dB to Amplitude Converter
Convert any decibel value to a linear amplitude ratio using A = 10^(dB/20). Output: amplitude ratio, power ratio (P = A² = 10^(dB/10)), percentage of full scale, voltage example, and zone classification across +60 dB gain down to noise-floor levels.
Input
Result
Common dB → Amplitude / Power Reference
| dB | Amplitude Ratio | Power Ratio | % of Full Scale |
|---|---|---|---|
| +40 dB | 100 | 10,000 | 10,000 % |
| +20 dB | 10 | 100 | 1,000 % |
| +12 dB | 3.9811 | 15.849 | ~398 % |
| +6 dB | 1.9953 | 3.9811 | ~199.5 % |
| +3 dB | 1.4125 | 1.9953 | ~141.3 % |
| 0 dB | 1.0000 (unity) | 1.0000 | 100 % |
| −3 dB | 0.7079 | 0.5012 (half power) | ~70.8 % |
| −6 dB | 0.5012 (half amplitude) | 0.2512 | ~50.1 % |
| −10 dB | 0.3162 | 0.1 (one-tenth power) | ~31.6 % |
| −12 dB | 0.2512 | 0.0631 | ~25.1 % |
| −20 dB | 0.1 (one-tenth) | 0.01 | 10 % |
| −40 dB | 0.01 | 0.0001 | 1 % |
| −60 dB | 0.001 (audible noise floor) | 1e-6 | 0.1 % |
| −96 dB | ~1.585e-5 (16-bit floor) | ~2.51e-10 | ~0.0016 % |
| −120 dB | 1e-6 | 1e-12 | 0.0001 % |
| −144 dB | ~6.31e-8 (24-bit floor) | ~3.98e-15 | ~6.3e-6 % |
About Decibels & Amplitude
The decibel (dB) is a logarithmic ratio between two values — a way to compress huge dynamic ranges into manageable numbers. Going from 0 dB to −120 dB spans a linear range of 1,000,000 to 1 — a million-to-one ratio expressed as a single number. The conversion to linear ratio is direct: A = 10^(dB / 20) for amplitude (voltage, SPL, dBFS), or P = 10^(dB / 10) for power.
Why two divisors (10 vs 20)?
Power dB uses divisor 10: 10·log₁₀(P/P₀). Amplitude dB uses divisor 20: 20·log₁₀(A/A₀). The factor of 2 difference comes from the relationship Power = Amplitude². A 10× amplitude increase = 100× power increase, and both equal +20 dB. A 2× amplitude = 4× power = +6 dB. A "−3 dB" point has half the power but ~71% of the amplitude.
Common dB benchmarks in audio
The "−3 dB point" is the standard cutoff for filter design — where power has dropped to half. −6 dB = half amplitude (the user-perceived "half as loud" guideline is closer to −10 dB though). −20 dB = 10× quieter amplitude. −96 dB = 16-bit theoretical noise floor (matches CD quality). −144 dB = 24-bit theoretical noise floor.
dBFS — Decibels Full Scale
In digital audio, "0 dBFS" is the maximum representable value (just below clipping). All real signals are negative dBFS. A song mastered to peak at −1 dBFS leaves 1 dB of headroom. A song peaking at −12 dBFS is "quiet" (lots of headroom). The conversion to linear amplitude is the same: amplitude = 10^(dBFS / 20).