# Convert voltage, power and decibels

Calculators and formulas for converting between voltage, power and decibels

## Conversion of power, voltage and db

This function converts the linear relationship between two voltages or powers into decibels, and decibels 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

Linear / db - calculator

 What should be calculated? Voltage to db db to voltage Power to db db to power Input Reference voltage kV V mV µV Reference power kW W mW µW Output voltage kV V mV µV Output power kW W mW µW Decibel db Decimal places 0 1 2 3 4 6 8 10 Result Output voltage Output power Decibel

## 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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