Noise Pollution Calculator Formula

Understand the math behind the noise pollution calculator. Each variable explained with a worked example.

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Formulas Used

Combined Sound Level

combined_db = 10 * log(pow(10, source1_db / 10) + pow(10, source2_db / 10)) / log(10)

Safe Exposure Time (OSHA)

safe_hours = 8 / pow(2, (10 * log(pow(10, source1_db / 10) + pow(10, source2_db / 10)) / log(10) - 90) / 5)

Variables

VariableDescriptionDefault
source1_dbSource 1 Level(dB)80
source2_dbSource 2 Level(dB)75

How It Works

Combining Noise Sources

Sound levels in decibels are logarithmic, so you cannot simply add them. Two 80 dB sources produce 83 dB, not 160 dB.

Formula

Combined dB = 10 x log10(10^(L1/10) + 10^(L2/10))

OSHA Exposure Limit

Safe Hours = 8 / 2^((Combined dB - 90) / 5)

OSHA permits 8 hours at 90 dB, with halving for each 5 dB increase.

Worked Example

Two machines produce 80 dB and 75 dB respectively.

source1_db = 80source2_db = 75
  1. 0110^(80/10) = 100,000,000
  2. 0210^(75/10) = 31,622,776
  3. 03Sum = 131,622,776
  4. 04Combined = 10 x log10(131,622,776) = 81.2 dB
  5. 05Safe exposure = 8 / 2^((81.2 - 90)/5) = 8 / 2^(-1.76) = 27.1 hours

Ready to run the numbers?

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