Decibel ↔ Linear Ratio Converter
Sound Pressure Level Summation
Add multiple sound source dB values to calculate the combined total. Note: 80 dB + 80 dB ≈ 83 dB, not 160 dB.
dB Gain / Loss Calculator
📖 Decibel Quick Reference
What is a decibel?
A decibel (dB) is a logarithmic unit that expresses the ratio between two physical quantities. It is widely used in acoustics, audio engineering, and telecommunications. Rather than an absolute measurement, it represents how much a value differs from a reference on a log scale.
Core formulas
- Power ratio: dB = 10 × log₁₀(P₁ / P₂)
- Amplitude ratio: dB = 20 × log₁₀(A₁ / A₂) (voltage, sound pressure)
- Level summation: L = 10 × log₁₀(Σ 10^(Lᵢ/10))
Common dB reference table
| dB | Power ratio | Amplitude ratio | Meaning |
|---|---|---|---|
| 0 dB | 1× | 1× | No change |
| 3 dB | 2× | 1.41× | Double power |
| 6 dB | 4× | 2× | Double amplitude |
| 10 dB | 10× | 3.16× | 10× power |
| 20 dB | 100× | 10× | 10× amplitude |
| −3 dB | 0.5× | 0.71× | Half power |
| −10 dB | 0.1× | 0.32× | 1/10 power |
| −20 dB | 0.01× | 0.1× | 1/10 amplitude |
Common sound pressure levels
| Level | Example |
|---|---|
| 0 dB | Threshold of hearing |
| 30 dB | Whisper, quiet bedroom |
| 60 dB | Normal conversation |
| 70 dB | Vacuum cleaner, busy street |
| 85 dB | Heavy traffic (hearing damage with prolonged exposure) |
| 100 dB | Chainsaw, motorcycle |
| 120 dB | Rock concert (threshold of pain) |
| 140 dB | Jet engine at takeoff (instant damage) |
❓ Frequently Asked Questions
What is a decibel (dB)?
A decibel is a logarithmic unit expressing the ratio between two physical quantities, used for sound pressure, power, and voltage. For power ratios, dB = 10×log10(P1/P2); for amplitude ratios, dB = 20×log10(A1/A2). Every 3 dB increase roughly doubles the power, and every 10 dB multiplies it by 10.
How do you sum multiple sound pressure levels?
Sound levels cannot be added directly. Use the formula L_total = 10×log10(Σ 10^(Li/10)). For example, two 80 dB sources combine to about 83 dB, not 160 dB. The "Sound Level Sum" tab in this calculator handles this automatically.
What is the difference between power dB and amplitude dB?
Power ratios use a factor of 10: dB = 10×log10(P1/P2). Amplitude ratios (voltage, sound pressure) use a factor of 20: dB = 20×log10(A1/A2). This is because power is proportional to amplitude squared, and 10×log(x²) = 20×log(x).
Why does 3 dB mean double the power?
Using dB = 10×log10(P1/P2), when P1/P2 = 2, dB = 10×log10(2) ≈ 3.01 dB. So doubling power adds about 3 dB, and halving it subtracts about 3 dB.
What is the difference between dBm, dBW, and dBA?
dBm is an absolute power unit referenced to 1 mW (0 dBm = 1 mW). dBW is referenced to 1 W (0 dBW = 1 W). dBA is an A-weighted sound pressure level approximating human hearing sensitivity. This calculator works with relative dB values.