Decibel Reference
Decibel math, power/voltage ratios, reference levels (dBm, dBu, dBV), and everyday SPL examples.
Reference
Formulas
- dB (power)
- 10 · log₁₀(P₁ / P₀)
- dB (voltage / field)
- 20 · log₁₀(V₁ / V₀)
- Ratio → dB
- ×2 ≈ 3 dB (power), 6 dB (voltage); ×10 = 10 dB (power), 20 dB (voltage)
- dB → ratio
- 10^{dB/10} (power) or 10^{dB/20} (voltage)
Common dB values
| dB | Power ratio | Voltage ratio |
|---|---|---|
| 0 dB | 1 | 1 |
| 1 dB | 1.26 | 1.12 |
| 3 dB | 2 | 1.41 |
| 6 dB | 4 | 2 |
| 10 dB | 10 | 3.16 |
| 20 dB | 100 | 10 |
| 30 dB | 1 000 | 31.6 |
| 40 dB | 10 000 | 100 |
| 60 dB | 10⁶ | 1 000 |
| 100 dB | 10¹⁰ | 100 000 |
| 120 dB | 10¹² | 10⁶ |
Reference levels
- dBm
- Power relative to 1 mW. 0 dBm = 1 mW, 30 dBm = 1 W.
- dBW
- Power relative to 1 W. dBW = dBm − 30.
- dBu
- Audio voltage; 0 dBu = 0.775 V_rms (into 600 Ω).
- dBV
- 0 dBV = 1 V_rms. dBu = dBV + 2.22.
- dBFS
- Digital full-scale. 0 dBFS = clipping point.
- dB SPL
- Sound pressure level, reference 20 µPa (threshold of hearing).
Everyday SPL
| Source | dB SPL |
|---|---|
| Threshold of hearing | 0 |
| Whisper | 30 |
| Quiet library | 40 |
| Normal conversation | 60 |
| Busy street | 80 |
| Lawn mower | 90 |
| Rock concert | 110 |
| Jet engine (30 m) | 140 |
| Threshold of pain | ≥130 |
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