Editing Decibel (section)

=== Power quantities ===
When referring to measurements of ''[[Power (physics)|power]]'' quantities, a ratio can be expressed as a level in decibels by evaluating ten times the [[base-10 logarithm]] of the ratio of the measured quantity to reference value. Thus, the ratio of ''P'' (measured power) to ''P''<sub>0</sub> (reference power) is represented by ''L''<sub>''P''</sub>, that ratio expressed in decibels,<ref>{{Cite book |title=Microwave Engineering |author-first=David M. |author-last=Pozar |edition=3rd |publisher=Wiley |date=2005 |author-link=David M. Pozar |isbn=978-0-471-44878-5 |page=63}}</ref> which is calculated using the formula:<ref>IEC 60027-3:2002</ref>
: <math>
L_P = \frac{1}{2} \ln\!\left(\frac{P}{P_0}\right)\,\text{Np} = 10 \log_{10}\!\left(\frac{P}{P_0}\right)\,\text{dB}
</math>

The base-10 logarithm of the ratio of the two power quantities is the number of bels. The number of decibels is ten times the number of bels (equivalently, a decibel is one-tenth of a bel).  ''P'' and ''P''<sub>0</sub> must measure the same type of quantity, and have the same units before calculating the ratio. If {{nowrap|1=''P'' =}} ''P''<sub>0</sub> in the above equation, then ''L''<sub>''P''</sub>&nbsp;= 0. If ''P'' is greater than ''P''<sub>0</sub> then ''L''<sub>''P''</sub> is positive; if ''P'' is less than ''P''<sub>0</sub> then ''L''<sub>''P''</sub> is negative.

Rearranging the above equation gives the following formula for ''P'' in terms of ''P''<sub>0</sub> and ''L''<sub>''P''</sub> :
: <math>
P = 10^\frac{L_P}{10\,\text{dB}} P_0
</math>