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dB Gain Calculator

Determine dB gain by entering initial and final power levels into the dB gain calculator.

Clear
Ratio in decibels23.0103 dB10 log₁₀(200) — the factor is 10 because this is a a power quantity
Plain ratio200:1
As a percentage20,000%
Read as the other quantity type46.0206 dBexactly double — this is the error you make by picking the wrong factor
3 dB is1.995262×about double the power, on the power convention in use here
6 dB is3.981072×about double the amplitude, on the power convention in use here
10 dB is10×ten times the power, on the power convention in use here
20 dB is100×ten times the amplitude, on the power convention in use here
-3 dB is0.501187×half the power, on the power convention in use here
Adding decibels multiplies ratios46.0206 dB is 40,000×which is why gains and losses along a chain simply add up

The formula

dB = 10 log₁₀(P₁/P₂) for power, 20 log₁₀(A₁/A₂) for amplitude

Ten or twenty, and why it matters

A decibel is ten times the base-ten logarithm of a power ratio. For amplitude quantities — voltage, sound pressure, field strength — the factor is twenty instead, because power goes as the square of amplitude and the square becomes a factor of two once you take the logarithm.

Choosing the wrong factor gives an answer exactly double or half the right one, which is shown above so the size of the mistake is visible. The rule is simple: watts and intensity take 10, volts and pressure take 20.

The point of the scale is that multiplication becomes addition. A chain of amplifiers and losses can be totalled by adding decibels rather than multiplying ratios, and the landmark figures are easy to carry: 3 dB doubles power, 10 dB multiplies it tenfold, and 6 dB doubles amplitude. Note also that a decibel is always a ratio — a bare "50 dB" means nothing without a reference, which is why the useful units are suffixed ones like dBm, dBW or dB SPL.