Decibel Calculator

Online calculator for voltage, power, and decibel conversions

Calculation

dB
Result
Output Voltage:
Output Power:
Decibel:


Good to know

What is decibel (dB)?

Decibel is a logarithmic unit of measurement that expresses the ratio of quantities. It is used to express differences between two power or voltage levels.

Basic formulas
Power: \[dB = 10 \cdot \log_{10}\left(\frac{P_1}{P_2}\right)\]
Voltage: \[dB = 20 \cdot \log_{10}\left(\frac{U_1}{U_2}\right)\]
Example calculation

Voltage ratio: \(U_1 = 10\text{ V}\), \(U_2 = 1\text{ V}\)

\[dB = 20 \cdot \log_{10}\left(\frac{10}{1}\right) = 20 \cdot \log_{10}(10) = 20 \text{ dB}\]
Key values
Voltage:
0 dB ≡ factor 1
6 dB ≡ factor 2
12 dB ≡ factor 4
20 dB ≡ factor 10
Power:
0 dB ≡ factor 1
3 dB ≡ factor 2
6 dB ≡ factor 4
10 dB ≡ factor 10

Convert linear differences to dB

Voltage (V) or power (W) cannot be directly converted to decibel (dB), because decibel is a logarithmic unit that measures the ratio of quantities, such as the difference between two voltages. Decibel is used to express the difference between two power or voltage levels.

Power ratio in dB

The logarithmic unit for describing the ratio of two powers is the Bel.
1 Bel corresponds to a power ratio of 10:1. It is calculated by the formula:

\[\displaystyle x[\text{Bel}] = \log_{10} \left(\frac{P_1}{P_2}\right)\]
Example
\[P_1 : P_2 = 10 : 1 = 1 \text{ Bel}\] \[P_1 : P_2 = 100 : 1 = (10 \times 10) : 1 = 2 \text{ Bel}\]

In practice, the power ratio is given in tenths of a Bel (Deci=Bel), abbreviated dB.

\[10 \text{ dB} = 1 \text{ Bel}\]

Voltage ratio in dB

The power ratio is proportional to the square of the voltages.

\[\displaystyle \frac{P_1}{P_2} = \frac{U_1^2}{U_2^2} = \left(\frac{U_1}{U_2}\right)^2\]

It follows:

\[\displaystyle dB(W) = 10 \cdot \log_{10}\left(\frac{P_1}{P_2}\right)\] \[\displaystyle = 10 \cdot \log_{10}\left(\frac{U_1}{U_2}\right)^2\] \[\displaystyle = 20 \cdot \log_{10}\left(\frac{U_1}{U_2}\right)\]

A voltage ratio of 1:10 thus corresponds to 20 dB.

Conversion formulas

Linear to logarithmic (dB):
\[\displaystyle x[\text{dB}] = 10 \cdot \log_{10} \left(\frac{P_1}{P_2}\right)\]
\[\displaystyle x[\text{dB}] = 20 \cdot \log_{10} \left(\frac{U_1}{U_2}\right)\]
Logarithmic (dB) to linear:
\[\displaystyle a = 10^{\left(\frac{x[\text{dB}]}{10}\right)}\]
\[\displaystyle a = 10^{\left(\frac{x[\text{dB}]}{20}\right)}\]
a is the factor \((P_1/P_2)\) or \((U_1/U_2)\)
Applications

This type of conversion is often used in audio and communications technology to represent differences in volume or signal strength. In electronics, it is also used to describe voltage gains or attenuations.


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