ATAcoustic Toolbox

Sound levels

Decibel Calculator

Combine sound levels, calculate an energetic average, or correct a measured level for background noise.

Add sound levels

Enter two or more sound levels. Empty rows are ignored.

Combined level

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dB

FormulaLtotal = 10 log10(Σ 10Lᵢ/10)

Why decibels cannot be added arithmetically

A decibel is a logarithmic representation of a power ratio. Adding 70 dB and 70 dB as ordinary numbers would imply 140 dB, which is physically incorrect. The levels must first be converted to linear energy ratios, summed, and converted back to decibels.

Worked example

For two independent sources at 70 dB:

10 log10(1070/10 + 1070/10) = 73.01 dB

The combined level is therefore 3.01 dB higher than either source alone.

Background noise correction

A measurement often includes both the source and ambient background noise. Energetic subtraction estimates the source-only level. It is valid only when the measured total is greater than the background. When their difference is small, uncertainty becomes large.