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dB Addition Calculator
Decibels cannot be added arithmetically — use this calculator to correctly combine multiple sound sources using the logarithmic power summation formula.
Sound Sources
Combined Level
Total Combined SPL
74.8
dB
Sources
3
Dominant Source
70 dB
Above Quietest
4.8 dB
Above Loudest
+4.8 dB
Formula
Ltotal = 10 × log₁₀(Σ 10^(Lᵢ/10))
Rule of Thumb
2equal sources+3 dB
4equal sources+6 dB
8equal sources+9 dB
10equal sources+10 dB
Why You Can't Simply Add Decibels
The decibel scale is logarithmic, not linear. A level of 70 dB does not mean "70 units of sound" — it means an intensity of 10⁷ times the reference level (10⁻¹² W/m²). Adding two 70 dB sources gives 70 + 70 = 140 dB only on paper; in physical reality, you're doubling the intensity, which equals 10×log₁₀(2) ≈ 3 dB increase, for a total of 73 dB.
The correct formula converts each dB level to a linear intensity ratio, sums those ratios, then converts back: L_total = 10 × log₁₀(Σ 10^(Li/10)). This tool does that calculation instantly for any number of sources.
Practical Scenarios
- HVAC Noise Assessment — An office has three air handlers at 55, 58, and 52 dB. The combined level is not 165 dB but approximately 61.5 dB — well within comfort standards.
- Industrial Hygiene — Workers exposed to multiple machines must have their total noise dose calculated. The dominant source contributes most; a source 10+ dB below the loudest adds less than 0.5 dB to the total.
- Speaker Arrays — Two identical speakers at the same SPL add 6 dB (coherent summation, on-axis). Incoherent summation (different frequencies or positions) gives +3 dB. This tool calculates the incoherent (power-summing) case.
- Environmental Noise Modeling — Road traffic from multiple lanes, combined with rail and aircraft noise, requires logarithmic addition to predict community exposure levels accurately.
Frequently Asked Questions
What happens when you add two identical dB sources?
Two identical, incoherent sound sources double the acoustic power, which equals a 3 dB increase. Two 80 dB sources combine to 83 dB. Four identical sources give +6 dB, ten give +10 dB, and one hundred identical sources give +20 dB. The increase is always 10×log₁₀(N) where N is the number of identical sources.
Does a quiet source affect the total if the dominant source is much louder?
Very little. A source 10 dB below the dominant source adds only 0.41 dB to the total. A source 20 dB below adds just 0.04 dB — negligible in practice. This is why noise control engineers focus on reducing the loudest source first; quieter sources barely affect the total.
Is this calculator for coherent or incoherent addition?
This calculator performs incoherent power addition — the standard method for uncorrelated noise sources (e.g., different machines, fans, or traffic lanes). Coherent sources (same frequency, fixed phase relationship like speaker arrays) can add by up to 6 dB on-axis, which requires a different analysis based on source spacing and wavelength.