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Decibel Addition Calculator

Add two decibel levels together.

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What is Decibel Addition?

Decibel addition calculates the combined sound level when multiple noise sources operate simultaneously. Two identical 60 dB air conditioners running together don't produce 120 dB — they produce 63 dB. Decibels use logarithmic scaling, not linear addition.

Sound engineers use decibel addition when mixing multiple instruments or speakers. Adding a second speaker playing at the same volume increases the sound level by only 3 dB, not double. Ten identical speakers produce 10 dB more than a single speaker, not ten times more.

Workplace safety officers calculate combined noise exposure from multiple machines. A factory with a 85 dB compressor and an 88 dB conveyor doesn't expose workers to 173 dB (instant hearing damage). The actual combined level is about 90 dB — still hazardous, but calculable and manageable with proper protection.

Decibel Addition Formulas with Worked Calculations

Decibels cannot be added directly. Convert to linear intensity, add, then convert back:

L_total = 10 × log₁₀(10^(L₁/10) + 10^(L₂/10) + ... + 10^(Lₙ/10))

Where L₁, L₂, ..., Lₙ are the individual sound levels in decibels.

Worked example: Three noise sources: 70 dB, 75 dB, and 80 dB.

Convert each to intensity ratio:

10^(70/10) = 10^7 = 10,000,000

10^(75/10) = 10^7.5 = 31,622,777

10^(80/10) = 10^8 = 100,000,000

Sum the intensities: 10,000,000 + 31,622,777 + 100,000,000 = 141,622,777

Convert back to decibels: L_total = 10 × log₁₀(141,622,777) = 10 × 8.151 = 81.51 dB

Result: The combined level is 81.5 dB — only 1.5 dB higher than the loudest source (80 dB).

For two identical sources (both L dB):

L_total = L + 10 × log₁₀(2) = L + 3.01 dB

Two 80 dB sources produce 83.01 dB combined.

How to Add Decibels: 6 Steps

  1. List all sound levels: You have four machines: 72 dB, 78 dB, 75 dB, and 80 dB. Write them down in order from loudest to quietest for easier calculation.
  2. Divide each by 10: 80/10 = 8, 78/10 = 7.8, 75/10 = 7.5, 72/10 = 7.2. These are the exponents for the next step.
  3. Calculate 10 raised to each exponent: 10^8 = 100,000,000; 10^7.8 = 63,095,734; 10^7.5 = 31,622,777; 10^7.2 = 15,848,932. These represent relative intensities.
  4. Sum all intensities: 100,000,000 + 63,095,734 + 31,622,777 + 15,848,932 = 210,567,443. The loudest source dominates the sum.
  5. Take base-10 logarithm: log₁₀(210,567,443) = 8.323. Use a scientific calculator or spreadsheet for this step.
  6. Multiply by 10: 8.323 × 10 = 83.23 dB. This is the combined sound level. Notice it's only 3.23 dB higher than the loudest machine (80 dB).

5 Decibel Addition Examples

Example 1 — Two identical speakers: Each speaker produces 85 dB at the listening position. L_total = 85 + 10 × log₁₀(2) = 85 + 3.01 = 88.01 dB. Doubling the number of identical sources always adds 3 dB, regardless of the starting level. Four speakers would add another 3 dB (91 dB), eight speakers would be 94 dB.

Example 2 — Large difference between sources: A 90 dB machine and a 70 dB machine operate together. The 20 dB difference means the quieter source contributes almost nothing. 10^(90/10) = 1,000,000,000; 10^(70/10) = 10,000,000. Sum = 1,010,000,000. L_total = 10 × log₁₀(1,010,000,000) = 90.04 dB. The 70 dB source adds only 0.04 dB — inaudible in practice.

Example 3 — Office noise floor: HVAC (45 dB), computers (48 dB), conversation (52 dB), printer (50 dB). Convert: 10^4.5 = 31,623; 10^4.8 = 63,096; 10^5.2 = 158,489; 10^5 = 100,000. Sum = 353,208. L_total = 10 × log₁₀(353,208) = 55.48 dB. The combined office noise is 55.5 dB — acceptable for most work but potentially distracting for concentration tasks.

Example 4 — Concert sound system: Main PA (105 dB), monitors (98 dB), crowd noise (88 dB). Convert: 10^10.5 = 31,622,776,602; 10^9.8 = 6,309,573,445; 10^8.8 = 630,957,344. Sum = 38,563,307,391. L_total = 10 × log₁₀(38,563,307,391) = 105.86 dB. The PA dominates; monitors add 0.6 dB, crowd adds 0.26 dB. Total increase is less than 1 dB over the PA alone.

Example 5 — Residential noise complaint: Traffic (62 dB), neighbor's AC (58 dB), refrigerator (45 dB), TV through wall (55 dB). Convert: 10^6.2 = 1,584,893; 10^5.8 = 630,957; 10^4.5 = 31,623; 10^5.5 = 316,228. Sum = 2,563,701. L_total = 10 × log₁₀(2,563,701) = 64.09 dB. Combined residential noise is 64 dB — above the 55 dB typical limit for residential zones at night, potentially warranting a complaint.

4 Common Decibel Addition Mistakes

  • Adding decibels linearly: Assuming 80 dB + 80 dB = 160 dB. This would be louder than a rocket launch (180 dB) and instantly fatal. The correct answer is 83 dB. Decibels are logarithmic — you must convert to intensity, add, then convert back.
  • Ignoring the dominant source: When one source is 10+ dB louder than others, it dominates the sum. A 95 dB machine with a 75 dB machine produces 95.04 dB — essentially just the louder machine. Don't waste effort reducing the quieter source; focus on the dominant noise.
  • Forgetting time weighting: Decibel meters use A-weighting (dBA) for environmental noise, C-weighting (dBC) for peak levels, and Z-weighting (dBZ) for flat response. Adding 80 dBA to 80 dBC is meaningless — they measure different things. Always ensure all sources use the same weighting.
  • Not accounting for distance: Sound levels decrease 6 dB for every doubling of distance. A 90 dB machine at 1 meter is 84 dB at 2 meters, 78 dB at 4 meters. When adding sources at different distances from the measurement point, first adjust each to the same reference distance.

5 Tips for Decibel Calculations

  • Use the 3 dB rule: Doubling identical sources adds 3 dB. Ten identical sources add 10 dB. One hundred add 20 dB. This mental shortcut works for quick estimates without calculation. Eight speakers at 85 dB each produce 85 + 9 = 94 dB (since 8 = 2³, add 3×3 = 9 dB).
  • Apply the 10 dB rule: If two sources differ by 10+ dB, the quieter contributes less than 0.5 dB and can be ignored. An 88 dB machine plus a 75 dB machine produces 88.1 dB — close enough to just 88 dB for most purposes.
  • Use a spreadsheet: For multiple sources, create columns: dB value, dB/10, 10^exponent, sum, log(sum), ×10. This automates the calculation and reduces errors. Excel formula: =10*LOG10(SUM(10^(A1:A10/10))) entered as an array formula.
  • Check with online calculators: After manual calculation, verify with a decibel addition calculator. Input your individual levels and compare. Discrepancies usually indicate arithmetic errors in the exponent or logarithm steps.
  • Consider phase relationships: For coherent sources (same frequency, fixed phase), interference can cause peaks and nulls. The formula assumes incoherent sources (random phase), which is true for most real-world noise. For speakers playing identical signals, actual levels may vary ±3 dB depending on listener position.

4 Decibel Addition FAQs

Decibels represent ratios on a logarithmic scale, not absolute quantities. A 10 dB increase means 10× more acoustic power. Adding decibels directly would be like adding exponents: 10² + 10² ≠ 10⁴. You must convert to linear intensity (undo the logarithm), add, then reapply the logarithm.

Doubling sources adds 3 dB. To add 10 dB, you need 10 identical sources. To add 20 dB, you need 100 sources. Each +10 dB requires 10× more sources. This is why stacking more speakers has diminishing returns — 100 speakers produce only 20 dB more than one speaker.

Yes, but differently. If both earpieces play 80 dB, your brain perceives about 83 dB (the physical addition). However, perceived loudness also depends on frequency content and individual hearing. For noise isolation, 30 dB attenuation plus 80 dB ambient produces 50 dB at your ear — subtraction, not addition.

Consumer sound meters have ±2 dB accuracy; professional meters achieve ±0.5 dB. Since adding two sources differs by only 3 dB at most, measurement error can exceed the calculation's effect. For compliance testing, use calibrated Type 1 or Type 2 meters. For rough estimates, smartphone apps are adequate despite ±3-5 dB error.

Written and reviewed by the CalcToWork editorial team. Last updated: 2026-04-29.

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Frequently Asked Questions

Decibels represent ratios on a logarithmic scale, not absolute quantities. A 10 dB increase means 10× more acoustic power. Adding decibels directly would be like adding exponents: 10² + 10² ≠ 10⁴. You must convert to linear intensity (undo the logarithm), add, then reapply the logarithm.
Doubling sources adds 3 dB. To add 10 dB, you need 10 identical sources. To add 20 dB, you need 100 sources. Each +10 dB requires 10× more sources. This is why stacking more speakers has diminishing returns — 100 speakers produce only 20 dB more than one speaker.
Yes, but differently. If both earpieces play 80 dB, your brain perceives about 83 dB (the physical addition). However, perceived loudness also depends on frequency content and individual hearing. For noise isolation, 30 dB attenuation plus 80 dB ambient produces 50 dB at your ear — subtraction, not addition.
Consumer sound meters have ±2 dB accuracy; professional meters achieve ±0.5 dB. Since adding two sources differs by only 3 dB at most, measurement error can exceed the calculation's effect. For compliance testing, use calibrated Type 1 or Type 2 meters. For rough estimates, smartphone apps are adequate despite ±3-5 dB error.