# 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 Power 10db / Dec Voltage 20 db / Dec Value in db Decimal places 0 1 2 3 4 6 8 10 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