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dB  power ratio  amplitude ratio  

100  10 000 000 000  100 000  
90  1 000 000 000  31 623  
80  100 000 000  10 000  
70  10 000 000  3 162  
60  1 000 000  1 000  
50  100 000  316  .2  
40  10 000  100  
30  1 000  31  .62  
20  100  10  
10  10  3  .162  
6  3  .981  1  .995 (~2) 
3  1  .995 (~2)  1  .413 
1  1  .259  1  .122 
0  1  1  
−1  0  .794  0  .891 
−3  0  .501 (~1/2)  0  .708 
−6  0  .251  0  .501 (~1/2) 
−10  0  .1  0  .316 2 
−20  0  .01  0  .1 
−30  0  .001  0  .031 62 
−40  0  .000 1  0  .01 
−50  0  .000 01  0  .003 162 
−60  0  .000 001  0  .001 
−70  0  .000 000 1  0  .000 316 2 
−80  0  .000 000 01  0  .000 1 
−90  0  .000 000 001  0  .000 031 62 
−100  0  .000 000 000 1  0  .000 01 
An example scale showing power ratios x and amplitude ratios √x and dB equivalents 10 log_{10} x. It is easier to grasp and compare 2 or 3digit numbers than to compare up to 10 digits. 
dB  power ratio  amplitude ratio  

100  10 000 000 000  100 000  
90  1 000 000 000  31 623  
80  100 000 000  10 000  
70  10 000 000  3 162  
60  1 000 000  1 000  
50  100 000  316  .2  
40  10 000  100  
30  1 000  31  .62  
20  100  10  
10  10  3  .162  
6  3  .981  1  .995 (~2) 
3  1  .995 (~2)  1  .413 
1  1  .259  1  .122 
0  1  1  
−1  0  .794  0  .891 
−3  0  .501 (~1/2)  0  .708 
−6  0  .251  0  .501 (~1/2) 
−10  0  .1  0  .316 2 
−20  0  .01  0  .1 
−30  0  .001  0  .031 62 
−40  0  .000 1  0  .01 
−50  0  .000 01  0  .003 162 
−60  0  .000 001  0  .001 
−70  0  .000 000 1  0  .000 316 2 
−80  0  .000 000 01  0  .000 1 
−90  0  .000 000 001  0  .000 031 62 
−100  0  .000 000 000 1  0  .000 01 
An example scale showing power ratios x and amplitude ratios √x and dB equivalents 10 log_{10} x. It is easier to grasp and compare 2 or 3digit numbers than to compare up to 10 digits. 
The decibel (dB) is a logarithmic unit used to express the ratio between two values of a physical quantity, often power or intensity. One of these quantities is often a reference value, and in this case the decibel can be used to express the absolute level of the physical quantity, as in the case of sound pressure. The number of decibels is ten times the logarithm to base 10 of the ratio of two power quantities,^{[1]} or of the ratio of the squares of two field amplitude quantities. One decibel is one tenth of one bel, named in honor of Alexander Graham Bell. The bel is seldom used without the deci prefix.
The definition of the decibel is based on the measurement practices in telephony of the early 20th century in the Bell System in the United States. Today, the unit 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 signaltonoise ratios are often expressed in decibels. The decibel confers a number of advantages, such as the ability to conveniently represent very large or small numbers, and the ability to carry out multiplication of ratios by simple addition and subtraction.
A change in power by a factor of 10 corresponds to a 10 dB change in level. A change in power by a factor of two approximately corresponds to a 3 dB change. A change in voltage by a factor of 10 results in a change in power by a factor of 100 and corresponds to a 20 dB change. A change in voltage ratio by a factor of two approximately corresponds to a 6 dB change.
The decibel symbol is often qualified with a suffix that indicates which reference quantity has been used or some other property of the quantity being measured. For example, dBm indicates a reference level of one milliwatt, while dBu is referenced to approximately 0.775 volts RMS.^{[2]}
In the International System of Quantities, the decibel is defined as a unit of level or of level difference, equal to onetenth of a bel. The bel is then defined in terms of the neper, an alternative unit of level of rootpower quantities, applicable when the natural logarithm (base e) is used to define the level.^{[3]}
The decibel originates from methods used to quantify signal losses in telephone circuits. These losses were originally measured in units of Miles of Standard Cable (MSC), where 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 roughly matched the smallest attenuation detectable to the average listener. Standard telephone cable was defined as "a cable having uniformly distributed resistance of 88 ohms per loop mile and uniformly distributed shunt capacitance of .054 microfarad per mile" (approximately 19 gauge).^{[4]}
The transmission unit (TU) was devised by engineers of the Bell Telephone Laboratories in the 1920s to replace the MSC. 1 TU was defined as ten times the base10 logarithm of the ratio of measured power to a reference power level.^{[5]} The definitions were conveniently chosen such that 1 TU approximately equaled 1 MSC (specifically, 1.056 TU = 1 MSC).The threshold of hearing is 25 dB^{[6]} In 1928, the Bell system renamed the TU the decibel,^{[7]} being one tenth of a newly defined unit for the base10 logarithm of the power ratio. It was named the bel, in honor of their founder and telecommunications pioneer Alexander Graham Bell.^{[8]} The bel is seldom used, as the decibel was the proposed working unit.^{[9]}
The naming and early definition of the decibel is described in the NBS Standard's Yearbook of 1931:^{[10]}
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 by N decibels 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 April 2003, the International Committee for Weights and Measures (CIPM) considered a recommendation for the decibel's inclusion in the International System of Units (SI), but decided not to adopt the decibel as an SI unit.^{[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, which favors rootpower. In spite of their widespread use, suffixes (as in dBA or dBV) are not recognized by the IEC or ISO.
The decibel (dB) is one tenth of the bel (B): 1B = 10dB. The bel is (1/2) ln(10) nepers.
The bel represents a ratio between two power quantities of 10:1, and a ratio between two field quantities of √10:1.^{[14]} A field quantity is a quantity such as voltage, current, pressure, electric field strength, velocity, or charge density, the square of which in linear systems is proportional to power.^{[15]} A power quantity is a power or a quantity directly proportional to power, e.g., energy density, acoustic intensity and luminous intensity.
The method of calculation of a ratio in decibels depends on whether the measured property is a power quantity or a field quantity.
Two signals that differ by one decibel have a power ratio of which is approximately 1.25892, and an amplitude (field) ratio of (1.12202).^{[16]}^{[17]}
Although permissible, the bel is rarely used with other SI unit prefixes than deci. It is preferred to use hundredths of a decibel rather than millibels.^{[18]}
The bel is defined by ISO Standard 800003:2006 as (1/2) ln(10) nepers (Np), where ln denotes the natural logarithm. Because the decibel is one tenth of a bel, it follows that 1 dB = (1/20) ln(10) Np. The same standard defines 1 Np as equal to 1 (thereby relating all of the units as nondimensional natural log of fieldquantity ratios, 1 dB = 0.11513..., 1 B = 1.1513...). 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  corresponding power ratio  corresponding field ratio 

1 dB  1 dB  0.1 B  0.11513 Np  10^{1/10} = 1.25893  10^{1/20} = 1.12202 
1 B  10 dB  1 B  1.1513 Np  10  10^{1/2} = 3.16228 
1 Np  8.68589 dB  0.868589 B  1 Np  e^{2} = 7.38906  e = 2.71828 
When referring to measurements of power or intensity, a ratio can be expressed in decibels by evaluating ten times the base10 logarithm of the ratio of the measured quantity to the reference level. Thus, the ratio of a power value P_{1} to another power value P_{0} is represented by L_{dB}, that ratio expressed in decibels,^{[19]} which is calculated using the formula:
The base10 logarithm of the ratio of the two power levels is the number of bels. The number of decibels is ten times the number of bels (equivalently, a decibel is onetenth of a bel). P_{1} and P_{0} must measure the same type of quantity, and have the same units before calculating the ratio. If P_{1} = P_{0} in the above equation, then L_{dB} = 0. If P_{1} is greater than P_{0} then L_{dB} is positive; if P_{1} is less than P_{0} then L_{dB} is negative.
Rearranging the above equation gives the following formula for P_{1} in terms of P_{0} and L_{dB}:
When referring to measurements of field amplitude, it is usual to consider the ratio of the squares of A_{1} (measured amplitude) and A_{0} (reference amplitude). This is because in most applications power is proportional to the square of amplitude, 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_{1} 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 rootpower quantity is introduced by ISO Standard 800001:2009 as a substitute of field quantity. The term field quantity is deprecated by that standard.
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.
, illustrating the consequence from the definitions above that has the same value, , 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.
A change in power ratio by a factor of 10 is a change of 10 dB. A change in power ratio by a factor of two is approximately a change of 3 dB. More precisely, the factor is 10^{3/10}, or 1.9953, about 0.24% different from exactly 2. Similarly, an increase of 3 dB implies an increase in voltage by a factor of approximately , or about 1.41, an increase of 6 dB corresponds to approximately four times the power and twice the voltage, and so on. In exact terms the power ratio is 10^{6/10}, or about 3.9811, a relative error of about 0.5%.
The decibel has the following properties:
According to several articles published in Electrical Engineering^{[27]} and the Journal of the Acoustical Society of America,^{[28]}^{[29]}^{[30]} the decibel suffers from the following disadvantages:
Hickling concludes "Decibels are a useless affectation, which is impeding the development of noise control as an engineering discipline".^{[29]}
Another disadvantage is that quantities in decibels are not necessarily additive,^{[31]}^{[32]} thus being "of unacceptable form for use in dimensional analysis".^{[33]}
For the same reason that decibels excel at multiplicative operations (e.g., antenna gain), they are awkward when dealing with additive operations. Peters (2013, p. 13)^{[34]} provides several examples:
The decibel is commonly used in acoustics as a unit of sound pressure level, for a reference pressure of 20 micropascals in air^{[35]} and 1 micropascal in water. The reference pressure 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:
The human ear has a large dynamic range in audio reception. The ratio of the sound intensity that causes permanent damage during short exposure to the quietest sound that the ear can hear is greater than or equal to 1 trillion (10^{12}).^{[36]} Such large measurement ranges are conveniently expressed in logarithmic scale: the base10 logarithm of 10^{12} is 12, which is expressed as a sound pressure level of 120 dB re 20 micropascals. 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.)
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". Zero dBm is the level corresponding to one milliwatt, and 1 dBm is one decibel greater (about 1.259 mW).
In professional audio specifications, a popular unit is the dBu. The suffix u stands for unloaded, and was probably chosen to be similar to lowercase v, as dBv was the older name for the same unit. It was changed to avoid confusion with dBV.^{[citation needed]} The dBu is a root mean square (RMS) measurement of voltage that uses as its reference approximately 0.775 V_{RMS}. Chosen for historical reasons, the reference value is the voltage level which delivers 1 mW of power in a 600 ohm resistor, which used to be the standard reference impedance in telephone circuits.
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 electronic 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.^{[37]}
In spectrometry and optics, the blocking unit used to measure optical density is equivalent to −1 B.
In connection with video and digital image sensors, decibels generally represent ratios of video voltages or digitized light levels, using 20 log of the ratio, even when the represented optical power is directly proportional to the voltage or level, not to its square, as in a CCD imager where response voltage is linear in intensity.^{[38]} Thus, a camera signaltonoise ratio or dynamic range of 40 dB represents a power ratio of 100:1 between signal power and noise power, not 10,000:1.^{[39]} 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.^{[40]}
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 "signaltonoise" (of the camera) would be specified in 20 log dBs, 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 also often use an alternative base2 log unit, the fstop, and in software contexts these image level ratios, particularly dynamic range, are often loosely referred to by the number of bits needed to represent the quantity, such that 60 dB (digital photographic) is roughly equal to 10 fstops or 10 bits, since 10^{3} is nearly equal to 2^{10}.
Suffixes are commonly attached to the basic dB unit in order to indicate the reference value against which the decibel measurement is taken. For example, dBm indicates power measurement relative to 1 milliwatt.
In cases such as this, where the numerical value of the reference is explicitly and exactly stated, the decibel measurement is called an "absolute" measurement, in the sense that the exact value of the measured quantity can be recovered using the formula given earlier. If the numerical value of the reference is not explicitly stated, as in the dB gain of an amplifier, then the decibel measurement is purely 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 600273,^{[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 disciplinespecific practices. Sometimes the suffix is a unit symbol ("W","K","m"), sometimes it's a transliteration of a unit symbol ("uV" instead of μV for micro volt), sometimes it's an acronym for the units name ("sm" for m^{2}, "m" for mW), other times it's a mnemonic for the type of quantity being calculated ("i" for antenna gain w.r.t. 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 Aweighted sound pressure level). The suffix is often connected with a dash (dBHz), with a space (dB HL), with no intervening character (dBm), or enclosed in parentheses, dB(sm).
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
dBu or dBv
dBmV
dBμV or dBuV
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:^{[44]} 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
An RMS sound pressure of one pascal corresponds to a level of 94 dB SPL.
dB SIL
dB SWL
dB(A), dB(B), and dB(C)
dB HL or 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.^{[citation needed]}
dB Q is sometimes used to denote weighted noise level, commonly using the ITUR 468 noise weighting^{[citation needed]}
dBTP
dBsm
dBi
dBd
dBiC
dBq
dBsm
dBm^{−1}
dBHz
dBov or dBO
dBr
dBrnC
dBK
dB/K
Np or cNp
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 100meter run with a 3.5 dB/km fiber yields a loss of 0.35 dB = 3.5 dB/km × 0.1 km.

