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Decibel Calculator

Convert a power or amplitude ratio to decibels and back. Decibels use a logarithmic scale: dB = 10·log₁₀(P/P₀) for power, or 20·log₁₀(A/A₀) for amplitude.

 

Formula

$$ dB = 10\,\log_{10}\!\frac{P}{P_0} \qquad dB = 20\,\log_{10}\!\frac{A}{A_0} \qquad \text{ratio} = 10^{\,dB/n} $$

Worked example

A power ratio of 1000 is \( 10\log_{10}(1000) = 30\ \text{dB} \). Every +10 dB is a 10× power increase, and +3 dB is roughly a doubling of power.

How it works

The decibel expresses a ratio on a logarithmic scale, which compresses the huge range of powers and amplitudes we deal with in sound and signals. For power, dB = 10·log₁₀(P/P₀); for amplitude or voltage, the factor is 20 because power scales with amplitude squared.

Choose the ratio type and direction, then enter either the ratio or the decibel value. Handy rules: +3 dB ≈ double the power, +10 dB = ten times the power, and +20 dB = 100 times.

Frequently asked questions

How do you convert a ratio to decibels?

For power, dB = 10·log₁₀(P/P₀). For amplitude or voltage, use dB = 20·log₁₀(A/A₀). A power ratio of 1000 is 30 dB.

Why is amplitude 20·log and power 10·log?

Because power is proportional to amplitude squared. Taking the log of a square brings down a factor of 2, turning 10·log into 20·log for amplitude or voltage ratios.

How much is 3 dB and 10 dB?

+3 dB is approximately double the power, and +10 dB is exactly ten times the power. Decibels add when ratios multiply.

How do you convert decibels back to a ratio?

Raise 10 to the power dB/n, where n is 10 for power or 20 for amplitude: ratio = 10^(dB/n). So 30 dB of power is 10^3 = 1000.

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