engineering and Operations in the Bell System |edition=2nd |publisher=AT&T Bell Laboratories |place=Murray Hill, NJ |isbn=0-932764-04-5 |page=230 }}</ref>
; dB{{sub| K}} : '''dB(K)''' – decibels relative to 1&nbsp;[[kelvin|K]]; used to express [[noise temperature]].<ref>{{cite book |first=K.N. Raja |last=Rao |date=2013-01-31 |df=dmy-all |title=Satellite Communication: Concepts and applications |page=[{{Google books |plainurl=yes |id=pjEubAt5dk0C |page=126 }} 126] |url={{Google books |plainurl=yes |id=pjEubAt5dk0C }} |via=Google |access-date=2013-09-16 }}</ref>
; dB{{sub| K⁻¹}} or dB{{sub|/K}} : dB(K⁻¹) – decibels relative to 1&nbsp;K⁻¹.<ref>{{cite book |first=Ali Akbar |last=Arabi |year= |title=Comprehensive Glossary of Telecom Abbreviations and Acronyms |page=[{{Google books |plainurl=yes |id=DVoqmlX6048C |page=79 }} 79] |url={{Google books |plainurl=yes |id=DVoqmlX6048C }} |via=Google |access-date=2013-09-16 |df=dmy-all }}</ref> — ''not'' decibels per Kelvin: Used for the {{mvar|{{sfrac| G | T }} }} [[G/T|(G/T) factor]], a [[figure of merit]] used in [[satellite communications]], relating the [[antenna gain]] {{mvar|G}} to the [[receiver (radio)|receiver]] system noise equivalent temperature {{mvar|T}}.<ref>{{cite book |first=Mark E. |last=Long |year=1999 |title=The Digital Satellite TV Handbook |place=Woburn, MA |publisher=Newnes Press |page=[{{Google books |plainurl=yes |id=L4yQ0iztvQEC |page=93 }} 93] |url={{Google books |plainurl=yes |id=L4yQ0iztvQEC }} |access-date=2013-09-16 |df=dmy-all }}</ref><ref>{{cite book |first=Mac E. |last=van&nbsp;Valkenburg |date=2001-10-19 |df=dmy-all |title=Reference Data for Engineers: Radio, electronics, computers, and communications |series=Technology & Engineering |editor-first=Wendy M. |editor-last=Middleton |place=Woburn, MA |publisher=Newness Press |isbn=9780-08051596-0 |page=[{{Google books |plainurl=yes |id=U9RzPGwlic4C |page=SA27-PA14 }} 27·14] |url={{Google books |plainurl=yes |id=U9RzPGwlic4C }} |via=Google |access-date=2013-09-16}}</ref>

=== List of suffixes in alphabetical order ===

==== Unpunctuated suffixes ====
; dB{{sub| A}} : see [[dB(A)]].
; dB{{sub| a}} : see [[dBrn adjusted|dB{{sub| rn}} adjusted]].
; dB{{sub| B}} : see [[dB(B)]].
; [[dBc|dB{{sub| c}}]] : relative to carrier – in [[telecommunications]], this indicates the relative levels of noise or sideband power, compared with the carrier power. 
; dB{{sub| C}} : see [[dB(C)]].
; dB{{sub| D}} : see [[dB(D)]].
; dB{{sub| d}} : dB(dipole) – the forward gain of an [[antenna (electronics)|antenna]] compared with a half-wave [[dipole antenna]]. 0&nbsp;dBd = 2.15&nbsp;dB{{sub| i}}
; dB{{sub| e}} : dB electrical.
; dB{{sub| f}} : dB(fW) – power relative to 1&nbsp;[[femtowatt]].
; [[dBFS|dB{{sub| FS}}]] : dB([[full scale]]) – the amplitude of a signal compared with the maximum which a device can handle before [[clipping (signal processing)|clipping]] occurs. Full-scale may be defined as the power level of a full-scale [[Sine wave|sinusoid]] or alternatively a full-scale [[Square wave (waveform)|square wave]]. A signal measured with reference to a full-scale sine-wave appears 3&nbsp;dB weaker when referenced to a full-scale square wave, thus: 0&nbsp;dB{{sub| FS}} (fullscale sine wave)&nbsp;= −3&nbsp;dB{{sub| FS}} (full-scale square wave).
; dB{{sub| G}} : [[G-weighted]] spectrum
; dB{{sub| i}} : dB(isotropic) – the forward [[antenna gain|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.
; dB{{sub| iC}} : dB(isotropic circular) – the forward gain of an antenna compared to a [[Circular polarization|circularly polarized]] isotropic antenna. There is no fixed conversion rule between dB{{sub| iC}} and dB{{sub| i }}, as it depends on the receiving antenna and the field polarization.
; dB{{sub| J}} : energy relative to 1&nbsp;[[joule]]: 1&nbsp;joule&nbsp;= 1&nbsp;watt-second&nbsp;= 1 watt per hertz, so power spectral density can be expressed in dB{{sub| J }}.
; dB{{sub| k}} : dB(kW) – power relative to 1&nbsp;[[kilowatt]].
; dB{{sub| K}} :'''dB(K)''' – decibels relative to [[kelvin]]: Used to express [[noise temperature]].
; [[dBm|dB{{sub| m}}]] : dB(mW) – power relative to 1 [[milliwatt]]. 
; dB{{sub| m²}} or dB{{sub| sm}} : dB(m²) – decibel relative to one square meter
; [[dBm0|dB{{sub| m0}}]] : Power in dB{{sub| m}} measured at a zero transmission level point.
; dB{{sub| m0s}} : Defined by ''Recommendation ITU-R V.574''.
; dB{{sub| mV}} : dB(mV<sub>RMS</sub>) – voltage relative to 1&nbsp;millivolt across 75&nbsp;Ω.
; dB{{sub| o}} : dB optical. A change of 1&nbsp;dB{{sub| o}} in optical power can result in a change of up to 2&nbsp;dB{{sub| e}} in electrical signal power in system that is thermal noise limited.
; dB{{sub| O}} : see dB{{sub| ov}} 
; dB{{sub| ov}} or dB{{sub| O}} : dB(overload) – the amplitude of a signal (usually audio) compared with the maximum which a device can handle before [[Clipping (signal processing)|clipping]] occurs.
; dB{{sub| pp}} : relative to the peak to peak [[sound pressure]].
; dB{{sub| pp}} : relative to the maximum value of the peak [[electrical power]].
; dB{{sub| q}} : dB(quarterwave) – the forward gain of an antenna compared to a quarter wavelength whip. Rarely used, except in some marketing material. 0&nbsp;dBq&nbsp;= −0.85&nbsp;dB{{sub| i}}
; dB{{sub| r}} : 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{{sub| rn}}]] : dB above [[reference noise]].  See also '''dB{{sub| rnC}}'''
; dB{{sub| rnC}} : '''dB{{sub| rnC}}''' 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.
; dB{{sub| sm}} : see dB{{sub| m²}}
; dB{{sub| TP}} : dB(true peak) – [[peak amplitude]] of a signal compared with the maximum which a device can handle before clipping occurs.
; dB{{sub| u}} or dB{{sub| v}} : RMS voltage relative to <math>\ \sqrt{0.6\; }\ \mathsf{V}\ \approx 0.7746\ \mathsf{V}\ \approx -2.218\ \mathsf{dB_V} ~.</math>
; dB{{sub| u0s}} : Defined by ''Recommendation ITU-R V.574''.
; dB{{sub| uV}} : see dB{{sub| μV}}
; dB{{sub| uV/m}} : see dB{{sub| μV/m}}
; dB{{sub| v}} : see dB{{sub| u}}
; dB{{sub| V}} : dB(V<sub>RMS</sub>) – voltage relative to 1 volt, regardless of impedance.
; dB{{sub| VU}} : dB(VU) dB [[volume unit]]
; dB{{sub| W}} : dB(W) – power relative to 1&nbsp;[[watt]].
; dB{{sub| W·m⁻²·Hz⁻¹}} : [[Jansky#dBW·m−2·Hz−1|spectral density]] relative to 1 W·m⁻²·Hz⁻¹<ref>{{cite web |title=Units and calculations |website=iucaf.org |url=http://www.iucaf.org/sschool/mike/Units_and_Calculations.ppt |last1=Davis |first1=Mike |format=PPT |date=June 2002 |access-date=2025-03-12 |url-status=live |archive-url=https://web.archive.org/web/20160303223821/http://www.iucaf.org/sschool/mike/Units_and_Calculations.ppt |archive-date=2016-03-03 }}</ref>
; [[DBZ (meteorology)|dB{{sub| Z}}]] : dB(Z) – decibel relative to Z&nbsp;= 1&nbsp;mm<sup>6</sup>⋅m<sup>−3</sup>
; dB{{sub| μ}} : see dB{{sub| μV/m}}
; dB{{sub| μV}} or dB{{sub| uV}} : dB(μV<sub>RMS</sub>) – voltage relative to 1&nbsp;root mean square microvolt.
; dB{{sub| μV/m }}, dB{{sub| uV/m }}, or dB{{sub| μ }} : dB(μV/m) – [[electric field strength]] relative to 1&nbsp;[[microvolt]] per [[meter]].

==== Suffixes preceded by a space ====
; dB HL : dB hearing level is used in [[audiogram]]s as a measure of hearing loss. 
; dB Q : sometimes used to denote weighted noise level
; dB SIL : dB [[sound intensity level]] – relative to 10<sup>−12</sup>&nbsp;W/m<sup>2</sup> 
; dB SPL : dB SPL (sound pressure level) – for sound in air and other gases, relative to 20&nbsp;μPa in air or 1&nbsp;μPa in water
; dB SWL : dB [[sound power level]] – relative to 10<sup>−12</sup>&nbsp;W.

==== Suffixes within parentheses ====
; [[dB(A)]], [[dB(B)]], [[dB(C)]], [[dB(D)]], [[dB(G)]],<!-- possibly also dB(M), but I haven't seen this in practise yet --> and [[dB(Z)]] : These symbols are often used to denote the use of different [[weighting filter]]s, used to approximate the human ear's [[Stimulus (psychology)|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<sub>A</sub> or dBA.

==== Other suffixes ====
; dB{{sub| Hz}} or dB-Hz : dB(Hz) – bandwidth relative to one [[Hertz (unit)|Hertz]]
;  dB{{sub| K⁻¹}} or dB{{sub| /K}} : dB(K⁻¹) – decibels relative to [[multiplicative inverse|reciprocal]] of [[kelvin]]
; dB{{sub| m⁻¹}} : dB(m⁻¹) – decibel relative to reciprocal of meter: measure of the [[antenna factor]]

; mB{{sub| m}} : {{anchor|Millibel}} mB(mW) – power relative to 1&nbsp;[[milliwatt]], in millibels (one hundredth of a decibel). 100&nbsp;mB{{sub| m}} = 1&nbsp;dB{{sub| m }}. This unit is in the Wi-Fi drivers of the [[Linux]] kernel<ref>{{cite web |title=Setting {{sc|TX}} power |series=en:users:documentation:iw |website=wireless.kernel.org |url=http://wireless.kernel.org/en/users/Documentation/iw#Setting_TX_power }}</ref> and the regulatory domain sections.<ref>{{cite web |title=Is your Wi Fi ap missing channels&nbsp;12 and 13&nbsp;? |date=16 May 2013 |website=Pentura Labs |via=wordpress.com  |url=http://penturalabs.wordpress.com/2013/05/16/is-your-wifi-ap-missing-channels-12-13/ }}</ref>

== See also ==
{{div col begin|colwidth=8}}
* [[Apparent magnitude]]
* [[Cent (music)]]
* [[Day–evening–night noise level]] (L<sub>den</sub>) and [[day-night average sound level]] (Ldl), European and American standards for expressing noise level over an entire day
* [[dB drag racing]]
* [[Decade (log scale)]]
* [[Loudness]]
* [[Neper]] 
* {{Section link|One-third octave|Base 10}}
* [[pH]]
* [[Phon]]
* [[Richter magnitude scale]]
* [[Sone]]
{{div col end}}

== Notes ==
{{notelist}}

== References ==
{{reflist|25em}}

== Further reading ==
* {{cite journal |author-last=Tuffentsammer |author-first=Karl |title=Das Dezilog, eine Brücke zwischen Logarithmen, Dezibel, Neper und Normzahlen |language=de |trans-title=The decilog, a bridge between logarithms, decibel, neper and preferred numbers |journal=VDI-Zeitschrift |volume=98 |date=1956 |pages=267–274}}
* {{cite book |title=Logarithmen, Normzahlen, Dezibel, Neper, Phon - natürlich verwandt! |language=de |trans-title=Logarithms, preferred numbers, decibel, neper, phon - naturally related! |author-first=Eugen |author-last=Paulin |date=2007-09-01 |url=http://www.rechenschieber.org/Normzahlen.pdf |access-date=2016-12-18 |url-status=live |archive-url=https://web.archive.org/web/20161218223050/http://www.rechenschieber.org/Normzahlen.pdf |archive-date=2016-12-18}}

== External links ==
* [http://www.phys.unsw.edu.au/jw/dB.html What is a decibel? With sound files and animations]
* [http://www.sengpielaudio.com/calculator-soundlevel.htm Conversion of sound level units:  dBSPL or dBA to sound pressure p and sound intensity J]
* [https://www.osha.gov/pls/oshaweb/owadisp.show_document?p_table=STANDARDS&p_id=9735 OSHA Regulations on Occupational Noise Exposure]
* [http://learnemc.com/working-with-decibels Working with Decibels] (RF signal and field strengths)
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{{Decibel}}
{{SI units}}
{{Authority control}}

[[Category:Acoustics]]
[[Category:Audio electronics]]
[[Category:Radio frequency propagation]]
[[Category:Telecommunications engineering]]
[[Category:Units of level]]