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Decibel (dB) Gain Calculator

Find the gain in decibels.

How it is calculated

The decibel expresses a ratio of two power values on a logarithmic scale: dB = 10 × log10(P1 ÷ P0). P1 is the measured or output power and P0 the reference or input power, in the same unit (watts, milliwatts, anything). Both must be above zero because the logarithm of zero or a negative number does not exist. A positive result means gain, a negative one means loss, and 0 dB means no change. Every tenfold increase in power adds 10 dB and a doubling adds about 3 dB. For voltage or sound pressure the factor is 20 rather than 10, which this power formula does not use.

Worked example

An amplifier takes in 2 W and delivers 200 W. The ratio is 200 ÷ 2 = 100. log10(100) = 2. Multiply by 10: 10 × 2 = 20. The tool shows 20.00 dB. Swapping the two values gives −20.00 dB, a loss of the same size.

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Common mistakes

  • Using this power formula for voltage or current. For amplitudes the multiplier is 20, so the same ratio would give twice as many dB.
  • Mixing units between the two powers, such as watts and milliwatts. The ratio would be off by 1,000, adding 30 dB by mistake.
  • Entering the dB values themselves. The fields take plain power, not decibel numbers.
  • Swapping input and output and misreading the sign. The reference goes in P0; a negative answer means attenuation.
  • Adding ratios instead of dB values in chains. Gains in dB add up; the underlying ratios multiply.

About this calculator

This calculator finds the power gain between two power levels using the logarithmic formula dB = 10 × log₁₀(P2/P1), converting a ratio that can span many orders of magnitude (like a 1,000,000:1 power increase) into a manageable number (60 dB) — because decibels compress multiplicative changes into additive ones, doubling power always adds exactly 3 dB regardless of the starting level.

Audio engineers setting gain staging on a mixing console, RF and telecom engineers calculating signal loss over a cable run or antenna gain, and electronics hobbyists comparing amplifier specifications all use decibels because sound and signal power are perceived and measured logarithmically, not linearly.

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