Decibel Addition Calculator
Adding sound levels in decibels requires converting each level back to intensity, summing the intensities, and converting the result back to decibels. The formula is L_total = 10 log10(sum of 10^(Li/10)). This matters in acoustics because two machines each producing 80 dB do not give 160 dB together: they give 83 dB. This calculator accepts up to six dB levels (comma-separated) and computes the correct combined level. It is used in environmental noise assessments, occupational health, and multi-source audio system design.
Decibel addition formula
Ltotal = 10 × log10(∑ 10Li/10)
Each level Li is converted to a linear intensity ratio, the intensities are summed, and the result is converted back to dB. This is the only correct way to combine incoherent sound levels.
Quick reference: level increase from identical sources
- 2 sources: +3.01 dB
- 4 sources: +6.02 dB
- 10 sources: +10.00 dB
- 100 sources: +20.00 dB
Frequently asked questions
Why can't you just add decibels arithmetically?
Decibels are a logarithmic scale. Adding 80 dB + 80 dB does not give 160 dB; it gives 83 dB because you are doubling the intensity, not the level. The correct formula is L_total = 10 log10(10^(L1/10) + 10^(L2/10) + ...).
What is the result of two equal sources?
Two identical incoherent sources each at level L combine to L + 3.01 dB. This is because doubling intensity doubles the power, and 10 log10(2) = 3.01 dB.
What if the levels are very different?
When one source is 10 dB or more louder than the others, the quieter sources contribute less than 0.5 dB to the total. In practice, a source 13 dB quieter adds only 0.2 dB to the dominant source.
Does this apply to coherent sources?
This formula applies to incoherent (uncorrelated) sources such as independent noise sources. Coherent sources (e.g. two speakers driven by the same signal) can interfere constructively or destructively, requiring complex pressure addition.
Where is this used in practice?
Noise impact assessments, OSHA/NIOSH workplace noise exposure, acoustic modelling, and audio system design all require correct decibel addition. Incorrectly summing dB levels arithmetically is one of the most common acoustic calculation errors.
Official sources
- OSHA: Noise and Hearing Conservation.
- NIOSH: Noise and Hearing Loss Prevention.
- OpenStax University Physics Vol. 1, Chapter 17: Sound.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.