dB to Linear Factor Calculator

Online calculator for converting decibel to power or voltage ratio

Calculation

dB
Result
Linear factor:
Tip

You can convert real values of voltage, power, and dB here

Good to know

Convert dB to linear factor

This function converts a decibel value into the linear ratio. For example: \(-6\text{ dB}\) corresponds to a factor of \(0.25\), i.e. a ratio of \(1:4\).

Scaling
  • Power (10 dB/decade): For power ratios
  • Voltage (20 dB/decade): For voltage ratios
Example calculation

For \(3\text{ dB}\) power (10 dB/decade):

\[\text{Factor} = 10^{\frac{3}{10}} = 10^{0.3} \approx 2.0\]
Conversion formulas
Power: \[a = 10^{\frac{x[\text{dB}]}{10}}\]
Voltage: \[a = 10^{\frac{x[\text{dB}]}{20}}\]
a = linear factor

Convert dB value to linear factor

To convert a dB value (decibel) into a linear factor, use the inverse formula for calculating decibels. There are two common formulas, depending on whether you are converting for voltage or power.

Power ratio

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

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:

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

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

Conversion formulas

Linear to logarithmic (dB):
\[\displaystyle x[\text{dB}] = 10 \times \log_{10} \left(\frac{P_1}{P_2}\right)\]
\[\displaystyle x[\text{dB}] = 20 \times \log_{10} \left(\frac{U_1}{U_2}\right)\]
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 \((U_1/U_2)\)
Key values
Power (10 dB/decade):
0 dB ≡ factor 1
3 dB ≡ factor 2
6 dB ≡ factor 4
10 dB ≡ factor 10
Voltage (20 dB/decade):
0 dB ≡ factor 1
6 dB ≡ factor 2
12 dB ≡ factor 4
20 dB ≡ factor 10

Is this page helpful?            
Thank you for your feedback!

Sorry about that

How can we improve it?


Battery Capacity  •  Capacitor Capacitance  •  Decibel, votage, power converter  •  Decibel - factor converter  •  Electric Power  •  Electric Energy  •  Electric Charge  •  Electrostatic force, Coulombs Law  •  Internal resistance of a power source  •  Ohm's law and power  •  Table of temperature coefficients  •  Temperature drift of resistance  •  Voltage drop  •  Wire resistance  •