Bel Ratio Calculator
Decibels express the logarithmic ratio of two quantities. For power, dB = 10 log10(P2/P1); for amplitude (voltage, pressure), dB = 20 log10(A2/A1). This calculator converts in both directions: enter a dB value to get the corresponding linear ratios, or enter a power or amplitude ratio to get the decibel equivalent. These conversions are fundamental to audio engineering, telecommunications, and acoustics.
dB to ratio formulas
Power ratio = 10dB/10
Amplitude ratio = 10dB/20
Reverse: dB = 10 log10(power ratio) = 20 log10(amplitude ratio).
Common dB values and their ratios
- 0 dB: power ratio 1.00x, amplitude ratio 1.00x
- 3 dB: power ratio 2.00x, amplitude ratio 1.41x
- 6 dB: power ratio 3.98x, amplitude ratio 2.00x
- 10 dB: power ratio 10.00x, amplitude ratio 3.16x
- 20 dB: power ratio 100.00x, amplitude ratio 10.00x
- -3 dB: power ratio 0.50x, amplitude ratio 0.71x
Frequently asked questions
What is the difference between bel and decibel?
A bel is 10 decibels. The decibel (dB) is the unit actually used in practice because a bel is too large a step for most audio applications. One bel = 10 dB, so a 3 dB change corresponds to 0.3 bels.
How do I convert dB to a power ratio?
Power ratio = 10^(dB/10). For 10 dB: 10^(10/10) = 10. For 3 dB: 10^(3/10) approximately 2. For 6 dB: 10^(6/10) approximately 4.
How do I convert dB to an amplitude ratio?
Amplitude (voltage or pressure) ratio = 10^(dB/20). For 20 dB: 10^(20/20) = 10. For 6 dB: 10^(6/20) approximately 2. The factor of 20 (instead of 10) arises because power is proportional to the square of amplitude.
Why do power and amplitude ratios use different factors?
Power P is proportional to amplitude A squared (P = A^2/R). Taking the log: 10 log10(P2/P1) = 10 log10((A2/A1)^2) = 20 log10(A2/A1). So the same dB value corresponds to different linear ratios depending on whether you are measuring power or amplitude.
What is a 0 dB ratio?
0 dB corresponds to a power ratio of 1 (no change) and an amplitude ratio of 1 (no change). This is not silence; it means the output equals the input.
Official sources
- NIST: National Institute of Standards and Technology.
- AES: Audio Engineering Society.
- OpenStax University Physics Vol. 1, Chapter 17: Sound.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.