Calculators and formulas for converting between voltage, power and decibels
This function converts the linear relationship between two voltages or powers into decibels, and decibels in power or voltage gain or attenuation.
With the radio button you can choose between the following calculations

The logarithmic unit of measurement for describing the relationship between two power values is the Bel .
1 Bel corresponds to a performance ratio of 10: 1. It is calculated using the formula:
\(\displaystyle x[Bel]=log_{10} \left(\frac{P_1}{P_2}\right) \)
\(\displaystyle P_1 : P_2 = 10 : 1 = 1 Bel \)
\(\displaystyle P_1 : P_2 = 100 : 1 = (10 · 10) : 1 = 2 Bel \)
In practice, the power ratio is given in tenths of a Bel (Deci = Bel), db for short.
\(\displaystyle 10db = 1 Bel\)
\(\displaystyle x[db]=10· log_{10} \left(\frac{P_1}{P_2}\right) \)
\(\displaystyle a=10^{\left(\displaystyle \frac{x[db]}{10}\right)} \)
a is the factor (P1 / P2) here
0 db ≡ factor 1
3 db ≡ factor 2
6 db ≡ factor 4
10 db ≡ factor 10
The power ratio is proportional to the square of the voltages.
\(\displaystyle \frac{P_1}{P_2}=\frac{U_1^2}{U_2^2}=\left(\frac{U_1}{U_2}\right)^2\)
\(\displaystyle db(W) = 10·log_{10}\left(\frac{P_1}{P_2}\right) \) \(\displaystyle = 10·log_{10}\left(\frac{U_1}{U_2}\right)^2\) \(\displaystyle = 20·log_{10}\left(\frac{U_1}{U_2}\right)\)
A voltage ratio of 1:10 therefore corresponds to 20 db.
\(\displaystyle x[db]=20· log_{10} \left(\frac{U_1}{U_2}\right) \)
\(\displaystyle a=10^{\left(\displaystyle \frac{x[db]}{20}\right)} \)
0 db ≡ factor 1
6 db ≡ factor2
12 db ≡ factor 4
20 db ≡ factor 10
