Engineering · Civil Engineering
Noise Pollution Calculator
Calculates combined noise levels, sound pressure level attenuation with distance, and noise exposure dose from multiple sources.
Calculator
Formula
L_combined is the total combined sound pressure level (dB) from multiple sources. L1, L2, L3 are the individual source levels in dB. L_dist is the attenuated SPL at distance d2 given a reference level Ls at distance d1. α is the atmospheric absorption coefficient (dB/m). D is the noise exposure dose as a percentage, where T is the actual exposure duration and T_crit is the permissible exposure time at the measured level per OSHA/ISO standards.
Source: ISO 9613-1:1993 Acoustics — Attenuation of sound during propagation outdoors; OSHA 29 CFR 1910.95 Occupational Noise Exposure Standard.
How it works
Noise pollution is measured in decibels (dB), a logarithmic scale representing sound pressure level (SPL) relative to the threshold of human hearing (20 µPa). Because the decibel scale is logarithmic, sound levels from multiple sources cannot be simply added arithmetically — they must be combined using the power-sum formula. Two identical 90 dB sources together produce approximately 93 dB, not 180 dB. This non-linear behavior is central to all noise impact assessments.
This calculator implements three core acoustic engineering calculations. First, the combined noise level is found by converting each source level from dB to intensity (10^(L/10)), summing them, and converting back to dB. Second, distance attenuation follows the inverse-square law (−20 log₁₀(d₂/d₁)) with an additional term for atmospheric absorption (α × distance), modelling how noise dissipates as it travels through air. Atmospheric absorption is frequency-dependent; typical broadband values range from 0.003 to 0.01 dB/m. Third, the noise exposure dose uses the OSHA criterion of 90 dB as the 8-hour permissible exposure limit, with the permitted duration halving for every 5 dB increase in level.
These calculations are applied across a wide range of disciplines: road traffic noise assessments, industrial plant permitting, construction site management, occupational safety audits, urban planning noise contour mapping, and airport environmental impact studies. Outputs can be compared directly to regulatory thresholds such as WHO community noise guidelines (55 dB daytime, 45 dB nighttime), EU Environmental Noise Directive limits, and OSHA/NIOSH workplace exposure limits.
Worked example
Scenario: An industrial site has three noise sources — a compressor at 85 dB, a conveyor at 80 dB, and a generator at 78 dB — measured at a common reference point. A residential receiver is located 100 m away from the combined source, which was measured at 92 dB at a reference distance of 1 m. The atmospheric absorption coefficient is 0.005 dB/m. A worker is exposed to 88 dB for 7 hours.
Step 1 — Combined noise level:
L_combined = 10 × log₁₀(10^(85/10) + 10^(80/10) + 10^(78/10))
= 10 × log₁₀(316,227,766 + 100,000,000 + 63,095,734)
= 10 × log₁₀(479,323,500)
= 10 × 8.6807 = 86.81 dB
Step 2 — Distance attenuation to receiver at 100 m:
L_dist = 92 − 20 × log₁₀(100/1) − 0.005 × (100 − 1)
= 92 − 20 × 2.0 − 0.495
= 92 − 40 − 0.495 = 51.5 dB
This is below the WHO daytime community noise guideline of 55 dB, indicating acceptable impact at the receptor.
Step 3 — Noise exposure dose:
T_crit at 88 dB = 8 / 2^((88−90)/5) = 8 / 2^(−0.4) = 8 / 0.758 = 10.56 hours
Dose = (7 / 10.56) × 100 = 66.3%
This is below the 100% OSHA action level, so the worker's exposure is within permissible limits, though PPE review is advisable.
Limitations & notes
This calculator models simplified free-field (point-source) propagation using the inverse-square law and does not account for complex terrain effects, barriers, ground absorption, diffraction, or reflections from buildings, which are covered by full ISO 9613-2 and CNOSSOS-EU models. The atmospheric absorption coefficient α is treated as a constant; in practice it varies significantly with frequency, temperature, and humidity. The combined noise level calculation assumes incoherent sources (no phase correlation); coherent sources (e.g., identical machines in phase) can produce different combined levels. The noise dose calculation uses OSHA's 5 dB exchange rate and 90 dB criterion level; NIOSH recommends a 3 dB exchange rate and 85 dB criterion, which would yield significantly higher doses at the same exposure. Results should be validated with calibrated sound level measurements and full acoustic modelling software for regulatory submissions or legal proceedings.
Frequently asked questions
Why can't I simply add decibel values from two sources?
Decibels are a logarithmic unit representing sound power ratios, not linear quantities. To combine two noise sources, you must convert each to linear intensity (10^(L/10)), sum the intensities, then convert back to dB. Two identical 90 dB sources produce 93 dB, not 180 dB. This is why the power-sum formula is essential in all noise assessments.
What is the OSHA permissible noise exposure limit?
OSHA sets the permissible exposure limit (PEL) at 90 dB(A) for an 8-hour time-weighted average, using a 5 dB exchange rate (the allowed duration halves for every 5 dB increase). The action level triggering hearing conservation programmes is 85 dB(A) TWA. NIOSH uses a more protective 85 dB criterion with a 3 dB exchange rate.
How does noise level decrease with distance?
For a point source in a free field, sound pressure level decreases by 20 dB for every tenfold increase in distance — equivalent to 6 dB per doubling of distance. This follows the inverse-square law: L = Ls − 20 log₁₀(d₂/d₁). Additional losses from atmospheric absorption, ground effects, and barriers are added in detailed models.
What is a noise exposure dose of 100%?
A noise dose of 100% represents the maximum permissible occupational noise exposure under OSHA regulations. Exceeding 100% means the worker has received more acoustic energy than allowed during a work shift, requiring immediate hearing protection, engineering controls, or administrative measures to reduce exposure duration or level.
What atmospheric absorption coefficient should I use?
The atmospheric absorption coefficient α depends on frequency, temperature, and relative humidity. For broadband environmental noise assessments, values between 0.003 and 0.01 dB/m are typical. ISO 9613-1 provides detailed tables for calculating α at specific frequencies. For low-frequency noise or short distances (<50 m), the effect is minimal and can often be neglected compared to geometric spreading.
Last updated: 2025-01-15 · Formula verified against primary sources.