dB gain calculator
Voltage gain in decibels is 20·log₁₀ of output over input. Going from 0.1 V to 2 V is a gain of 26 dB. Separately, sound level falls 6 dB for every doubling of distance from a point source.
How to calculate gain
The inverse square law — 6 dB lost per doubling of distance; holds for a point source in free space and is optimistic indoors, where reflections keep the level up, and pessimistic outdoors over absorbing ground. It is why moving a microphone from 10 cm to 20 cm from a source halves the level while moving it from 2 m to 2.1 m barely changes anything: what matters is the ratio of distances, not the absolute change.
Questions
20·log₁₀(out ÷ in) for voltage, or 10·log₁₀ for power.
About twenty times the voltage, or four hundred times the power.
Six decibels per doubling of distance from a point source in free space.
Because the ratio matters. Going from 10 to 20 cm is a doubling; going from 2 to 2.1 m is not.
Only near the source. Beyond the critical distance, reflections dominate and the level stops falling.