Decibel Gain Ratio
Calculator
Results
- Amplitude (voltage) ratio
- 1.995262
- Power ratio
- 3.981071
- Amplitude as a percentage of the original
- 199.526231
Music and audio results
| Amplitude (voltage) ratio | 1.995262 |
| Power ratio | 3.981071 |
| Amplitude as a percentage of the original | 199.526231 |
formula-map diagram
- Amplitude (voltage) ratio
- 1.995262
- Power ratio
- 3.981071
- Amplitude as a percentage of the original
- 199.526231
Musical and acoustic relationship
Formula
amplitude ratio = 10^(dB ÷ 20)= 1.9952623149689
Note
This result is a simplified model: it applies the displayed standard formula to the values you entered, assuming twelve-tone equal temperament, a speed of sound of 343 m/s in dry air at 20 °C, an ideal free field with no reflections or air absorption, purely resistive speaker loads and Sabine's diffuse-field assumption. Real rooms, instruments, codecs and amplifiers depart from these idealisations, so measure with proper instruments for critical work.
More in Music and audio
See all →Frequently asked questions
How does a decibel value convert to an amplitude or power ratio?+
For voltage/amplitude, ratio = 10^(dB/20); for power, ratio = 10^(dB/10), because decibels are a logarithmic scale and power is proportional to amplitude squared. A +6 dB gain roughly doubles amplitude, while +10 dB roughly doubles perceived loudness.
Why are there two different formulas depending on whether it's power or amplitude?+
Power is proportional to the square of amplitude, so converting power ratios to dB uses a factor of 10 (10 x log10), while amplitude (voltage, sound pressure) ratios use a factor of 20 (20 x log10) to account for that squared relationship. Mixing up the two formulas is a common source of error when working with dB by hand.
Why does +6 dB roughly double the signal instead of, say, +3 dB?+
Doubling amplitude corresponds to 20 x log10(2) ≈ 6.02 dB, which is why +6 dB is the well-known 'roughly doubles the level' rule of thumb in audio engineering. +3 dB instead roughly doubles power, which is why it's the standard reference for doubling perceived sound intensity in acoustics.
Why does 0 dB mean 'no change' rather than 'silence'?+
A decibel value expresses a ratio relative to a reference level, so 0 dB simply means the ratio is 1:1, no gain and no attenuation, not an absence of signal. This is why a mixer fader set to '0 dB' passes the signal through unchanged rather than muting it.
How is this useful when setting gain staging in a mix?+
Knowing that every +6 dB roughly doubles amplitude helps you predict how much a fader or gain knob move will actually affect perceived level, rather than guessing, which is especially useful for matching levels between tracks or compensating for a plugin's makeup gain. It turns an abstract dB number into a concrete sense of how much louder or quieter something will get.