Why decibels do not add normally
The decibel scale is logarithmic: every 10 dB step means ten times more sound energy. Two machines at 80 dB do not make 160 dB; together they make 83 dB. To combine levels, you must convert them back to energy, add, and convert again.
The formula
L_total = 10 × log10(10^(L1/10) + 10^(L2/10) + … + 10^(Ln/10))
The calculator also shows how much the total exceeds the loudest single source and how many sources equal to the loudest one would give the same total.
Worked example
Two identical air compressors each produce 80 dB at your position:
- 10^(80/10) = 10⁸ for each, 2 × 10⁸ in total.
- 10 × log10(2 × 10⁸) = 80 + 3.01 = 83.0 dB.
Add a third source at 75 dB and the total rises only to about 83.6 dB.
Quick addition table
| Difference between two levels | Add to the higher level |
|---|---|
| 0 dB | +3.0 dB |
| 1 dB | +2.5 dB |
| 2 dB | +2.1 dB |
| 3 dB | +1.8 dB |
| 5 dB | +1.2 dB |
| 10 dB | +0.4 dB |
| 15 dB or more | about 0 |
To add several sources by hand, combine them two at a time, starting with the quietest.
What the numbers mean for hearing
- +3 dB: twice the sound energy, just noticeable to the ear.
- +10 dB: ten times the energy, perceived as about twice as loud.
- OSHA’s permissible exposure limit is 90 dBA over 8 hours, with a hearing conservation program required from 85 dBA. NIOSH recommends a stricter 85 dBA limit with a 3 dB exchange rate, meaning the safe time halves for every 3 dB increase.
So two machines that are each “safe” at 82 dBA together reach 85 dBA, the point where hearing protection programs start.
Subtracting background noise
The same logic works in reverse. If a machine measures 85 dB with the background on and the background alone is 80 dB, the machine alone is 10 × log10(10^8.5 − 10^8) ≈ 83.3 dB.
Limits
The formula assumes the sources are uncorrelated, which is true for different machines, voices or vehicles. Two speakers playing the same signal in phase can add up to 6 dB at some points and cancel at others.