Two 60 dB machines make 63 dB
Not 120. The decibel is a logarithm, so adding two levels is not adding two numbers — you convert each back to a power, add the powers, and convert the total forward again.
Doing that for two equal sources gives 10·log₁₀(2) = 3.01 dB above either one. So doubling the number of identical machines, voices or lanes of traffic costs you three decibels, every time, however many you already have.
Identical 60 dB sources, and the total they produce together| How many | Total | Above one alone |
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| 1 | 60.00 dB | — |
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| 2 | 63.01 dB | +3.01 |
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| 4 | 66.02 dB | +6.02 |
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| 10 | 70.00 dB | +10.00 |
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| 100 | 80.00 dB | +20.00 |
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| 1000 | 90.00 dB | +30.00 |
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Every tenfold increase adds exactly ten decibels, which is the definition doing its job. And since roughly ten decibels is what most people perceive as twice as loud, it takes ten identical machines to sound twice as loud as one. Two machines sound very nearly the same as one.
The reverse is the useful bit for anyone trying to reduce noise. Halving the number of sources — or halving the acoustic power of one — buys 3 dB, which is close to the smallest change a person reliably notices. Meaningful reduction means going after an order of magnitude, not a fraction.
The quiet source that adds nothing
The same arithmetic has a consequence that saves a great deal of wasted effort. When sources are unequal, the loud one wins almost completely.
A 60 dB source standing beside an 80 dB one produces a total of 80.04 dB. The quieter source contributes four hundredths of a decibel — about 1% of the acoustic power, and far below anything a person or an ordinary meter would notice.
So if a workshop has one loud machine and five quiet ones, silencing all five quiet ones achieves essentially nothing. All of the available improvement is in the loud one, and the calculator above shows exactly how much each source is really contributing so that the effort goes where it can matter.
A rule of thumb worth carrying: anything more than about 10 dB below the loudest source can be ignored, because it changes the total by less than 0.5 dB. Anything within 3 dB of it matters as much as the loudest source does.
Is double +3 dB or +6 dB?
Both, and which one applies depends entirely on what is being doubled. This is the most common way to be confidently wrong about decibels.
A decibel is defined on a power ratio as 10·log₁₀. Doubling the power is therefore +3.01 dB. But many of the quantities people measure are not powers — they are amplitudes: voltage, current, sound pressure. Power goes as the square of amplitude, so the log picks up a factor of two and the formula becomes 20·log₁₀. Doubling the voltage is +6.02 dB.
The same decibel figures read as a power ratio and as an amplitude ratio| Decibels | As power | As amplitude |
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| +3 dB | ×2.00 | ×1.41 |
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| +6 dB | ×3.98 | ×2.00 |
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| +10 dB | ×10.0 | ×3.16 |
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| +20 dB | ×100 | ×10.0 |
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| +40 dB | ×10,000 | ×100 |
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Notice that the power column is always the square of the amplitude column — so choosing the wrong formula does not give you an answer that is a bit off, it gives you one that is squared or square-rooted. At 40 dB that is the difference between a hundredfold and a ten-thousandfold change.
The practical test is simply what you are measuring. Watts, acoustic intensity and radiated power take 10·log₁₀. Volts, amps and sound pressure take 20·log₁₀. Sound pressure level in particular is an amplitude quantity, which is why doubling your distance from a source costs 6 dB rather than 3.
A decibel is always relative to something
“The level is −10 dB” is not a statement about the world. A decibel expresses a ratio, so an absolute figure only means something once you know what it is a ratio to — and that is what the suffix is for.
dB SPL is referenced to 20 micropascals, chosen because it is roughly the quietest sound a healthy young ear can detect. So 0 dB SPL is not silence; it is the threshold of hearing, and negative values are perfectly possible in an anechoic chamber.
dB(A) is the same scale with a frequency filter applied that de-emphasises the low end, approximating the ear’s own response. Nearly every published noise limit is A-weighted, and an A-weighted figure is not comparable with an unweighted one — the difference can be tens of decibels for low-frequency noise.
dBm is referenced to a milliwatt and dBW to a watt, so 0 dBW is 30 dBm. dBV is referenced to a volt and dBu to 0.7746 V — the voltage that dissipates a milliwatt in 600 ohms, a leftover of telephone practice — putting a fixed 2.22 dB between them. That is why consumer gear at −10 dBV and professional gear at +4 dBu do not match, and the gap is nearly 12 dB rather than the 14 the numbers suggest.
dBFS is digital full scale, and is the odd one out: it is always zero or negative, because 0 dBFS is the largest number a sample can hold. Exceed it and the waveform does not get louder, it clips.
Same noise, two legal answers
Occupational noise limits work on a dose: a level, and how long you may be exposed to it. Halving the permitted time is allowed to buy you some extra decibels — and how many is a policy choice that two major jurisdictions have made differently.
The EU and ISO use a 3 dB exchange rate, which is the equal-energy rule: 3 dB is a doubling of acoustic power, so it halves the permitted time. Eight hours at 85 dB(A), four at 88, two at 91.
US OSHA uses a 5 dB exchange rate from a 90 dB(A) criterion, on the historical reasoning that intermittent noise and recovery between exposures make the equal-energy rule too strict.
Permitted daily exposure at the same measured A-weighted level| Level | EU / ISO | US OSHA |
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| 85 dB(A) | 8 hours | 16 hours |
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| 90 dB(A) | 2.5 hours | 8 hours |
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| 95 dB(A) | 48 minutes | 4 hours |
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| 100 dB(A) | 15 minutes | 2 hours |
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| 105 dB(A) | 5 minutes | 1 hour |
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At 100 dB(A) — a nightclub, a chainsaw — one regime permits a quarter of an hour and the other two hours. An eightfold difference from an identical measurement, and the gap widens as the noise gets louder.
Which is worth knowing for two reasons. A figure quoted as “the safe exposure time” is meaningless without saying whose rule it follows. And since hearing damage is cumulative and permanent, the more conservative of two defensible answers is the one worth acting on.
Sources and methodology
The logarithms need no authority. What the sources settle is everything the logarithms are attached to: that the factor depends on whether a quantity is a power or a field quantity, what the 20 µPa reference and the A-weighting curve actually are, and — the part with real consequences — that two major jurisdictions apply different exchange rates to the same measurement and therefore permit different exposures.