Decibel Sum Calculator

Frequently Asked Questions

Why is adding 85 + 85 dB only 88 dB and not 170 dB?

Doubling acoustic energy is a factor of 2, and 10 x log10(2) is approximately 3 dB. Perceived loudness roughly doubles only around +10 dB.

When is energy summation not the right method?

When sources are correlated - such as the same signal through two speakers or standing waves. Coherent sources can add up to +6 dB or cancel entirely.

Why does the quietest source barely affect the total?

A source 10 dB lower carries one-tenth the energy, so it adds less than 0.5 dB to the combined level.

What is the energy average (Leq) used for?

It represents the equivalent continuous level carrying the same total energy as the actual varying levels, and is used in occupational noise exposure standards.

Is this suitable for hearing-safety planning?

It is a useful estimate, but occupational exposure calculations must follow the relevant standard with calibrated instruments. Treat this as educational.

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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 It 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 formula for n incoherent sources with levels Li in decibels is: L = 10 x log10(sum of 10^(Li / 10)). A useful shortcut: doubling the energy (two equal sources) adds exactly 10 x log10(2), approximately 3.01 dB.

Use Cases

Decibel summation is used in audio engineering and acoustic planning:

Estimating combined SPL from multiple PA speakers on a stage or in a venue

Adding noise contributions from different mechanical sources in a recording studio

Planning an outdoor concert to assess the combined level at a distance

Evaluating how much a secondary source adds to a dominant noise floor

Checking whether adding more speakers to a system materially raises the level

Tips

Two equal sources together add about 3 dB, not double the level. Perceived loudness roughly doubles only around +10 dB.

A source 10 dB lower carries one-tenth the energy and adds less than 0.5 dB to the total - it barely matters.

This energy sum is valid for incoherent sources. For coherent sources (same pure tone, fixed phase), use pressure-amplitude addition instead.

Keep A-weighted and unweighted values separate - do not mix the two in the same list.

The energy average (Leq) is what exposure standards use for time-weighted noise measurement, not the peak combined level.

FAQ

Why is adding 85 + 85 dB only 88 dB?

Doubling acoustic energy is a factor of 2, and 10 x log10(2) is approximately 3 dB. Perceived loudness roughly doubles only around +10 dB, not for a simple level doubling.

When is energy summation not valid?

When sources are correlated - such as the same signal through two speakers, or standing waves. Coherent sources can add up to +6 dB or cancel entirely.

Why does the quietest source barely affect the total?

A source 10 dB lower carries one-tenth the energy and a source 20 dB lower one-hundredth, so it adds only a fraction of a decibel to the combined level.

What is the energy average used for?

The energy average (Leq) is what occupational noise exposure standards use. It represents the equivalent continuous level that carries the same total energy as the actual varying levels.

Is this suitable for hearing-safety planning?

It is a useful estimate, but occupational exposure calculations must follow the relevant standard with calibrated instruments. Treat this as educational.

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