Fun Acoustics

dB gain calculator

Mode

Input

Output

Measuring

Gain 26.021 dB

20 · log₁₀(2 ÷ 0.1)

Linear ratio 20×

Power ratio 400×

Doublings of voltage 4.322

−6 dB per doubling of distance

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

1 Enter input and output levels in the same units.

2 Say whether they are voltage or power.

3 Read the gain in decibels.

4 Switch to the distance tab for how level falls with range.

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

How do I calculate dB gain? −

20·log₁₀(out ÷ in) for voltage, or 10·log₁₀ for power.

What is 26 dB of gain? +

How much does sound drop with distance? +

Why does moving a mic slightly change so much? +

Does the 6 dB rule work indoors? +

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