About this calculator
Decibels compress enormous ranges into manageable numbers and turn multiplication into addition, which is why every gain, loss and signal level in audio and RF is quoted in them. The catch is that there are two formulas — one for power and one for voltage — and picking the wrong one puts you out by a factor of two.
This calculator handles both, plus the absolute scales (dBm, dBV, dBu) where a reference level is built into the unit rather than being a ratio between two things you measured.
How it works
A decibel is a tenth of a bel, and a bel is the base-10 logarithm of a power ratio. So dB = 10 × log10(P2/P1). That is the definition; everything else follows from it.
Voltage gets a factor of 20 instead of 10 because power goes as voltage squared. Substituting P = V²/R into the power formula pulls the square out of the logarithm as a factor of two, giving dB = 20 × log10(V2/V1). Both expressions describe the same change in power — they just start from different measurements.
That is why +3 dB means twice the power but only 1.41× the voltage, and +6 dB means twice the voltage but four times the power. Neither is wrong; they are the same physical change viewed through different instruments.
Plain decibels are always a ratio between two things. dBm pins one end down: it is power relative to one milliwatt, so 0 dBm is 1 mW and 30 dBm is 1 W. Because it is absolute, you can convert it to volts — but only once you state the impedance, since the same power produces different voltages across different loads.
Worked example
A preamp turns a 10 mV microphone signal into 1 V. What is its gain in dB, and what does that mean in power terms?
- Voltage ratio: 1 V / 10 mV = 100×
- dB = 20 × log10(100) = 20 × 2 = 40 dB
- Power ratio at the same impedance: 100² = 10000×
- Check: 10 × log10(10000) = 10 × 4 = 40 dB — same answer
40 dB of gain. The two routes agree, as they must: a 100× voltage increase into a fixed impedance is a 10,000× power increase.
Practical notes
- Memorise three anchors and you can estimate almost anything in your head: 3 dB is double the power, 6 dB is double the voltage, and 20 dB is ten times the voltage.
- Decibels add where ratios multiply. A chain of +20 dB, −6 dB and +14 dB stages nets out to +28 dB, no multiplication required — this is the main reason the unit exists.
- A "dB" with no reference is meaningless as an absolute level. If someone quotes a signal as "−20 dB", ask relative to what.
- The common absolute scales: dBm is relative to 1 mW, dBW to 1 W, dBV to 1 volt RMS, and dBu to 0.7746 V RMS (the voltage that produces 1 mW in 600 Ω).
- In audio, professional line level is +4 dBu and consumer line level is −10 dBV — which are about 1.23 V and 0.316 V RMS respectively, a difference of roughly 12 dB.
- Filter corner frequencies are quoted at −3 dB because that is the half-power point, not because voltage has halved.
Frequently asked questions
Why is it 20 log for voltage and 10 log for power?
Because power is proportional to voltage squared. Putting V² inside a logarithm brings the exponent out as a multiplier, turning 10 into 20. Both formulas describe the same power change.
What does 3 dB mean?
Twice the power, or about 1.41× the voltage. It is where a filter's cutoff frequency is defined, because half the power is getting through at that point.
What is dBm?
Power relative to one milliwatt, on a logarithmic scale. 0 dBm is 1 mW, +30 dBm is 1 W, −30 dBm is 1 µW. Unlike plain dB it is an absolute level, which is why RF power is almost always quoted this way.
How do I convert dBm to volts?
Convert dBm to watts with P = 10^(dBm/10) / 1000, then use Vrms = √(P × Z). You must know the impedance — 0 dBm is 0.224 V RMS in 50 Ω but 0.775 V RMS in 600 Ω.
Is a negative dB value a loss?
Yes. Negative decibels mean the output is smaller than the input. −3 dB is half the power, −6 dB is half the voltage, and −20 dB is a tenth of the voltage.