Combining Two Sound Levels

Decibels are logarithmic, so you cannot add sound levels in dB directly. This formula converts each level back into a linear sound-intensity scale, adds those intensities, and then converts the result back into decibels. It works because dB is defined relative to a reference intensity, so equal-looking dB differences can correspond to very different physical power contributions.

Use this when two independent sound sources are present at the same point and you want the resulting overall sound level, such as two speakers, two machines, or a background noise plus a new source. It is also useful in acoustics problems involving combined noise exposure or overlapping signals.

• Adding the dB values directly instead of converting to intensity first
• Using the wrong logarithm base or forgetting the factor of 10
• Assuming the louder source and the total differ by 3 dB regardless of the level gap