Decibel Calculator
A Scale Built for Enormous Ranges
The human ear can detect sound intensities spanning roughly twelve orders of magnitude between a whisper and a jet engine, which makes a linear scale useless for everyday description. The decibel solves that by measuring sound — or any signal — on a logarithmic scale relative to a reference level, compressing that huge range into numbers that stay in the tens and hundreds. This calculator converts a power or amplitude ratio into decibels.
The Formulas
Amplitude/intensity ratio: dB = 20 × log&sub10;(A2 / A1)
The factor differs because power is proportional to amplitude squared, so a given amplitude ratio corresponds to twice as many decibels as the same numeric power ratio. A positive result means P2 or A2 is larger than the reference; negative means smaller.
Where the Decibel Shows Up
- Occupational noise limits — workplace exposure standards are set in decibels precisely because the scale reflects how loudness is actually perceived.
- Audio engineering — gain, headroom, and signal-to-noise ratio in mixing and amplification are all expressed and adjusted in dB.
- Telecommunications — signal strength and attenuation over cables or wireless links are specified in decibels for the same reason: the numbers stay manageable across huge ranges.
- Seismology and acoustics research — any measurement comparing one intensity to a reference benefits from the compression a log scale provides.
What Common Ratios Translate To
| Ratio | dB (power, 10×log&sub10;) | dB (amplitude, 20×log&sub10;) |
|---|---|---|
| 2× | 3.01 dB | 6.02 dB |
| 4× | 6.02 dB | — |
| 10× | 10 dB | 20 dB |
| 100× | 20 dB | — |
| 1,000× | 30 dB | — |
Every 10 dB (power) or 20 dB (amplitude) represents a full order-of-magnitude change in the underlying ratio — this is why a "3 dB louder" speaker is roughly twice the acoustic power, not a small tweak.
How to Use This Calculator
- Choose a mode: Power Ratio or Amplitude/Intensity Ratio.
- For power ratio, enter Reference Power P1 and Measured Power P2, in watts.
- For amplitude ratio, enter Reference Amplitude A1 and Measured Amplitude A2 (any consistent unit).
- Select Calculate to get the result in decibels along with the worked formula.
Related Calculations
For the underlying wave properties behind a sound, see the Frequency Calculator, or convert that frequency into a physical wavelength with the Wavelength Calculator.