By Zencalcy Editorial TeamLast reviewed About us
In a free field, sound from a point source spreads over a growing sphere, so the level drops 6 dB each time the distance doubles. This distance loss explains why a loudspeaker is much quieter across a large room. The rule assumes no reflections, absorption, wind or terrain effects.
Level change with distance in a free field.
L₂ = L₁ − 20 log₁₀(r₂ / r₁)
L is the level at each distance in a free field. The 20 multiplier matches pressure-like quantities; the same result follows from 10 log₁₀ of the intensity ratio.
| Symbol | Meaning |
|---|---|
| L₁ | Level at the near distance. |
| L₂ | Level at the far distance. |
| r₁ | Near distance from the source. |
| r₂ | Far distance from the source. |
L₂ = 80 − 20 log₁₀(2) = 80 − 6.02 = 74.0 dB. Moving to 4 m would give 68.0 dB, and so on for each doubling.
Continue with the Mach Number Calculator, Resonance Tube Calculator, or the Room Mode Calculator — or browse more acoustics and sound tools and all physics calculators.
It fails indoors, where reflections build a reverberant field, and over long outdoor paths, where air absorption and ground effects add loss. It also assumes a point source rather than a line or area source.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026