# Decibel

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 or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a power ratio of 10^{1/10} (approximately 1.26) or root-power ratio of 10^{.mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}1⁄20} (approximately 1.12).[1][2]

The unit expresses a relative change or an absolute value. In the latter case, the numeric value expresses the ratio of a value to a fixed reference value; when used in this way, the unit symbol is often suffixed with letter codes that indicate the reference value. For example, for the reference value of 1 volt, a common suffix is "V" (e.g., "20 dBV").[3][4]

Two principal types of scaling of the decibel are in common use. When expressing a power ratio, it is defined as ten times the logarithm in base 10.[5] That is, a change in *power* by a factor of 10 corresponds to a 10 dB change in level. When expressing root-power quantities, a change in *amplitude* by a factor of 10 corresponds to a 20 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 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.

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

100 | 10000000000 | 100000 | ||

90 | 1000000000 | 31623 | ||

80 | 100000000 | 10000 | ||

70 | 10000000 | 3162 | ||

60 | 1000000 | 1000 | ||

50 | 100000 | 316 | .2 | |

40 | 10000 | 100 | ||

30 | 1000 | 31 | .62 | |

20 | 100 | 10 | ||

10 | 10 | 3 | .162 | |

6 | 3 | .981 ≈ 4 | 1 | .995 ≈ 2 |

3 | 1 | .995 ≈ 2 | 1 | .413 ≈ √2 |

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

0 | 1 | 1 | ||

−1 | 0 | .794 | 0 | .891 |

−3 | 0 | .501 ≈ 1⁄2 | 0 | .708 ≈ √1⁄2 |

−6 | 0 | .251 ≈ 1⁄4 | 0 | .501 ≈ 1⁄2 |

−10 | 0 | .1 | 0 | .3162 |

−20 | 0 | .01 | 0 | .1 |

−30 | 0 | .001 | 0 | .03162 |

−40 | 0 | .0001 | 0 | .01 |

−50 | 0 | .00001 | 0 | .003162 |

−60 | 0 | .000001 | 0 | .001 |

−70 | 0 | .0000001 | 0 | .0003162 |

−80 | 0 | .00000001 | 0 | .0001 |

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

−100 | 0 | .0000000001 | 0 | .00001 |

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