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 Noise Level

combined_level = combined_db

Level at Distance

at_dist = at_distance

vs WHO Limit (65 dB)

vs_who = at_distance - 65

Safe Exposure at This Level

max_safe_hours = 8 / pow(2, (at_distance - 85) / 3)

Variables

VariableDescriptionDefault
source1_dbPrimary Noise Source(dB)70
source2_dbSecondary Noise Source(dB)60
exposure_hoursDaily Exposure Hours(hours)8
distance_ftDistance from Source(feet)50
combined_dbDerived value= 10 * log(pow(10, source1_db / 10) + pow(10, source2_db / 10)) / log(10)calculated
at_distanceDerived value= combined_db - 20 * log(distance_ft / 3) / log(10)calculated

How It Works

How to Calculate Noise Pollution

Noise levels are measured in decibels (dB) on a logarithmic scale.

Combining Sources

Combined dB = 10 * log10(10^(dB1/10) + 10^(dB2/10))

Distance Attenuation

dB at distance = Source dB - 20 * log10(distance / reference)

Reference Levels

  • Whisper: 30 dB
  • Conversation: 60 dB
  • Traffic: 70-85 dB
  • Construction: 80-100 dB
  • WHO recommends daytime limit of 55-65 dB

    • Worked Example

    A 70 dB traffic noise and 60 dB HVAC system, 8 hours exposure at 50 feet.

    source1_db = 70source2_db = 60exposure_hours = 8distance_ft = 50
    1. 01Combined: 10 * log10(10^7 + 10^6) = 10 * log10(11,000,000) = 70.4 dB
    2. 02At 50 ft: 70.4 - 20 * log10(50/3) = 70.4 - 24.4 = 46.0 dB
    3. 03vs WHO: 46.0 - 65 = -19.0 dB (below limit)

    Frequently Asked Questions

    What is a safe noise level?

    The WHO recommends 55 dB for outdoor daytime and 40 dB for nighttime sleep. Occupational limits are 85 dB for 8 hours. Every 3 dB increase doubles the sound intensity.

    How does noise affect health?

    Chronic noise above 65 dB increases risk of cardiovascular disease, sleep disruption, stress, and cognitive impairment. The WHO estimates 1.6 million healthy life years are lost annually in Western Europe from traffic noise.

    How is the decibel scale different from linear?

    Decibels are logarithmic. A 10 dB increase sounds about twice as loud and represents 10x more sound intensity. Adding two equal sources increases the level by 3 dB, not double.

    Ready to run the numbers?

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