Decibel Gain Calculator
dB gain from power or voltage ratios, with multiple.
What it does
Decibels compress huge ratios into small numbers. Ten times the power is just +10 dB, double is +3.01, and a hundredfold is +20. Audio, radio, and optics all speak this log language because gains multiply while decibels add.
The tool above runs power and voltage gains. Enter two levels and it prints dB, the linear multiple, and the percent change. Defaults give +10 dB at 10x and +900 % for 1 to 10 watts. Voltage mode uses the 20 log form for equal impedances.
Metrology backs the definitions. NIST defines the bel and decibel on decimal logarithms of power ratios, and Virginia Tech course notes derive the 10 log power form with the 20 log voltage step through V squared over R. Reference points check out: 2x is +3.01, 10x is +10.
Signs carry losses too. A quarter power reads -6.02 dB, and halving voltage reads -6.02 as well. Absolute scales like dBm and dB SPL add references to the same log core; this page stays with pure ratios.
How to use
- Pick power or voltage gain.
- Enter the starting level.
- Enter the ending level.
- Read dB first, then the multiple.
- Read the percent change.
- Mind equal impedance for voltage power claims.
Formula
- mode
- Power or voltage gain selector.
- in1
- Starting level above 0.
- in2
- Ending level above 0.
NIST defines the decibel as one tenth of a bel on decimal logs. The 20x voltage form needs equal impedances for power meaning.
Worked example
Example: 1 W to 10 W
Defaults: power 1 W to 10 W.
- Inputs: power mode, 1 W to 10 W.
- Ratio: 10 / 1 = 10x.
- dB: 10 x log10(10) = 10 x 1 = +10 dB.
- Percent: (10 minus 1) x 100 = +900 %.
- Tool shows +10 dB, 10x, +900%.
Reference table
| Power ratio | dB | Voltage twin |
|---|---|---|
| 0.25x | -6.02 | 0.5x at -6.02 |
| 0.5x | -3.01 | 0.707x at -3.01 |
| 2x | +3.01 | 2x at +6.02 |
| 4x | +6.02 | 4x at +12.04 |
| 10x | +10.00 | 10x at +20.00 |
| 100x | +20.00 | 100x at +40.00 |
Limits
- Pure ratios only. Absolute scales need references.
- Voltage power meaning needs equal impedances.
- Positive levels only; zero breaks logs.
- Small rounding near unity gains.
Common mistakes
- Using 10 log for voltage ratios.
- Reading dB as linear percent.
- Mixing absolute and relative dB scales.
- Forgetting impedance on voltage claims.
- Logging zero or negative levels.
Try it yourself
Quick checks. Answers sit tucked under each question.
Voltage 1 V to 2 V?
20 x log10(2) = 20 x 0.30103 = +6.02 dB. 2x, +100 %.
Power 100 W to 25 W?
10 x log10(0.25) = 10 x -0.60206 = -6.02 dB. 0.25x, -75 %.
Questions
How is gain in dB figured?
Power: 10 x log10 of the ratio. Voltage: 20 x log10 (equal impedances). Here 10 x log10(10) = +10 dB.
What dB doubles things?
+3.01 dB doubles power; +6.02 dB doubles voltage. Ten times power is +10 dB.
How do I go back from dB?
Ten to the dB over 10 for power: 10^(10/10) = 10x. Voltage uses over 20.
Do losses work the same?
Yes, with a minus sign: 100 to 25 W is 10 x log10(0.25) = -6.02 dB.
Why 20 for voltage?
The square law: 10 log of V squared equals 20 log of V. Needs equal impedances to mean power.
Are there absolute dB scales?
Yes. dB SPL uses 20 micropascals reference and dBm uses 1 mW; this page does pure ratios.
Sources
- NIST: Definitions of Radian, Neper, Bel, Decibel
- Virginia Tech / LibreTexts: Decibel Scale for Power Ratio