Decibel ↔ Gain Converter

Convert between decibels and a linear amplitude factor — the multiplier you actually apply to a signal in code. Edit any field: gain = 10^(dB/20), and dB = 20·log₁₀(gain).

Handy anchors: 0 dB = ×1, +6 dB ≈ ×2, −6 dB ≈ ×0.5, −∞ dB = silence. More in the decibel reference.

How it works

Decibels are a ratio on a logarithmic scale, and the formula depends on whether you are measuring amplitude or power.

amplitude (voltage):  dB = 20 × log10(new / old)
power:                dB = 10 × log10(new / old)

gain factor from dB:  factor = 10 ^ (dB / 20)

Audio faders and plugin gain controls work in amplitude, so the 20× form is the one you want almost always.

Worked example

• Doubling amplitude: 20 × log10(2) = +6.02 dB
• Halving amplitude: 20 × log10(0.5) = −6.02 dB
• +6 dB as a factor: 10^(6/20) = 1.995×
• +10 dB as a factor: 10^(10/20) = 3.162×

In practice

• +6 dB doubles, +10 dB feels twice as loud. These are different things and the gap between them explains a lot of confusion about gain.
• −3 dB is half the power, which is why filter cutoff points are defined there.
• 1 dB is roughly the smallest change most people notice on a sustained sound; below that you are usually imagining it.
• dBFS is negative by definition. 0 dBFS is digital full scale, so your mix lives below it. Leave headroom — aim for peaks well under 0.
• Level-matched comparisons only. Louder reliably sounds better, so match levels before deciding whether a plugin actually improved anything.

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