Decibel Power Ratio Calculator
The decibel expresses a ratio of two powers on a logarithmic scale. Enter two power values to find the gain or loss in decibels, or enter a decibel figure to recover the equivalent power ratio. The decibel uses a factor of ten for power quantities, so a tenfold increase is exactly 10 dB and a doubling is about 3 dB. Negative decibels indicate attenuation.
Use P1 and P2 to get decibels, or enter a decibel value to get its power ratio.
Decibel power formula
dB = 10 * log10(P2 / P1)
Power ratio = 10^(dB / 10)
(factor of 10 applies to power quantities)
For field quantities such as voltage or sound pressure use a factor of 20 instead, because power is proportional to their square.
Worked example
An amplifier raises power from 1 W to 100 W. dB = 10 * log10(100 / 1) = 10 * 2 = 20.00 dB. Going the other way, 20 dB corresponds to a power ratio of 10^(20 / 10) = 10^2 = 100.00.
Decibel power ratio: frequently asked questions
How do you convert a power ratio to decibels?
Decibels equal ten times the base-10 logarithm of the power ratio: dB = 10 * log10(P2 / P1). A ratio of 2 is about 3.01 dB, a ratio of 10 is exactly 10 dB, and a ratio of 100 is 20 dB.
How do you go from decibels back to a power ratio?
Raise 10 to the power of the decibels divided by ten: ratio = 10^(dB / 10). For example 6 dB corresponds to a power ratio of about 3.98.
Why is the factor 10 and not 20?
The factor of 10 applies to power, intensity, or any quantity proportional to power. A factor of 20 is used for field quantities such as voltage or sound pressure, because power is proportional to their square.
What does a negative decibel value mean?
A negative decibel value means the output power is less than the reference (a ratio below 1), that is, attenuation rather than gain. For instance -3 dB is roughly half the power.
Sources
- NIST: SI units and the decibel.
- The power decibel definition dB = 10 log10(P2/P1) is a standard logarithmic-ratio result.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.