Decibel Gain Calculator (Power & Voltage)
Convert a power or voltage ratio into decibels of gain — or a loss — with the correct 10 log or 20 log rule.
How it works
Power: dB = 10·log₁₀(P_out ÷ P_in) · Voltage: dB = 20·log₁₀(V_out ÷ V_in)
The decibel is a logarithmic ratio, so it turns huge spans of gain into manageable numbers and lets cascaded stages add instead of multiply. Power ratios use 10·log₁₀, but because power scales with the square of voltage or current, amplitude ratios use 20·log₁₀ — the factor of two comes straight from that squaring. A handy landmark: +3 dB doubles power, and +6 dB doubles voltage.
Worked example
An amplifier turns 1 W into 100 W. As a power ratio the gain is 10·log₁₀(100/1) = 10 × 2 = 20 dB. If instead 1 V became 100 V, the voltage gain would be 20·log₁₀(100) = 20 × 2 = 40 dB.
Sources: Decibel — Wikipedia
Frequently asked questions
Why does voltage use 20·log and power use 10·log?
Power is proportional to voltage squared (P ∝ V²). Taking the log brings the exponent 2 out front, turning 10·log into 20·log for amplitude ratios — so the same physical change reads as the same number of decibels either way.
What does a negative decibel value mean?
A negative dB is a loss or attenuation: the output is smaller than the input. −3 dB power means the signal dropped to half its original power.
Why use decibels at all?
Because gains multiply through a chain of stages, and logarithms turn multiplication into addition. Adding the dB of each stage is far easier than multiplying ratios, and it matches how our senses perceive loudness and brightness.
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This calculator is for educational purposes. Double-check important results before acting on them.