Convert db to linear factor

Online calculator and formulas for converting decibels into power or voltage ratio

Convert decibel to factor


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).


Convert db to linear factor

 Input
Scaling
Value in db
Decimal places
 Result
Factor

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


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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