Although decibels are the main unit for expressing the ratios of gain and loss for quantities like electrical power in electronic and other systems, the neper is also used.

The neper is not particularly widely used, but has advantages in some instances where its mathematical advantages can be used.

## What is a neper

The neper uses the symbol Np and is a logarithmic unit for ratios of measurements of physical field and power quantities, such as gain and loss of electronic signals.

The neper is named after John Napier who invented logarithms. Napier was a scot who lived between 1550 and 1617, and his latinised name was Ioannes Neper, from which the unit name of neper has come.

Like the decibel and the bel, the neper is a unit that comes under the International System of Quantities, ISQ. However it is not part of the International System of Units, SI, but it is accepted for use alongside the SI.

The neper is a logarithmic scale, but instead of being based on the decadic system using log_{10}, the neper uses natural logarithms using log_{e} - these are natural logarithms based on Euler's number, e, i.e. 2.71828 . .

The equation for calculating nepers is given by:

## Neper to dB conversion

The neper and dB are related by the following relationships:

$1Np=20{\mathrm{log}}_{10}edB$

$1Np=8.6858896dB$

Conversely to convert dB to nepers:

$1dB=\frac{1}{20{\mathrm{log}}_{e}}Np$

$1dB=0.11512925Np$

Using these equations it is easy to convert from nepers to dB and dB to nepers. It should be remembered that the figures for the conversion are not exact, but the number of significant figures given should be sufficient for most engineering applications.

## Decibel, dB to neper conversion table

The table below gives some of the more popular conversion points for nepers to dB and vice versa.

Decibel, dB to neper conversion chart | ||
---|---|---|

DeciBels, dB | Nepers | Power Ratio |

0.1 | 0.01 | 1.023 |

0.2 | 0.02 | 1.047 |

0.3 | 0.03 | 1.071 |

0.4 | 0.05 | 1.096 |

0.5 | 0.6 | 1.122 |

0.6 | 0.07 | 1.148 |

0.7 | 0.08 | 1.175 |

0.8 | 0.09 | 1.202 |

0.9 | 0.10 | 1.230 |

1.0 | 0.12 | 1.259 |

2.0 | 0.23 | 1.585 |

3.0 | 0.35 | 1.995 |

4.0 | 0.46 | 2.512 |

5.0 | 0.58 | 3.162 |

6.0 | 0.69 | 3.981 |

7.0 | 0.81 | 5.012 |

8.0 | 0.92 | 6.310 |

9.0 | 1.04 | 7.943 |

10 | 1.15 | 10.000 |

15 | 1.73 | 31.62 |

20 | 2.30 | 100.00 |

30 | 3.45 | 1000.0 |

40 | 4.60 | 10000 |

50 | 5.76 | 100 000 |

The neper is rarely used, but it appears in some calculations because it use natural logarithms rather than use a base ten which is a far more arbitrary figure, but convenient for us as we use base ten figures.

Often when using the neper system it is useful to have a quick conversion back to decibels that are far more familiar.