Convert dB to linear factor
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).
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Tip: To convert real values of voltage, power and dB, click here
To convert a dB (decibel) value to a linear factor, use the reverse formula for calculating in decibels. There are two common formulas, depending on whether you are converting for voltage or power.
Convert power ratio to dB
The logarithmic unit of measurement for describing the relationship between two power levels is the Bel.
1 Bel corresponds to a power 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 ratio of the power is given in tenths of a Bel (Deci=Bel), or dB for short.
\[\displaystyle 10\; dB = 1\; Bel\]
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)
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 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 a linear voltage ratio is:
\[\displaystyle a=10^{\left(\displaystyle \frac{x[dB]}{20}\right)} \]
Values to remember
0 dB ≡ Factor 1
6 dB ≡ Factor 2
12dB ≡ Factor 4
20dB ≡ Factor 10
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