Distance Attenuation Calculator — Inverse Square Law (Sound & Light)

Formula

How this is calculated

A point source radiating energy uniformly in all directions spreads that energy over a sphere whose surface area grows as 4πd². Because power is conserved, intensity (power per unit area) falls off as 1/d². This is the inverse square law. For sound, the quantity usually measured is the sound pressure level (SPL) in decibels, and because sound pressure is proportional to the square root of intensity, it falls off as 1/d — so the dB attenuation is 20·log₁₀(d₁/d₂) rather than 10·log₁₀. For every doubling of distance the attenuation is 20·log₁₀(0.5) ≈ −6.02 dB, the well-known "6 dB per doubling of distance" rule for sound in free space.

For radiant intensity (light, electromagnetic radiation, or radiation dose rate), the energy per unit area follows 1/d², and the dB relationship is 10·log₁₀(I₂/I₁) = 20·log₁₀(d₁/d₂) — numerically identical to the SPL formula because the reference unit already uses an intensity (quadratic) scale.

Important limitations: the inverse square law assumes a point source radiating freely in all directions with no reflections or absorption. In a room, reflected sound creates a reverberant field that levels off at longer distances. Outdoors, ground reflections, wind, temperature gradients, and atmospheric absorption add further complexity. This calculator models the ideal free-field case only — real-world attenuation is typically less than predicted at long distances in reverberant environments and more at high frequencies outdoors.