# dB to Linear Gain Calculator

This tool converts a Power Gain in deciBel (dB) to a Linear Gain Value for each of the following:

• Power (Pout/Pin)
• Voltage (Vout/Vin)

## Formula for dB to Linear Gain

PdB = 10*Log10(P1/P2)

PdB = 20*Log10(V1/V2)

and therefore the ratios

P1/P2 = 10(PdB/10)

V1/V2 = 10(PdB/20)

## Example Calculations

A 10 dB value gives a power gain of 10 and a voltage gain of 3.162.

A -10 dB value gives a power gain of 0.1 and a voltage gain of 0.3162.

Note that negative dB values have a higher voltage gain value than power gain. The reverse is true for positive dB values.

## Notes

• PdB is a real number and can be positive or negative. A positive number indicates a linear gain, while a negative number represents linear attenuation.

It is important to note that the dB scale is logarithmic, meaning that small changes in dB correspond to large changes in the power or voltage ratios. This conversion ratio is widely used in various fields such as telecommunications, radio frequency engineering and audio engineering.

### Is it 10*Log or 20*Log?

When dealing with Power, it is 10*Log and when dealing with Voltage it is 20*Log.

Let’s get into the details.

From [1] If P1 and P2 are two powers, their ratio expressed in decibels is:

PdB = 10*Log10 (P1 / P2)

Where P1 = V12/R1 and P2 = V22/R2

where R1 and R2 are impedance or resistance values (ohm or Ω)

V1 and V2 are both Root-Mean-Square (RMS) values of voltage which can be calculated from

• a sequence of voltage values or
• using a closed form expression for RMS voltage when the waveform is known.

If R1=R2, then

PdB = 10*Log10 (V12/ V22)

or PdB = 20*Log10 (V1/ V2)

Hence it is 20*Log when calculated using a ratio of voltage and 10*Log when using a ratio of power.

## References

[2] DeciBel on Wikipedia

## Related Calculators

• dB to Power Ratio
• dB to Voltage Ratio
• dB to times computes the number of times a number is larger than another based on the dB value