How this calculation works
Decibel levels represent logarithmic quantities, so two equal sources do not add by summing their displayed numbers. The contributions must be converted to relative energy, combined and converted back.
Receiver source level = reference level − 20log10(distance/reference distance); incoherent sum = 10log10(Σ10^(level/10))A worked example
Each example source is 80 dB at one metre. At two metres, its ideal contribution is about 73.9794 dB. Two equal incoherent contributions combine to about 76.9897 dB, an increase of about 3.0103 over either alone. It is neither 147.9588 dB nor an unchanged single-source level.
Good to know
Ideal point sources and compatible incoherent levels only; no room response, phase interference, hearing exposure, safety threshold or regulatory assessment. The modeled level is conditional on the acoustic assumptions. A real sound-system or exposure assessment needs appropriate measurements and expertise.
Reference: OpenStax — sound intensity levels (opens in a new tab) ↗
What this calculation answers
Decibel levels represent logarithmic quantities, so two equal sources do not add by summing their displayed numbers. The contributions must be converted to relative energy, combined and converted back.
This page first moves each entered point-source level to the selected receiver distance under a free-field assumption. It then combines those contributions as incoherent sources, with optional background already specified at the receiver.
The Room reverberation Sabine and Eyring calculator estimates a diffuse decay from surface absorption. Its room assumptions are different from this direct free-field distance model.
Use the right input conventions
Every source level must use a compatible weighting, bandwidth and reference. Distances are from that source to the same receiver concept; the reference distance belongs to the entered source-level measurement.
The optional background is not moved through a distance correction. Enter it as the already applicable receiver level, and do not include the same sound as both background and a separate source row.
Interpret the result
Doubling distance reduces an ideal point-source level by about 6.02 dB. Real near-field behavior, directivity, barriers, absorption and reflections can change that result; the page does not decide whether the free-field condition applies.
The sum assumes incoherent contributions. Phase-related interference from correlated loudspeakers can produce position-dependent peaks or cancellations that this energy-sum model intentionally does not predict.
Work through the example
Each example source is 80 dB at one metre. At two metres, its ideal contribution is about 73.9794 dB.
Two equal incoherent contributions combine to about 76.9897 dB, an increase of about 3.0103 over either alone. It is neither 147.9588 dB nor an unchanged single-source level.
Where the model stops
Ideal point sources and compatible incoherent levels only; no room response, phase interference, hearing exposure, safety threshold or regulatory assessment.
The modeled level is conditional on the acoustic assumptions. A real sound-system or exposure assessment needs appropriate measurements and expertise.
A few questions, answered
Why do equal sources add only about 3 dB?
Their relative energies double; ten times log10 of two is about 3.0103 dB.
Can this model two phase-aligned speakers?
Not their interference pattern. The sum assumes incoherent contributions.