Decibel Gain Calculator

Voltage gain in decibels is twenty times the base-10 logarithm of output over input, gainDb = 20 * log10(Vout / Vin). A voltage ratio of 10 works out to exactly 20 dB, and a ratio of 100 to 40 dB.

Power is proportional to voltage squared, so the logarithm of a power ratio is twice that of the matching voltage ratio. Doubling the factor from 10 to 20 keeps a given physical change reading the same number of decibels whether you measure it as power or as amplitude.

Raise 10 to the decibels divided by the factor, so ratio = 10^(dB / 20) for voltage or 10^(dB / 10) for power. Switch the Enter menu to Decibels and the calculator does this for you: 6 dB of voltage gain returns a ratio of about 1.9953.

In power terms 3 dB is close to a doubling, since 10^(3/10) is about 1.9953, which is why the half-power point of a filter is called its 3 dB point. For voltage the same near-doubling of the ratio lands at about 6 dB.

Yes. When the output is smaller than the input the ratio falls below 1 and the decibel figure is negative, which represents attenuation or loss. A voltage ratio of 0.5, for example, reads as roughly minus 6 dB.

Any units, as long as both boxes use the same one, because only their ratio matters. Volts against volts, watts against watts, or two readings from the same meter all give the correct decibel result.

The gain depends on the logarithm of the ratio, and the logarithm of zero or a negative number is undefined. If you enter a non-positive input or output the tool shows a prompt to enter positive values instead of a result.

The engine computes with full floating-point precision and rounds to nine decimal places, then the display shows up to four decimals. That is far finer than typical measurement error, so the figure you copy is limited by your instruments, not the maths.

No. The calculation runs entirely in your browser with no server call, so your measurements stay on your device and the tool keeps working offline once loaded.