Case 1
- Output voltage
- 10V
- Input voltage
- 1V
20.0000dB
Open with these valuesDecibel Gain Calculator
20.0000dB
Result: 20.0000 dBFor voltage the factor is twenty, not ten: power goes with the square of voltage, and the square doubles the logarithm. Ten times the voltage is 20 dB of gain, twice the voltage is 6.02 dB, and an output below the input comes out negative.
Worked examples
Case 2
- Output voltage
- 2V
- Input voltage
- 1V
6.0206dB
Open with these valuesCase 3
- Output voltage
- 1V
- Input voltage
- 2V
-6.0206dB
Open with these valuesHow it's calculated
gain = 20 × log₁₀(V_out ÷ V_in)
- StepEnter the voltage coming out of the stage.
- StepEnter the voltage going into it.
- ResultRead the gain in decibels; below zero means attenuation.
Reference table
| Output, input (V) | Voltage ratio | Gain (dB) |
|---|---|---|
| 1, 1 | Unity — a buffer | 0 |
| 2, 1 | Twice the voltage | 6.0206 |
| 10, 1 | Ten times | 20 |
| 100, 1 | A hundred times | 40 |
| 1, 2 | Halved — a divider | -6.0206 |
Questions
Why 20 log instead of 10 log?
Power is proportional to the square of voltage, and the logarithm of a square is twice the logarithm. The factor 20 is the same rule as 10, applied to a field quantity.
What does 6 dB of gain mean?
Roughly twice the voltage — 6.020599913 dB exactly. Twelve decibels is four times, eighteen is eight times.
Does this work for current or sound pressure?
Yes. Current and sound pressure are field quantities like voltage, so the same factor of 20 applies.
What if the output is smaller than the input?
The result turns negative, which is attenuation rather than gain. Halving the voltage is −6.02 dB.
Sources and last check
Information, not professional advice.