# Nepers & Neper to dB Conversion Table

### - overview of nepers with equations and a chart or table with decibel to neper & neper to dB conversions.

### Decibel tutorial includes

When comparing power levels it is normal to use the decibel. However on some occasions nepers may be used.

Accordingly it is sometimes necessary to convert nepers to dB.

Nepers differ from decibels in that they use logarithms to the base "e" rather than to the base 20.

Accordingly it is sometimes necessary to convert between Nepers and decibels or vice versa.

## What are Nepers

The neper is a logarithmic unit for ratios of measurements. It is very similar to more familiar decibel and can be used for the comparison of physical quantities such as gain or loss in electronic circuits, or other physical quantities.

The neper has the symbol Np, and it derives its name from John Napier, the inventor of logarithms.

In the same way that the decibel is not a unit that has been incorporated into the SI International System of units, it is accepted for use alongside it.

While the decibel and the bel use the decadic or base-10 logarithm to compute ratios, the neper uses the natural logarithm, based on Euler's number, e. This equal to 2.71828 . . . .

The equation for calculating nepers is given by:

## Neper to dB conversion

The neper and dB are related by the following relationships:

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 | ||
---|---|---|

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 |

While nepers are not nearly as widely used as dB, they nevertheless occur in some applications because they 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..

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