Combined Sound Level from Multiple Sources

Calculates the total sound level when combining multiple noise sources, since decibels add logarithmically, not linearly.

Written by the Vorzep Team

EnvironmentalAir QualityNoise Pollution

⟹ Solve⟷L_total, L₁, L₂, L₃, L₄

Source 1 (L₁)

Source 2 (L₂)

Source 3 (L₃)

Source 4 (L₄)

Combined Level (L_total)

Presets:

Combined Level—

—

L₁: —L₂: —L₃: —L₄: —L_total: —

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Sound Level Gauge—

Low (< 60 dB) Moderate (60–80 dB) High (> 80 dB)

L_total = 10·log₁₀(10^L₁/10 + 10^L₂/10 + 10^L₃/10 + 10^L₄/10)

Variables

Symbol	Quantity	Unit
L_total	Combined sound level	dB
Li	Sound level of each individual source	dB

What it means

When multiple sound sources are present, the total sound level is not the arithmetic sum, but the logarithmic sum of the individual levels. This is because decibels are logarithmic. The formula calculates the total level by converting each source level to intensity (10^(Li/10)), summing these intensities, and then converting back to decibels. This is used in occupational noise monitoring, environmental noise mapping, and to ensure compliance with noise regulations. Example: Two machines produce 85 dB and 88 dB. Their combined level is 10×log₁₀(10^(8.5)+10^(8.8)) = 10×log₁₀(316,227,770 + 630,957,344) = 10×log₁₀(947,185,114) = 10×8.976 = 89.76 dB. The total is only about 2.8 dB above the louder source, illustrating that doubling sources adds only 3 dB.

Worked example

Combined Sound Level – Two Examples

Real‑World

Scenario: Two machines produce 70 dB and 70 dB. Find the combined sound level.

Parameter	Value
L1	70 dB
L2	70 dB

1L_total = 10 × log₁₀(10^7 + 10^7) = 10 × log₁₀(2×10^7) = 10 × (7+0.301) = 73.01 dB

Result 73.0 dB ✓ +3 dB

Scenario: Three sources at 65 dB, 65 dB, and 65 dB. Find the combined level.

Parameter	Value
L1	65 dB
L2	65 dB
L3	65 dB

1L_total = 10 × log₁₀(3×10^6.5) = 10 × (6.5 + 0.477) = 69.77 dB

Result 69.8 dB ✓ +4.77 dB

Environmental insight: Decibels add logarithmically – two equal sources add 3 dB, three equal sources add 4.8 dB.

Common mistakes

Li: Sound pressure level of each source – in dB (usually decibels relative to 20 µPa).
Logarithmic sum: The formula adds decibels logarithmically, not arithmetically. For two equal sources, total = L + 3 dB.
Units: All Li must be in dB – the result is also in dB.
Incoherent sources: This formula assumes uncorrelated sources (common for most environmental noise). For coherent sources, use vector addition.
Rounding: Report to the nearest 0.1 or 1 dB.

Applications

The combined sound level from multiple sources is obtained by logarithmically summing the individual sound pressure levels, using L_total = 10·log₁₀(Σ 10^(Li/10)). This is essential for environmental noise assessments where several sources (e.g., traffic, industrial plant, ventilation fans) contribute to the overall noise. Acoustic engineers use this calculation to predict cumulative noise exposure, to design quieter communities, and to ensure compliance with noise limits. It also supports the design of acoustic treatments and the selection of quieter equipment. By combining levels, professionals can accurately assess total noise impact and develop effective mitigation strategies.

Environmental noise assessments for multiple sources (road, rail, industry)
Indoor noise design for open‑plan offices and public spaces
Acoustic modelling for building services (HVAC, lifts)
Evaluation of noise from construction sites and events
Compliance with noise codes and regulations