Why decibels?
The decibel is a logarithmic ratio, which turns the huge dynamic ranges of signals into manageable numbers and turns multiplication into addition: cascade a +20 dB amplifier into a −3 dB cable and you have +17 dB, no multiplying required. A decibel is always a ratio; to express an absolute level you need a reference, which is what dBm (relative to 1 mW) provides.
Power vs amplitude: the factor of two
Power ratios use 10·log₁₀; voltage and current ratios use 20·log₁₀. The 20 isn't arbitrary — power goes as voltage squared, and log(V²) = 2·log(V). So the same +6 dB means 4× the power but only 2× the voltage. Mixing these up is the most common dB mistake.
Values worth memorizing
| dB | Power ratio | Amplitude 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× |
| 0 dB | 1× (equal) | 1× |
Common dBm levels
| Level | Power |
|---|---|
| 0 dBm | 1 mW |
| 20 dBm | 100 mW (typical Wi-Fi TX) |
| 30 dBm | 1 W |
| −67 dBm | strong Wi-Fi received signal |
| −90 dBm | weak but usable cellular |
| −130 dBm | GPS signal at the antenna |
Frequently asked questions
- Is −3 dB really "half"?
- For power, yes — −3.01 dB is exactly half the power, which is why the −3 dB point defines a filter's cutoff (half power, or 0.707× voltage). See the RC filter calculator.
- What's the difference between dB, dBm, and dBW?
- dB is a bare ratio. dBm and dBW are absolute, referenced to 1 mW and 1 W respectively (so 0 dBW = 30 dBm). This tool uses dBm.
- Can I add and subtract dB?
- Yes — that's the whole point. Gains and losses in a signal chain add directly in dB, as long as they're all the same kind (all power dB or all consistently referenced).
- Why 1 mW as the reference?
- Historical convention from telephony; it's a convenient small power for communications work, where signals span from watts at the transmitter to attowatts at a distant receiver.