Decibel Gain Calculator
The decibel is a logarithmic way of expressing a ratio between two power or amplitude levels. It is used throughout audio, radio, and signal processing because it compresses huge dynamic ranges into manageable numbers and turns multiplication of gains into addition. Enter an input and an output value, choose whether they are power or voltage quantities, and this calculator returns the gain in decibels. It also converts a decibel figure back into the equivalent linear power ratio and voltage ratio.
Decibel formula
Power gain (dB) = 10 * log10(output / input)
Voltage gain (dB) = 20 * log10(output / input)
Power ratio = 10^(dB / 10)
Voltage ratio = 10^(dB / 20)
Use the power formula when both values are powers, and the voltage formula when they are voltages, currents, or other amplitude quantities. The conversions return the linear ratios for a given decibel value.
Decibel context
- The decibel is one tenth of a bel and is always a ratio between two quantities.
- A 3 dB power change is roughly a factor of two; a 10 dB change is exactly a factor of ten in power.
- The factor of 20 for voltage arises because power scales with the square of voltage.
- Cascaded gains add in decibels, turning multiplication into simple addition.
- Negative decibels indicate attenuation, where the output is smaller than the input.
Decibel gain: frequently asked questions
How is decibel gain calculated?
For a power ratio the gain in decibels is 10 times the base-10 logarithm of output power divided by input power. For a voltage or amplitude ratio it is 20 times the logarithm, because power is proportional to the square of voltage. This calculator handles both.
Why is the voltage factor 20 and the power factor 10?
Power is proportional to voltage squared in a fixed resistance. Taking the logarithm of a square brings the exponent of 2 out in front, turning the factor of 10 used for power into 20 for voltage or any amplitude quantity.
What does a 3 dB change mean?
A 3 dB increase corresponds to roughly doubling the power, and a 3 dB decrease to roughly halving it. A 6 dB change corresponds to doubling or halving the voltage. A 10 dB change is a tenfold change in power.
How do I convert decibels back to a ratio?
Raise 10 to the power of the decibels divided by 10 to get the power ratio, or divided by 20 to get the voltage ratio. This calculator reports both linear ratios when you enter a decibel value.
Can decibel gain be negative?
Yes. A negative decibel value means the output is smaller than the input, that is, attenuation rather than amplification. A ratio of less than one gives a negative logarithm and therefore a negative decibel figure.
Official sources
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.