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dB Addition Calculator

Decibels cannot be added arithmetically — use this dB addition calculator to correctly combine sound levels from multiple noise 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

L_total = 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 (dB) scale is logarithmic, not linear. A sound pressure level (SPL) of 70 dB does not mean "70 units of sound" — it means an acoustic intensity of 10⁷ times the reference level (10⁻¹² W/m²). When you add decibels the wrong way — 70 + 70 = 140 dB — that is correct only on paper; in physical reality, you're doubling the acoustic power, which equals 10×log₁₀(2) ≈ 3 dB increase, for a total of 73 dB SPL.

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 decibel calculator does that calculation instantly for any number of incoherent noise sources. Note that this formula applies to power quantities (sound power, sound intensity, SPL); for voltage or pressure ratios the factor is 20×log₁₀, but the same logarithmic-summation principle applies. For a related calculation, the dB to watt converter lets you convert any of your individual source levels to absolute power values before or after summation.

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 typical comfort standards. Accurate combined SPL prediction is essential for LEED and WELL building certification.
Occupational Noise Exposure — Workers exposed to multiple machines must have their total noise dose calculated for OSHA compliance (85 dB TWA action level, 90 dB PEL over 8 hours). 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 +3 dB (incoherent power summation). Coherent summation on-axis at identical frequency and phase can reach +6 dB. This tool calculates the incoherent case, appropriate for broadband music or noise sources.
Environmental Noise Modeling — Road traffic from multiple lanes, combined with rail and aircraft noise, requires logarithmic addition to predict community noise exposure levels, Leq (equivalent continuous level), and Ldn (day-night level) for environmental impact assessments. Combined with the inverse square law calculator, you can model both source summation and distance attenuation together.

OSHA vs. NIOSH: Why the Exchange Rate Matters

Two major health standards govern occupational noise, and they disagree on a key parameter. OSHA's permissible exposure limit (PEL) is 90 dBA for an 8-hour shift, using a 5 dB exchange rate: allowable exposure time halves for every 5 dB increase. NIOSH's recommended exposure limit (REL) is stricter — 85 dBA for 8 hours with a 3 dB exchange rate, meaning allowable time halves for every 3 dB. The 3 dB rule directly reflects equal sound energy: because +3 dB represents a doubling of acoustic power, it is the physically correct threshold for equal dose.

The practical difference is significant. At 95 dBA, OSHA allows 4 hours of exposure; NIOSH allows only about 30 minutes. When you use this calculator to combine multiple noise sources and the total climbs, that combined level is the figure you compare against these limits — not each source individually. Use the noise exposure calculator to convert combined levels into a daily dose percentage, and the sound pressure level calculator to verify individual source measurements before adding them together.

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.

What is the maximum increase possible when adding more sound sources?

There is no fixed ceiling, but the increase diminishes as sources become unequal. Adding N identical sources increases the total by 10×log₁₀(N) dB: 10 sources add 10 dB, 100 sources add 20 dB, 1000 sources add 30 dB. In practice, once any single source dominates by 10 dB or more, additional weaker sources contribute less than 0.5 dB each regardless of how many you add. The dominant source sets the floor for the combined level.

How do I subtract decibels to find the noise floor of a single machine?

To isolate one source, measure the combined SPL with the machine running, then measure the background SPL with it off. Use the inverse formula: L_machine = 10×log₁₀(10^(L_combined/10) − 10^(L_background/10)). This only works reliably when the machine is at least 3 dB louder than background; if the difference is less than 1 dB the result is unreliable. Many acoustic consultants use a correction chart for this common measurement task.

Does dB addition work the same way for electrical signal levels?

The logarithmic-summation method is the same in principle, but dBV and dBu express voltage ratios (20×log₁₀), not power ratios (10×log₁₀). If you are summing audio signal voltages from multiple outputs into a mix bus, the same formula applies when expressed as power (dBm or dBW). For voltage-domain mixing, simply convert each voltage level to watts first, sum, then convert back. This calculator assumes all inputs are dB SPL or dB power quantities.

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