dB to Amplitude Converter
This dB to amplitude converter turns any decibel value into 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. This audio dB calculator makes that conversion instant: enter any decibel value and get the linear amplitude directly. The conversion from decibels to linear ratio is: 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. The same ÷20 formula applies to dBu (referenced to 0.775 V RMS) and dBV (referenced to 1 V RMS) used in professional and consumer audio interfaces respectively, making this converter directly useful for pro-audio level matching.
Common dB benchmarks in audio
The “−3 dB point” is the standard cutoff for filter design and crossover networks — 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. Understanding these benchmarks is essential for interpreting signal-to-noise ratio specs and headroom requirements in digital audio workstations.
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). Streaming platforms such as Spotify target an integrated loudness of −14 LUFS, which typically means true peaks well below −1 dBFS — a policy that has pushed mastering engineers toward lower peak amplitudes. You can cross-check the loudness maths with the signal-to-noise ratio calculator or verify dynamic range against the bit depth calculator.
Frequently Asked Questions
What is the amplitude at −6 dB?
Why is −3 dB called the "half-power" point?
How loud is "−10 dB"?
What is "0 dBFS"?
Is +6 dB really "double"?
What's the practical lower limit of dB?
What is the difference between dBFS, dBu, and dBV?
All three use the same ÷20 amplitude formula, but with different reference values. dBFS (Decibels Full Scale) references the maximum digital sample value — used inside DAWs and audio software. dBu references 0.775 V RMS (historically set by the impedance-matched power standard) — used on professional balanced audio equipment. dBV references 1 V RMS — used on consumer gear. A −10 dBV consumer line level ≈ 316 mV RMS; a +4 dBu professional level ≈ 1.23 V RMS. These are different scales, so 0 dBu and 0 dBFS are not the same signal level.
How do I convert a DAW fader position in dB to a volume knob multiplier?
Use the amplitude formula directly: multiply the audio sample by 10^(dB / 20). A fader at −6 dB means every sample in the signal is multiplied by ≈ 0.501. A fader at +3 dB multiplies samples by ≈ 1.412. At 0 dB the multiplier is exactly 1.0 (unity gain — no change). Most DAWs apply this calculation internally; this converter lets you verify or pre-compute the exact linear coefficient, which is handy when writing audio code or plugin processing.
Can decibels be positive, and what does a positive dB mean in audio?
Yes. A positive dB value means the signal is louder than the reference. In a DAW context, a channel strip with a +6 dBFS input and a +6 dB fader would be pushing above 0 dBFS — that is digital clipping. In an amplifier context, a +20 dB preamp gain means the output amplitude is 10× larger than the input. The converter handles any positive or negative value; the reference table above shows values from −144 dB (24-bit noise floor) up to +40 dB (100× amplitude). If you want to hear a practical example of what different dB steps sound like, the dB level trainer plays matched audio bursts at exact dB offsets.