# ネーパ

ネーパ (neper)
Sign Np
System SI combination unit
Quantity Quantity of no dimension
Definition Quantity to assume this x[Np] when the ratio of ex is in two standard value A and B
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ネーパ (with neper, ネーパー, Napier, ネーピア a sign: Np) is a credit to express the ratio (gain, loss). In international unit system (SI), I am considered to be "a unit to be used together with SI, but not to belong to SI". The name is associated with John Napier who invented the logarithm in Scottish mathematicians.

It is the unit of logarithm scale, but, in ネーパ, ネーパ is based on a natural logarithm for being based on common logarithm that a bell assumed 10 a bottom like a bell (decibels are usually used). The proportional value Np by ネーパ is defined as follows.

$Np=\ln {\frac {x_{1}}{x_{2}}}=\ln x_{1}-\ln x_{2}$ Here, x1 and x2 are values to intend for, and ln is a natural logarithm.

ネーパ is used for the voltage ratio and the current ratio well whereas I am used well though a decibel expresses the electricity ratio. ネーパ and the decibel are converted as follows.

$1\ {\mbox{Np}}={\frac {20}{\ln 10}}\ {\mbox{dB}}\approx 8.686\ {\mbox{dB}}$ Like a decibel, ネーパ is a credit of no dimension. For a bell using the common logarithm, ネーパ using the natural logarithm is considered to have SI and consistency, but is not adopted as official SI unit at the international weights and measures general meeting.