Decibel Calculator
The decibel calculator converts between dB values and the underlying linear ratios for power, voltage, and amplitude. Decibels are the standard unit for expressing gain and loss in audio systems, RF engineering, optical networks, and acoustics. Because the decibel scale is logarithmic, it compresses enormous ranges into manageable numbers: the human ear can detect sounds from 0 dB (threshold of hearing) to 194 dB (theoretical maximum in air). This tool supports conversion in both directions - enter a dB value to find the corresponding ratio, or enter two values (input and output) to find the dB gain or loss. Choose between power quantities (using the factor of 10) and voltage or pressure quantities (using the factor of 20).
Decibel formulas
Power dB = 10 * log10(P2 / P1)
Voltage dB = 20 * log10(V2 / V1)
Power ratio from dB = 10^(dB / 10)
Voltage ratio from dB = 10^(dB / 20)
Common dB reference values
- +3 dB: power doubled (approximately x2.00)
- +6 dB: voltage doubled (power x4)
- +10 dB: power increased tenfold
- +20 dB: voltage increased tenfold (power x100)
- -3 dB: power halved (the -3 dB point of a filter)
- 0 dB: no change, ratio = 1.00
Decibel calculator: frequently asked questions
What is a decibel?
A decibel (dB) is a logarithmic unit used to express ratios of power, voltage, or intensity. It is 1/10 of a Bel, named after Alexander Graham Bell. Because human perception of sound and signal levels is logarithmic, decibels are natural units for audio, radio, and optics. 0 dB means no change, positive dB means gain, and negative dB means attenuation.
What is the formula for decibels?
For power ratios: dB = 10 * log10(P2 / P1). For voltage or amplitude ratios: dB = 20 * log10(V2 / V1). The factor is 10 for power because power is proportional to voltage squared, giving 10 * log10(V^2/V1^2) = 20 * log10(V2/V1).
How many dB is double the power?
Doubling power corresponds to approximately +3.01 dB. Doubling voltage (with the same impedance) corresponds to +6.02 dB, because voltage doubling quadruples the power. Common reference points: +10 dB is a tenfold power increase, -10 dB is a tenfold power decrease.
What is dBm?
dBm is decibels relative to 1 milliwatt (mW). It is an absolute power level used in RF and telecommunications. 0 dBm = 1 mW, +10 dBm = 10 mW, +30 dBm = 1 W, -20 dBm = 0.01 mW. The formula is dBm = 10 * log10(P / 1 mW).
What is the difference between dB for power and dB for voltage?
For power: dB = 10 * log10(P2/P1). For voltage (or current, pressure, amplitude): dB = 20 * log10(V2/V1). Both formulas give the same dB value when comparing the same physical change in a fixed-impedance system, because power is proportional to voltage squared.
Official sources
- NIST: NIST SP 811 - Guide for the Use of SI Units.
- IEC: IEC 60027-3 - Letter symbols for quantities in telecommunications.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.