The decibel is a logarithmic ratio, not a unit of anything on its own. It exists because the quantities engineers care about span enormous ranges and because cascaded stages multiply — and logarithms turn multiplication into addition, so a chain of gains and losses becomes a sum.
Why there are two formulas
There is only one definition — the power one. Voltage gets a factor of 20 because power goes as voltage squared into a fixed impedance, and the square comes out of the logarithm as a factor of two. Use 10 for power, watts and intensity; use 20 for voltage, current, pressure and amplitude. Mixing them up is the single most common decibel error.
Figures worth memorising
| dB | Power ratio | Voltage ratio |
|---|---|---|
| 3 dB | 2× | 1.41× |
| 6 dB | 4× | 2× |
| 10 dB | 10× | 3.16× |
| 20 dB | 100× | 10× |
| −3 dB | 0.5× | 0.71× |
The −3 dB point being half power is why filter cutoffs are defined there.
Suffixed decibels are absolute
Adding a suffix pins the reference and makes the figure a real measurement. dBm is referenced to one milliwatt, so 0 dBm is 1 mW and 30 dBm is 1 W. dBV references one volt; dBu references 0.7746 V; dB SPL references the threshold of hearing. A bare “dB” is always relative to something else in the same system.