Why is the voltage formula 20·log10 and not 10·log10?

Decibels are defined on power, and power is proportional to voltage squared (P is proportional to V²). When you express the ratio in voltage, the squared term comes out of the log as a factor of 2, so 10·log10(V₂²/V₁²) becomes 20·log10(V₂/V₁). The 20 multiplier therefore applies to any amplitude quantity: voltage, current, sound pressure, or sample amplitude.

How much voltage gain is +6 dB?

+6 dB is almost exactly a doubling of voltage. The exact ratio is 10^(6/20) = 1.995, which is why engineers treat +6 dB as 2× amplitude. Each further +6 dB doubles again: +12 dB is 4×, +18 dB is 8×.

What does a negative dB value mean here?

A negative dB value is attenuation, where the output amplitude is smaller than the input. For example -6 dB is a voltage ratio of 0.501 (roughly half), and -20 dB is a ratio of 0.1 (one tenth). Pulling a fader down 20 dB cuts the signal to a tenth of its amplitude.

Is dBV or dBu the same as this conversion?

No. dBV and dBu are absolute levels referenced to 1 V and 0.775 V respectively. This tool converts relative gain or ratio, not absolute level. The 20·log10 relationship is the same, but here both ends are dimensionless ratios rather than referenced voltages.

Does this apply to sound pressure level (SPL)?

Yes. Sound pressure is an amplitude quantity, so the same 20·log10 formula converts an SPL change to a pressure ratio. A +6 dB SPL change doubles the acoustic pressure, while delivering that change typically requires 4× the acoustic power.

dB to Voltage Gain Converter

A precise, two-way converter between decibels and voltage (amplitude) ratios for audio and electronics work. Enter a dB figure to see the multiplier it represents, or enter a ratio to see its dB equivalent. Because this is an amplitude quantity, the tool uses the 20·log10 form of the decibel formula, which is the correct one for voltage, current, sound pressure, and sample amplitude.

How it works

Decibels are fundamentally a ratio of two powers. Voltage is an amplitude, and power scales with the square of amplitude, so converting a voltage ratio to decibels uses a multiplier of 20 instead of 10.

dB = 20 · log10(V₂ / V₁)

Voltage ratio = 10^(dB / 20)

To go from dB to a ratio, divide the dB value by 20 and raise 10 to that power. To go from a ratio to dB, take the base-10 logarithm of the ratio and multiply by 20. A ratio of exactly 1 corresponds to 0 dB (no change), ratios above 1 are positive dB (gain), and ratios below 1 are negative dB (attenuation).

Worked example

A mic preamp set to +40 dB of gain multiplies the input voltage by 10^(40/20) = 10^2 = 100×. A -3 dB fader move multiplies the signal by 10^(-3/20) = 0.708×, the classic “half-power” point where the perceived loudness drop is just becoming noticeable.

Useful reference points

dB	Voltage ratio	Plain description
+20 dB	10×	Ten times the amplitude
+12 dB	3.98×	About four times
+6 dB	2.00×	Double amplitude
+3 dB	1.41×	Square-root-of-two up
0 dB	1.00×	No change
-3 dB	0.708×	Half-power point
-6 dB	0.501×	Half amplitude
-20 dB	0.1×	One tenth

These figures are why +6 dB is the engineer’s shorthand for “double it” and why a fader pulled down 6 dB roughly halves the signal. Every calculation runs locally in your browser; nothing is uploaded.