Decibel Calculator
Convert between dB, dBm, watts and voltage ratios — with the factor of 10 or 20.
How it works
A decibel is a logarithm of a ratio, so on its own it means nothing — it always needs a reference. dBm means relative to one milliwatt, dBW to one watt, dBV to one volt. A bare "dB" is only ever a relative change: a gain, a loss, a difference between two things.
The single most common mistake in the whole subject is the factor:
dB = 10 log₁₀(P₂ ÷ P₁) for power
dB = 20 log₁₀(V₂ ÷ V₁) for voltage
Both describe the same physical change. Power goes with the square of voltage, so doubling the voltage quadruples the power, and 20 log(2) equals 10 log(4) equals 6.02 dB. The factor is not a convention you can pick — it is determined by which quantity you are measuring, and using 10 where you needed 20 halves your answer.
Three anchors are worth memorising, because between them you can do most of this in your head:
3 dB is a factor of 2 in power. 6 dB is a factor of 2 in voltage. 10 dB is a factor of 10 in power. 20 dB is a factor of 10 in voltage.
Decibels add where ratios multiply, which is the entire reason the unit exists. A chain of an amplifier at +20 dB, a cable at −3 dB and a splitter at −6 dB is +11 dB overall — arithmetic instead of multiplying 100 × 0.5 × 0.25.
dBm is the working unit of RF and telecoms because it makes absolute levels addable too. 0 dBm is 1 mW, 30 dBm is 1 W, and a −80 dBm received signal into a +20 dB amplifier is −60 dBm out, done in one step.
Common questions
10 log or 20 log?
10 for power, 20 for voltage, current or any other amplitude. They describe the same change: 6 dB is double the voltage and four times the power, and both expressions give 6.02. Using the wrong one is off by a factor of two in dB.
What is dBm exactly?
Decibels relative to one milliwatt. 0 dBm is 1 mW, 30 dBm is 1 W, −30 dBm is 1 µW. Because it has a reference it is an absolute level rather than a ratio, so you can add gains and losses in dB to it directly.
Why 3 dB for half power?
10 log(0.5) is −3.01. It is where a filter's response has fallen to half the power — the corner frequency — and also where the voltage has fallen to 1/√2, about 0.707, which is the same point described the other way.
Does impedance matter?
For converting between dBm and volts, yes, and it must be stated. 0 dBm is 0.224 V RMS into 50 Ω but 0.775 V into 600 Ω. Pure dB ratios do not care, as long as both measurements are at the same impedance.