Decibel Addition Calculator (Combining Sound Levels)
Combined sound level of two, three or four sources of different loudness, and how much louder the total is than the loudest one.
Results
Combined level
63.01
dB
Increase over the loudest source
3.01
dB
What this tool does
Decibels are logarithmic, so they do not add like ordinary numbers: two machines of 60 dB each make 63 dB, not 120. What adds is the sound energy, which is why the calculation converts each level back to intensity, sums and converts again. A source more than about 10 dB quieter than the loudest one hardly changes the total — switching off the quieter of two very unequal machines barely helps. This assumes the sources are unrelated (incoherent), which is true of nearly all real noise.
Formula
L = 10 × log₁₀(10^(L₁/10) + 10^(L₂/10) + …)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
l1 | Level of source 1 | dB |
l2 | Level of source 2 | dB |
l3 | Level of source 3 (0 = none) | dB |
l4 | Level of source 4 (0 = none) | dB |
L | Combined level | dB |
IN | Increase over the loudest source | dB |
Worked example
- Level of source 160 dB
- Level of source 260 dB
- Level of source 3 (0 = none)0 dB
- Level of source 4 (0 = none)0 dB
- Combined level63.01 dB
- Increase over the loudest source3.01 dB
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.