Convert decibels to gain factors

How much quieter is −6 dB, and how many decibels is half volume on a control? The calculator converts decibels into the factor a control multiplies the signal by (gain), into the power factor and back, in any direction. It gives the percentage on the control, roughly how loud that sounds and how much headroom is left to digital full scale.

Level: dB ↔ factor

How much quieter is −6 dB? Converts decibels into factors and back, for volume controls, mixers and amplifiers.

In the generator Mixer: level A/B · Amplifier (VCA): base level · Main Out: volume

dB Gain × Power ×

Explanation and formula

Gain is the factor a control multiplies the signal by. The bar shows the value relative to digital full scale (0 dB); above that it clips. Rules of thumb: +6 dB ≈ twice the gain, +10 dB ≈ twice as loud to the ear. The formula: dB = 20 · log₁₀(gain) = 10 · log₁₀(power).

How it is calculated

Decibels are a logarithmic measure of a ratio. For voltage or signal value (amplitude) the factor is 20, for power it is 10, because power grows with the square of the amplitude:

dB = 20 · log₁₀(gain) = 10 · log₁₀(power)
gain = 10^{dB / 20}, power = 10^{dB / 10}
+6 dB ≈ double the gain, +3 dB ≈ double the power
+10 dB is perceived as roughly twice as loud

Example: −6 dB gives a gain of 10^−6/20 ≈ 0.5012, almost exactly half the signal, but only a quarter of the power. In digital audio 0 dB (dBFS) is full scale; above it the signal is clipped and distorts.

Decibel table

dB	Gain	Power	On the control	Perceived
+12	3.981	15.85	–	× 2.3
+6	1.995	3.981	–	× 1.5
+3	1.413	1.995	–	× 1.2
0	1	1	100 %	× 1
−1	0.8913	0.7943	89 %	× 0.93
−3	0.7079	0.5012	71 %	× 0.81
−6	0.5012	0.2512	50 %	× 0.66
−10	0.3162	0.1	32 %	× 0.5
−12	0.2512	0.0631	25 %	× 0.44
−18	0.1259	0.01585	13 %	× 0.29
−20	0.1	0.01	10 %	× 0.25
−24	0.0631	0.003981	6.3 %	× 0.19
−30	0.03162	0.001	3.2 %	× 0.13
−40	0.01	1 · 10⁻⁴	1 %	× 0.063
−60	0.001	1 · 10⁻⁶	0.1 %	× 0.016

Gain and power rounded to four significant digits. “On the control”: the percentage on a volume control that multiplies the signal by the gain; none goes above 100 %.

Try it in the generator

ModuloOne is a modular synthesizer that runs in your browser: connect modules with cables and hear what comes out. There the mixer, the amplifier (VCA) and the volume in the main out show the gain in percent: 50 % is about −6 dB, 10 % is −20 dB. Open the generator

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