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Decibel Calculator

Convert power and amplitude ratios to decibels and back, and power to dBm, with the usual reference points such as 3 dB, 6 dB and 20 dB.

Formula

dB=10log⁡10P2P1\mathrm{dB} = 10\log_{10}\dfrac{P_2}{P_1}
dB=20log⁡10V2V1\mathrm{dB} = 20\log_{10}\dfrac{V_2}{V_1}
P2P1=10 dB/10\dfrac{P_2}{P_1} = 10^{\,\mathrm{dB}/10}
V2V1=10 dB/20\dfrac{V_2}{V_1} = 10^{\,\mathrm{dB}/20}
dBm=10log⁡10P1 mW\mathrm{dBm} = 10\log_{10}\dfrac{P}{1\ \mathrm{mW}}
PP
power
VV
amplitude: a voltage, current or pressure
dBm\text{dBm}
power in decibels relative to 1 milliwatt

How it works

A decibel is a logarithm of a ratio, which turns the multiplication of gains and losses into addition. For a power ratio the decibel is 10 times the logarithm to base 10; for an amplitude ratio, which goes as the square root of power, it is 20 times, so a factor of 10 in amplitude is 20 dB and a factor of 2 is about 6 dB.

A decibel is not a unit of a quantity, only a ratio, so dB values need a reference to describe a level: dBm is relative to 1 milliwatt and dBV to 1 volt. A drop of 3 dB is half the power, which is why it marks the cut-off of a filter.

Worked example

An amplifier raises a voltage by a factor of 10.

  1. dB = 20 log₁₀(10) = 20 dB.
  2. The power gain is 10^(20/10) = 100.

The gain is 20 dB in voltage and 100× in power. 1,000 mW is 30 dBm.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • Both amplitudes are measured across the same impedance, so that power goes as amplitude squared.

Common mistakes

  • Using 10 for a voltage ratio, which halves the answer.
  • Adding dB values that refer to different references.
  • Reading a dB value as an absolute level without knowing its reference.

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Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.