Two identical compressors, each 80 dBA at the operator's ear. Switch the second one on and the meter reads 83. Not 160, and not 85 either. This is the single most useful fact in site acoustics, and it is worth knowing exactly why.

Decibels are logarithms of energy, so they cannot be added. The route is to undo the logarithm, add the energies, and take the logarithm again: $L_t = 10\log_{10}\!\left(10^{L_1/10} + 10^{L_2/10}\right)$ — read aloud L-t equals ten log of ten-to-the-L-one-over-ten plus ten-to-the-L-two-over-ten. Here $L_1$ and $L_2$ are the two sound pressure levels in decibels, each measured at the same point with the other source switched off, and $L_t$ is what the meter reads with both running. The condition matters: levels measured at different places may never be combined.

Two equal sources are the easy case. $10^{8} + 10^{8} = 2 \times 10^{8}$, and $10\log_{10}2 = 3.01$, so the answer is always the level plus three. It does not matter what the level was.

Unequal sources fade fast, and this is the part that surprises people. A source 5 dB below the other adds about 1.2 dB. 6 dB below adds 1.0. 10 dB below adds 0.4 dB — the whole second machine, worth four tenths of a decibel, when the smallest change most people can hear is about 3. That is why silencing the second-loudest machine on a site so often changes nothing measurable, and why the money goes to the loudest one first.

Two sanity rails, and they never fail. The total is always above the louder source, and never more than 3 dB above it. If your answer falls outside that band, it is wrong before you check the arithmetic.