# 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