Decibel Sum Calculator

Frequently Asked Questions

How do I add decibel levels?

Decibels are logarithmic, so you cannot just add them. Combined level L = 10 × log10(Σ 10^(Li/10)). Two equal sources differ by exactly +3 dB, not double the number.

Why do two equal sounds add only 3 dB?

Doubling acoustic power adds 10 × log10(2) ≈ 3 dB. So two 80 dB sources combine to 83 dB, not 160 dB, because the scale measures power ratios logarithmically.

What happens when one source is much louder?

If sources differ by 10 dB or more, the louder one dominates and the sum is within ~0.4 dB of the louder level. An 80 dB and 60 dB source combine to about 80 dB.

When would I sum decibels in practice?

Combining noise from multiple machines, stacking speaker contributions, or estimating cumulative environmental noise all require energy summation rather than simple arithmetic addition of dB figures.

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Estimates for informational purposes only.

Important Disclaimer: Estimates for informational purposes only.

This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.

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How This Calculator Works

Decibels are logarithmic, so you cannot simply add two sound levels - 85 dB plus 85 dB is not 170 dB. This calculator combines multiple incoherent (uncorrelated) sound sources the way real noise sources behave: it converts each level back to relative acoustic energy, sums the energy, then converts the total back to decibels. This is the correct method for adding the SPL of separate machines, instruments, traffic lanes, or noise contributions that are not phase-locked. It reports the combined level, the energy-average level (useful for time-weighted exposure), the loudest single source, and how many decibels the combination adds on top of that loudest source. The result is often surprising: people instinctively expect levels to pile up quickly, but because the scale is logarithmic, even several loud sources together add only a handful of decibels over the loudest one. Understanding that is the difference between sensibly planning a stage, a rehearsal room, or a noisy worksite and badly overestimating - or dangerously underestimating - the combined exposure.

Formula / Method

For n incoherent sources with levels Lᵢ in decibels, the combined level is L = 10 · log₁₀(Σ 10^{(Lᵢ ÷ 10)}). Each term 10^Lᵢ÷10 is the power (energy) ratio relative to the reference; summing powers is physically valid because uncorrelated signals add in mean-square, not in amplitude. The energy average divides the energy sum by n before the log: 10 · log₁₀((Σ 10^Lᵢ÷10) ÷ n). A useful shortcut for two equal sources: doubling the energy adds exactly 10 · log₁₀(2) ≈ 3.01 dB.

Worked Example

Combine 85, 85, 80 and 78 dB. The energy terms are 10^8.5 ≈ 3.162×10⁸, again 3.162×10⁸, 10^8.0 = 1.0×10⁸, and 10^7.8 ≈ 6.31×10⁷. The sum is about 7.95×10⁸, and 10 · log₁₀ of that ≈ 89.0 dB. So four sources peaking at 85 dB together reach roughly 89 dB - only 4 dB over the loudest, not 28 dB as naive addition would suggest. The two equal 85 dB sources alone would make 88 dB (+3 dB for a doubling).

Common Mistakes

Adding decibels arithmetically - 85 + 85 dB is 88 dB, not 170 dB.

Using this energy sum for coherent sources (same pure tone, fixed phase); those can add up to +6 dB or cancel entirely.

Confusing the combined level with the energy average; exposure standards use the time-energy average (Leq).

Forgetting that two very different levels barely combine - adding a 60 dB source to a 90 dB source changes almost nothing.

Mixing A-weighted and unweighted values in the same list; keep one weighting throughout.

Tips & FAQ

Why only +3 dB for two equal sources? Doubling acoustic energy is a factor of 2, and 10 · log₁₀(2) ≈ 3 dB; perceived loudness roughly doubles only around +10 dB. When is this not valid? When sources are correlated - the same signal through two speakers, or standing waves - use the coherent (pressure-amplitude) addition instead. Why does the quietest source barely matter? A source 10 dB lower carries one-tenth the energy and a source 20 dB lower one-hundredth, so it adds a fraction of a decibel. Is this for hearing-safety planning? It is a useful estimate, but occupational exposure must follow the relevant standard (Leq, dose, and weighting); treat this as educational, not a substitute for a calibrated sound-level meter.

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