Inverse Square Sound Calculator
When sound travels outward from a point source in an open environment, its intensity decreases with the square of the distance. This means every time you double the distance from a speaker or other source, the sound pressure level drops by approximately 6 dB. The formula dB2 = dB1 - 20 log10(d2/d1) lets you predict what level will be measured at any new distance, given a known level at a reference distance. This is widely used in audio engineering, outdoor event production, and industrial noise assessment to estimate coverage zones and safe exposure distances.
Inverse square law formula
dB2 = dB1 - 20 × log10(d2 / d1)
Where dB1 is the known level at distance d1, and dB2 is the level at the new distance d2. The 20 factor arises because intensity is proportional to 1/r^2, so the dB drop is 10 log10(d2/d1)^2 = 20 log10(d2/d1).
Quick reference: distance vs level change
- 2x distance: -6.02 dB
- 4x distance: -12.04 dB
- 10x distance: -20.00 dB
- 100x distance: -40.00 dB
- Half the distance: +6.02 dB
Frequently asked questions
What is the inverse square law for sound?
The inverse square law states that sound intensity decreases proportionally to the square of the distance from a point source in free field. Doubling the distance reduces intensity by a factor of 4, which equals a 6 dB drop.
How is the formula derived?
Intensity spreads over a sphere of area 4 pi r^2. If r doubles, area quadruples, so intensity quarters. In decibels: dB2 = dB1 - 20 log10(d2/d1). The factor is 20 (not 10) because dB is defined as 10 log10(I) and I is proportional to 1/r^2.
Does the law apply to all sound sources?
The inverse square law applies to an ideal point source in a free, anechoic field. Real rooms add reflections and the law becomes less accurate at short distances or near large sources. Line sources (e.g. traffic on a highway) follow a different relationship.
What if I double the distance?
Doubling the distance (d2/d1 = 2) reduces the level by 20 log10(2) = 6.02 dB, commonly rounded to 6 dB. This is the standard rule of thumb in acoustics.
Can I use this to estimate outdoor speaker coverage?
Yes, as a first approximation for outdoor point-source speakers in the absence of reflections or ground effects. For precise coverage prediction, software such as EASE or CLF-formatted speaker data is recommended.
Official sources
- OSHA: Noise and Hearing Conservation.
- OpenStax University Physics Vol. 1, Chapter 17: Sound.
- NIST: NIST physical measurement laboratory.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.