Decibels
| dB | Power ratio | Amplitude ratio | ||
|---|---|---|---|---|
| 100 | 10000000000 | 100000 | ||
| 90 | 1000000000 | 31623 | ||
| 80 | 100000000 | 10000 | ||
| 70 | 10000000 | 3162 | ||
| 60 | 1000000 | 1000 | ||
| 50 | 100000 | 316 | .2 | |
| 40 | 10000 | 100 | ||
| 30 | 1000 | 31 | .62 | |
| 20 | 100 | 10 | ||
| 10 | 10 | 3 | .162 | |
| 6 | 3 | .981 | 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 | .3162 |
| −20 | 0 | .01 | 0 | .1 |
| −30 | 0 | .001 | 0 | .03162 |
| −40 | 0 | .0001 | 0 | .01 |
| −50 | 0 | .00001 | 0 | .003162 |
| −60 | 0 | .000001 | 0 | .001 |
| −70 | 0 | .0000001 | 0 | .0003162 |
| −80 | 0 | .00000001 | 0 | .0001 |
| −90 | 0 | .000000001 | 0 | .00003162 |
| −100 | 0 | .0000000001 | 0 | .00001 |
| An example scale showing power ratios x and amplitude ratios √x and dB equivalents 10 log10 x. | ||||
The decibel (dB) is a logarithmic unit used to express the ratio of two values of a physical quantity. One of these values is often a standard reference value, in which case the decibel is used to express the level of the other value relative to this reference.
The number of decibels is ten times the logarithm to base 10 of the ratio of two power quantities. A change in power by a factor of 10 corresponds to a 10 dB change in level. At the half power point an audio circuit or an antenna exhibits an attenuation of approximately 3 dB. A change in amplitude by a factor of 10 results in a change in power by a factor of 100, which corresponds to a 20 dB change in level. A change in amplitude ratio by a factor of 2 (equivalently factor of 4 in power change) approximately corresponds to a 6 dB change in level.
The definition of the decibel is based on the measurement of power in telephony of the early 20th century in the Bell System in the United States. One decibel is one tenth of one bel, named in honor of Alexander Graham Bell; however, the bel is seldom used. Today, the decibel is used for a wide variety of measurements in science and engineering, most prominently in acoustics, electronics, and control theory. In electronics, the gains of amplifiers, attenuation of signals, and signal-to-noise ratios are often expressed in decibels.
In the International System of Quantities, the decibel is defined as a unit of measurement for quantities of type level or level difference, which are defined as the logarithm of the ratio of power- or field-type quantities.
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