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

Convert power ratio to dB
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:
\(\displaystyle x[Bel]=log_{10} \left(\frac{P_1}{P_2}\right) \)
Example
\(\displaystyle P_1 : P_2 = 10 : 1 = 1 Bel \)
\(\displaystyle P_1 : P_2 = 100 : 1 = (10 · 10) : 1 = 2 Bel \)
In practice, the power ratio is given in tenths of a Bel (Deci = Bel), dB for short.
\(\displaystyle 10dB = 1 Bel\)
The formula for converting linear to logarithmic (dB) is:
\(\displaystyle x[dB]=10· log_{10} \left(\frac{P_1}{P_2}\right) \)
The formula for converting logarithmic (dB) to linear is:
\(\displaystyle a=10^{\left(\displaystyle \frac{x[dB]}{10}\right)} \)
a is the factor (P1 / P2) here
Values to remember
0 dB ≡ factor 1
3 dB ≡ factor 2
6 dB ≡ factor 4
10 dB ≡ factor 10
Convert voltage ratio to dB
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.
The formula for converting a linear voltage ratio to logarithmic (dB) is:
\(\displaystyle x[dB]=20· log_{10} \left(\frac{U_1}{U_2}\right) \)
The formula for converting logarithmic (dB) to the linear voltage ratio is:
\(\displaystyle a=10^{\left(\displaystyle \frac{x[dB]}{20}\right)} \)
Values to remember
0 dB ≡ factor 1
6 dB ≡ factor2
12 dB ≡ factor 4
20 dB ≡ factor 10
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