Decibels don’t add like ordinary numbers. Two sources of 80 dB together make about 83 dB, not 160. Ten of them make 90 dB. That’s because the decibel scale is logarithmic: every 3 dB is a doubling of sound energy, every 10 dB is ten times the energy, and a 10 dB increase sounds roughly twice as loud to most people.
Once you know three or four rules, you can do most decibel math in your head.
Why is the decibel scale logarithmic? #
Human hearing covers an enormous range. The loudest sounds you can tolerate carry about a trillion times the energy of the faintest you can hear. Writing that as ordinary numbers would be unwieldy, so sound level is expressed as 10 times the base-10 logarithm of an energy ratio. That turns a trillion-to-one range into roughly 0 to 120 dB.
It also happens to fit how we perceive loudness, which works more by ratios than by differences. Going from one fan to two sounds like a similar step whether the room was quiet or already noisy.
The rules of thumb #
| Change in level | Sound energy | Sound pressure | Perceived loudness (roughly) |
|---|---|---|---|
| +1 dB | 1.26× | 1.12× | Barely noticeable |
| +3 dB | 2× | 1.41× | Slightly louder |
| +6 dB | 4× | 2× | Clearly louder |
| +10 dB | 10× | 3.16× | About twice as loud |
| +20 dB | 100× | 10× | About four times as loud |
| +30 dB | 1,000× | 31.6× | About eight times as loud |
The “twice as loud per 10 dB” rule is an approximation from listening studies. It varies with frequency and between people, but it’s a useful guide.
How do you add two decibel levels? #
Convert each level to energy, add the energies, and convert back:
L_total = 10 × log10(10^(L1/10) + 10^(L2/10) + …)
For two sources, you can skip the formula and use the difference between them:
| Difference between the two levels | Add this to the louder one |
|---|---|
| 0 dB (equal) | +3.0 dB |
| 1 dB | +2.5 dB |
| 2 dB | +2.1 dB |
| 3 dB | +1.8 dB |
| 4 dB | +1.5 dB |
| 5 dB | +1.2 dB |
| 6 dB | +1.0 dB |
| 8 dB | +0.6 dB |
| 10 dB | +0.4 dB |
| More than 10 dB | Negligible |
Examples:
- A 70 dB dishwasher and a 70 dB range hood: 73 dB.
- A 75 dB vacuum and a 65 dB TV: the difference is 10 dB, so about 75.4. The TV barely changes the total.
- Four machines at 85 dB each: 85 + 3 + 3 = 91 dB.
- Ten identical sources: +10 dB.
That last pair explains a lot about workplaces. A shop floor where every machine is 85 dB doesn’t stay at 85 when you add more machines. Doubling the number of machines adds 3 dB, which halves the safe time under the NIOSH guideline.
Why does 3 dB matter so much for hearing? #
Hearing damage tracks the total sound energy your ears take in. Since +3 dB is double the energy, it’s equivalent to doubling the time. That’s why NIOSH’s recommended exposure limit halves the allowed time for every 3 dB above 85 dBA:
| Level | NIOSH daily limit |
|---|---|
| 85 dBA | 8 hours |
| 88 dBA | 4 hours |
| 91 dBA | 2 hours |
| 94 dBA | 1 hour |
| 97 dBA | 30 minutes |
| 100 dBA | 15 minutes |
OSHA uses a 5 dB exchange rate instead, which allows more time at higher levels. See NIOSH vs OSHA noise limits.
How do you subtract background noise? #
Say a machine plus the room reads 60 dB, and the room alone (machine off) reads 57 dB. How loud is the machine by itself?
L_source = 10 × log10(10^(L_total/10) − 10^(L_background/10))
Here that’s 10 × log10(10^6 − 10^5.7) ≈ 57 dB. When the total is only 3 dB above the background, the source and the background are about equal.
Practical rules:
- Source reading 10 dB or more above background: ignore the background. It isn’t affecting the reading.
- 3 to 10 dB above background: subtract using the formula or the table above in reverse.
- Less than 3 dB above background: the measurement isn’t reliable. Wait for a quieter time or move closer to the source.
This is why measuring the background matters in neighbor noise logs. See how to measure neighbor noise.
How do you average decibels? #
Not by adding and dividing. A room that sits at 60 dB for half an hour and 80 dB for the other half doesn’t average 70 dB. Average the energies:
10 × log10((10^6 + 10^8) ÷ 2) ≈ 77 dB
The loud half dominates. This energy average is called Leq, the equivalent continuous sound level, and it’s what hearing limits and noise rules use. A simple arithmetic average of decibel readings understates loud, spiky noise, sometimes by a lot. See what is Leq.
Sound Meter dB does this math for you. Its session statistics show Leq alongside min and max, and the app accumulates everything in the energy domain, converting to decibels only when it displays a number. That’s the way the sound level meter standard defines it, so a slammed door or a bass drop counts properly instead of disappearing into an average.
How does distance fit in? #
Distance works the same way. For a single source in open space, the level drops about 6 dB each time you double your distance, because the sound pressure halves. Moving from 1 meter to 2 meters from a speaker takes 90 dB to about 84 in open space. See sound level vs distance.
Frequently asked questions #
Is 60 dB twice as loud as 30 dB? #
No, far more. 60 dB carries 1,000 times the energy of 30 dB and sounds roughly eight times as loud, since each 10 dB step sounds about twice as loud.
Why do two speakers only add 3 dB? #
Two equal speakers double the sound energy, and doubling energy is +3 dB on the logarithmic scale. To get +10 dB, which sounds about twice as loud, you’d need ten times the energy, like ten speakers at the same level.
How many decibels is double the sound? #
It depends what you mean by “double.” Double the energy or power is +3 dB. Double the sound pressure is +6 dB. Twice as loud to the ear is about +10 dB.
Can decibel levels be negative? #
Yes. 0 dB is a reference point, the conventional threshold of human hearing, not silence. Sounds quieter than that reference, measurable in special labs, have negative decibel values. For everyday noise you’ll almost never see them.