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Decibel Calculator

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A decibel is not a unit — it is a logarithm of a ratio, which means a figure in dB says nothing until you know what it is a ratio of. Two things follow, and both are where mistakes happen: power ratios use a factor of ten while voltage and pressure ratios use twenty, and a suffixed unit like dBm is an absolute level while a bare dB is only a comparison. This handles all of it, and asks you which kind of quantity you have rather than guessing.

What are you converting?
Is the quantity a power or an amplitude?

2 for double, 0.5 for half, 100 for a hundredfold

How to use the decibel calculator

  1. 1Choose whether you are converting a ratio to decibels, decibels to a ratio, or working with an absolute unit such as dBm.
  2. 2For a ratio, say whether the quantity is a power or an amplitude — this sets the factor to 10 or 20, and getting it wrong doubles the answer.
  3. 3Enter the ratio, or the number of decibels.
  4. 4For absolute levels, pick the reference unit and enter either watts and volts, or the level in dB.
  5. 5Read the result, with the equivalent in the other domain shown alongside it.

Examples

The most quoted figure in the subject

Input
A power ratio of 2
Result
3.01 dB

Double the power is three decibels. Half the power is minus three, which is where the -3 dB corner frequency of a filter gets its name.

The same number, different domain

Input
An amplitude ratio of 2
Result
6.02 dB

Doubling a voltage is six decibels, because doubling the voltage quadruples the power. This is the single most common decibel error.

An absolute level

Input
30 dBm
Result
1 W

dBm is referenced to a milliwatt, so 0 dBm is 1 mW and every 10 dB is a factor of ten — 10 dBm is 10 mW, 20 is 100 mW, 30 is a full watt.

About the decibel calculator

Why anything is measured this way at all

Two reasons, and the first is range. The quietest sound a person can hear and the loudest they can tolerate differ by a factor of about ten million in pressure, and ten trillion in power. Writing that as a linear ratio is unmanageable; on a logarithmic scale it becomes 0 to 130, which fits on a dial and in a sentence.

The second is that logarithms turn multiplication into addition. A signal chain that passes through an amplifier with a gain of 100, a cable with a loss of 0.5 and a filter with a loss of 0.7 has an overall gain of 100 × 0.5 × 0.7. In decibels the same chain is +20, −3 and −1.5, and the total is +15.5 dB — arithmetic anybody can do in their head while looking at a block diagram. That property is why decibels survived the calculators that made the range argument less pressing.

The unit is named after Alexander Graham Bell. The bel itself — a factor of ten in power — turned out to be too coarse for practical use, so the decibel, a tenth of one, is what everybody actually uses. That is where the leading 10 in the power formula comes from.

The figures worth memorising

Three decibels is a doubling of power, and minus three is a halving. This is why the −3 dB point defines a filter's corner: it is where half the power gets through. Six decibels is a doubling of voltage or of sound pressure, and it is also a doubling of distance for a point source in free space — move twice as far from a speaker and the level drops 6 dB.

Ten decibels is a factor of ten in power, and twenty is a factor of ten in amplitude. Once those two are fixed, most everyday conversions can be done without a calculator: 23 dB is 20 plus 3, so a hundredfold power increase and then a doubling, which is 200 times. Minus 40 dB is a ten-thousandth of the power, or a hundredth of the voltage.

One decibel is roughly the smallest change in level most listeners can detect under good conditions, which is a useful sanity check on any audio specification. A claim that a change of a tenth of a decibel is audible is a claim about something below the threshold of the measurement, and it is worth treating with the scepticism it deserves.

Frequently asked questions

When do I use 10 log and when do I use 20 log?
Ten for power, twenty for amplitude. Power quantities are watts, and intensity; amplitude quantities are volts, amps, and sound pressure. The factor differs because power varies with the square of amplitude, and squaring a number inside a logarithm doubles the logarithm. Both conventions describe the same physical change — a doubling of voltage is 6 dB and the quadrupling of power that comes with it is also 6 dB, which is the consistency the two factors exist to preserve.
What is the difference between dB and dBm?
dB is relative and dBm is absolute. Saying an amplifier has 20 dB of gain describes a relationship between its input and output and tells you nothing about either in isolation. Saying its output is 20 dBm states a specific power — a hundred milliwatts — because dBm is referenced to one milliwatt. The suffix is what supplies the reference, which is why asking to convert a bare 3 dB into watts has no answer.
Why do decibels not add when I combine two sources?
Because the logarithm gets in the way. Two equally loud, independent sources produce twice the power, and twice the power is 3 dB more — not twice the decibels. So two 60 dB sources together make 63 dB, and it takes ten identical sources to reach 70 dB. This holds for uncorrelated sources such as separate noise generators. Two copies of the same signal in phase are a different case: there the amplitudes add, giving 6 dB.
Why is 10 dB described as twice as loud?
That is a statement about hearing rather than about physics. Ten decibels is a tenfold increase in power, and psychoacoustic experiments consistently find that listeners judge that as roughly a doubling of loudness. The two facts sit oddly together and both are true: you need ten times the amplifier power to sound twice as loud, which is why a 100 W amplifier is not noticeably louder than a 50 W one.
What is dBu, and why is its reference such an odd number?
It is referenced to 0.7746 volts, which is the voltage that dissipates exactly one milliwatt into a 600 ohm load. That impedance is a legacy of telephone line practice, where 600 ohms was the standard and power actually mattered. Modern audio equipment is voltage-driven with high input impedances, so the power reference is meaningless — but the voltage stuck, and professional gear is still specified with a nominal level of +4 dBu.

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