Decibel Calculator (dB)
Converts between ratios and decibels. Pick power or voltage first — using the wrong one puts every answer out by a factor of two.
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The formula
dB = 10 × log₁₀(P₂ ÷ P₁) dB = 20 × log₁₀(V₂ ÷ V₁)
The factor is 10 for power and 20 for voltage because power goes as voltage squared, and squaring inside a logarithm is the same as doubling outside it. Both expressions describe the same physical change — which is why doubling the voltage and quadrupling the power are both 6 dB.
What to watch out for
The only thing that regularly goes wrong is the factor:
- 10 log for power — watts, milliwatts, acoustic intensity.
- 20 log for amplitude — volts, amps, sound pressure.
They are not competing conventions. Power is proportional to voltage squared, so the same physical change gives the same decibel figure either way, as long as you use the matching factor.
Decibels are always relative. A bare "−90 dB" means nothing without a reference; dBm names one explicitly, being decibels relative to a milliwatt.
Frequently Asked Questions
Why is 3 dB double?
Because 10 × log₁₀(2) is 3.01. It is a power ratio, so 3 dB doubles the power and 6 dB quadruples it. In voltage terms 3 dB is a factor of 1.41, since 20 × log₁₀(1.41) is also 3.
When do I use 10 log and when 20 log?
10 log for anything measured in watts, 20 log for anything measured in volts, amps or sound pressure. Use the wrong one and your answer is out by a factor of two.
What is dBm?
Decibels relative to one milliwatt, so it is an absolute level rather than a ratio. 0 dBm is 1 mW, 30 dBm is 1 W, and −90 dBm is a typical weak radio signal.