A precise two-way converter between decibels and power ratios, using the 10·log10 form of the decibel that applies whenever your quantity is power: amplifier wattage, RF transmit power, acoustic power, or optical power. Enter dB to get the power multiplier, or a power ratio to get its dB value.
How it works
Decibels are defined directly on power. There is no squaring step, so the multiplier is 10, not 20.
dB = 10 · log10(P₂ / P₁)
Power ratio = 10^(dB / 10)
To convert dB to a ratio, divide the dB value by 10 and raise 10 to that power. To convert a ratio to dB, take its base-10 logarithm and multiply by 10. A power ratio of 1 is 0 dB, ratios above 1 are positive dB (gain), and ratios below 1 are negative dB (loss).
Why power dB differs from voltage dB
Power is proportional to the square of amplitude (P is proportional to V²).
That is the entire reason the voltage formula uses 20 while the power formula
uses 10. A change of +6 dB doubles amplitude but quadruples power;
a change of +3 dB doubles power but only raises amplitude by about 1.41×.
Choosing the wrong formula introduces a clean factor-of-two error in the dB
figure, so always match the formula to the quantity.
Worked example
Upgrading a PA amplifier from 250 W to 500 W is a power ratio of 2, which is
10 · log10(2) = 3.01 dB of extra output. To gain a full +10 dB (perceived
as roughly “twice as loud”) you would need 10× the power — 2500 W — which is why
chasing loudness with raw wattage hits diminishing returns fast.
Useful reference points
| dB | Power ratio | Plain description |
|---|---|---|
| +30 dB | 1000× | Three decades |
| +20 dB | 100× | Two decades |
| +10 dB | 10× | Ten times the power |
| +3 dB | 2.00× | Double power |
| 0 dB | 1.00× | No change |
| -3 dB | 0.501× | Half power |
| -10 dB | 0.1× | One tenth |
| -20 dB | 0.01× | One hundredth |
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