Why noise levels add logarithmically
Sound pressure levels in decibels are expressed on a base-10 logarithmic scale. The formula for combining n sources is:
L_total = 10 × log₁₀( Σ 10^(L_i / 10) )
Each source is first converted back to its linear energy equivalent (10^(L/10)), the energies are summed, and the result is converted back to decibels. This is necessary because decibels represent a ratio of power — you cannot simply add two dB numbers together.
The practical consequence: two sources at the same level produce a combined level that is exactly 3.01 dB higher than either source alone (10·log10(2) ≈ 3.01 dB). Doubling the number of identical sources always adds 3 dB, regardless of the starting level. Conversely, a source 10 dB louder than all others will dominate — the quieter sources contribute less than 0.5 dB to the total.
Common scenarios
- Two identical machines (e.g., both at 90 dBA): combined level = 93.0 dBA (+3 dB). The energy doubles, but the decibel scale compresses large ratios into small numbers.
- Ten identical machines at 80 dBA: combined level = 90.0 dBA. Each additional doubling of the number of sources adds another 3 dB (×2 → +3 dB, ×4 → +6 dB, ×8 → +9 dB, ×10 → +10 dB).
- One source dominates (90 dBA + 80 dBA + 75 dBA): combined level ≈ 90.6 dBA. The sources that are 10–15 dB quieter contribute less than 0.5 dB each — the loudest source dominates the sum.
- Background noise assessment (70 dBA ambient + 85 dBA machine): combined level ≈ 85.1 dBA. The ambient background adds only 0.1 dB — control efforts should focus on the dominant source.
- Sources at 85 dBA and 85 dBA after adding a barrier (reduction of 10 dB on one source): Before: 88.0 dBA. After (75 + 85 dBA): 85.4 dBA. A 10 dB reduction on the louder of two equal sources yields only a 2.6 dB improvement — both sources must be controlled to achieve meaningful reduction.
Frequently Asked Questions
Why doesn't 80 + 80 = 160 dB?
Decibels are a logarithmic unit, not a linear one. Adding two sources does not mean adding their dB values. When you add two sources at 80 dBA, you double the acoustic energy — and doubling energy corresponds to a 3 dB increase, not a doubling of the level. So 80 dBA + 80 dBA = 83 dBA. If you did add the raw numbers (80 + 80 = 160), you'd be confusing two completely different measurement scales.
What's the difference between dBA and dBC?
Both dBA and dBC measure sound pressure levels, but they use different frequency-weighting filters. The A-weighting (dBA) attenuates low and high frequencies to match the sensitivity of the human ear — it is the standard for occupational noise exposure assessments (OSHA, ACGIH TLVs, ISO 9612). The C-weighting (dBC) has a flatter response and better captures low-frequency energy; it is used for peak measurements and assessing low-frequency noise from equipment such as compressors, fans, and HVAC systems. The mathematical addition formula is identical for both — the calculator simply displays the unit you select.
Can I add levels measured at different times?
Yes, but with an important caveat: this calculator adds instantaneous or average sound levels assuming all sources are simultaneously present. If the measurements were taken at different times and the sources do not overlap in time, simply adding them with this formula overestimates the true combined exposure. For time-varying exposures where sources operate at different times, you should use a time-weighted average (TWA) calculation instead. This tool is best suited for assessing the simultaneous combination of multiple sources (e.g., multiple machines running at the same time in a workshop).
What if my measurements are below the noise floor?
If a measured source is within 3–5 dB of the background (noise floor), the background noise has contaminated the measurement and the true source level is lower than the reading. In that case, a background correction should be applied: measure with and without the source, then use the logarithmic subtraction formula (L_source = 10·log10(10^(L_total/10) − 10^(L_background/10))). Sources that are more than 10 dB below the noise floor can generally be disregarded — they contribute less than 0.5 dB to the combined level. Always confirm with a qualified industrial hygienist when borderline measurements affect compliance decisions.
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