Fun Acoustics

dB calculator

Mode
Decibels
dB
Voltage ratio 1.99526×
10^(6/20) for voltage, 10^(6/10) for power
Power ratio 3.98107×
As a percentage 199.53 %
Perceived loudness change 1.516×
3 dB doubles power · 6 dB doubles voltage

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.

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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 only 3 dB more, not double.

How to work with decibels

1 Pick the mode: converting a dB figure, measuring gain, or adding two sources.
2 For gain, say whether your levels are voltage or power — the formula differs.
3 For summing, remember two equal sources add just 3 dB.
4 Use the perceived-loudness row when talking about how loud something sounds.

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 rather than 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.

Questions

A doubling of power, or about 1.41 times the voltage. It is a small but audible change.

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