Decibels explained: 10 log or 20 log?
The decibel (dB) expresses a ratio on a logarithmic scale. That suits hearing, which responds to ratios of sound intensity rather than absolute differences.
Two formulas
| Quantity | Formula | Examples |
|---|---|---|
| Power or intensity | 10 · log₁₀(P₂ / P₁) | doubling power = +3 dB |
| Voltage or sound pressure | 20 · log₁₀(V₂ / V₁) | doubling voltage = +6 dB |
Power is proportional to the square of voltage or pressure, so the factor of 20 is just the factor of 10 applied to a squared ratio. Both formulas describe the same physical change as long as the impedance is the same. 1 V RMS across 4 Ω and across 8 Ω is a 0 dB voltage difference but a 3.01 dB power difference.
Numbers worth remembering
- +3 dB doubles power; +6 dB doubles voltage or pressure.
- +10 dB is ten times the power and is often described as roughly twice as loud.
- ±1 dB is about the smallest level change most people can notice in a direct comparison.
- −20 dB is one tenth of the voltage.
Why dB values cannot simply be added
Two sources at 80 dB do not make 160 dB. Combining uncorrelated sources means adding their powers, which for two equal sources gives +3 dB. See the Adding levels tool.
Reference levels
A bare "dB" is only a ratio. Absolute levels need a reference: dB SPL (20 µPa), dBu, dBV or dBFS. See dBu, dBV and dBFS.
Try it
Convert between decibels and ratios with the decibel ↔ ratio converter.
Draft: written by an AI assistant, awaiting technical review.
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