Online calculator and formulas for converting decibels into power or voltage ratio
This function converts a decibel value into the linear ratio between two voltages or powers. For example, if you enter the value 6 for the scaling "Power (10db / decade)", the result is 0.25 , So a performance ratio of 1/4.
With the Scaling menu you can choose between power calculation (10db / decade), or switch over voltage calculation (20db / decade).

Tip: To convert real values of voltage, power and db, click here
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
