dB calculator
Three decibels doubles power. Six decibels doubles voltage or amplitude. Ten decibels roughly doubles perceived loudness. All three are correct and they measure different things, which is why "twice as loud" is such a slippery phrase. A 3 dB increase doubles the amplifier work and is barely noticeable, while 10 dB sounds twice as loud and takes ten times the power.
Decibels are logarithmic: 20·log₁₀ of a voltage ratio, or 10·log₁₀ of a power ratio. Six decibels doubles voltage, three doubles power, and ten roughly doubles perceived loudness. Two equal sources sum to 3 dB more, not double, and a point source loses 6 dB per doubling of distance.
How to work with decibels
Adding decibels is where intuition fails hardest. Two 80 dB speakers together produce 83 dB, not 160. Ten of them produce 90. The reason is that decibels are a logarithmic ratio, so combining sources multiplies the underlying energy and not the dB figure. It also means quiet sources contribute almost nothing next to loud ones; an 80 dB and a 60 dB source together are 80.04 dB, which is why a single loud machine dominates a noise measurement completely.
Gain, and why the formula has two versions
Gain is the ratio between an output and an input expressed in decibels: 20·log₁₀ for voltage or amplitude, 10·log₁₀ for power. Going from 0.1 V to 2 V is 26 dB, which is about twenty times the voltage and four hundred times the power, the same physical change described by two different numbers depending on which quantity you name. The reason for the two versions is that power goes with the square of voltage, and squaring becomes a factor of two once it is inside a logarithm. Say which one your figures are and the rest follows; guess, and you are out by exactly double.
Level over distance
A point source in free space loses 6 dB for every doubling of distance, which is the inverse square law written in decibels. What matters is the ratio of the distances, not the change in metres: moving a microphone from 10 cm to 20 cm halves the level, while moving it from 2 m to 2.1 m barely registers. That is the whole of close-miking technique in one line, and it is also why a source 8 m away is 18 dB down on the same source at 1 m.
The rule is optimistic indoors and pessimistic outdoors. In a room, reflections keep the level up, and beyond the critical distance the reverberant field dominates and the level stops falling at all. Outdoors over absorbing ground (grass, snow, ploughed earth) the loss is steeper than 6 dB per doubling, so a noise assessment built on the free-field figure alone is an estimate and not a measurement.
What people use it for
- Working out amplifier headroom
- Adding noise sources for an assessment
- Understanding a gain specification
- Converting between dB and a ratio
- Specifying the gain of a preamp or an amplifier
- Estimating a sound level at a site boundary
- Working out microphone placement
Questions
A doubling of power, or about 1.41 times the voltage. It is a small but audible change.
A doubling of voltage or amplitude, which is four times the power.
About 10 dB, which takes ten times the power. It is a perceptual figure, not a physical one.
Convert each to a linear ratio, add those, and convert back. Two equal sources add 3 dB.
Because power goes with the square of voltage, and the square becomes a factor of two once inside the logarithm.
20·log₁₀(out ÷ in) for voltage or amplitude, 10·log₁₀(out ÷ in) for power. Say which your figures are and the tool applies the right one.
About twenty times the voltage, or four hundred times the power. Going from 0.1 V to 2 V is exactly that.
Six decibels per doubling of distance from a point source in free space. Eight metres from a one-metre reference is 18 dB down.
Because the ratio matters, not the absolute change. Going from 10 to 20 cm is a doubling; going from 2 to 2.1 m is not.
Only near the source. Beyond the critical distance, reflections dominate and the level stops falling.
Barely. An 80 dB source and a 60 dB source together measure 80.04 dB, which is why one loud machine dominates a survey.
The level of two identical sources that would carry the same total energy as the pair you entered. It sits 3 dB below the combined figure and is the right average to quote for a noise reading, because a plain arithmetic mean of two decibel values has no physical meaning.
Not directly. Those are decibels against a fixed reference, and this page works in ratios and differences, which are the same in every one of them. A 6 dB gain is 6 dB whether the scale is dBu, dBV or dBFS; only an absolute level needs the reference named.