Sound · inverse square law
Sound level and distance calculator.
Enter a level measured at one distance and a new distance. Get the level there, or the distance at which the sound falls to a level you choose. Free-field point source, outdoors and without reflections.
Inputs
Result
Enter a level and two distances.
The inverse square law for sound
Sound from a point source obeys the inverse square law when there are no reflections: intensity falls as 1/r squared, and sound pressure falls as 1/r. In decibels the level change is L2 = L1 - 20 x log10 (r2 / r1). Doubling the distance therefore costs 6 dB, and Sengpielaudio states the same rule: "a sound level drop of 6 dB per doubling of distance". HyperPhysics notes the law holds only if there are no reflections or reverberation.
Worked example. A speaker measures 90 dB at 1 metre. At 8 metres (three doublings) the level is 90 - 20 x log10 (8) = 71.9 dB, a drop of 18.1 dB. To fall to 70 dB the distance is 1 x 10^((90 - 70) / 20) = 10 metres.
Real rooms and streets are not free field. Indoors, reflections keep the level from falling this fast beyond a short distance, and the law applies to a source small compared with the distance. Outdoors, wind, ground and air absorption change the result at long range. Use this as an estimate for the near free field, not a prediction for a room.
Frequently asked questions
How much does sound drop when you double the distance?
About 6 dB in a free field, and the sound pressure halves.
Does the inverse square law work indoors?
Only roughly, close to the source. Reflections from walls add to the direct sound, so the level falls more slowly than 6 dB per doubling.
Why 20 log and not 10 log for distance?
Intensity falls with distance squared, and the 10 log of a square is 20 log of the distance ratio, so the level falls by 20 log10 (r2 / r1).
Can I use feet instead of metres?
Yes. Only the ratio of the two distances matters, so use the same unit for both, and the distance answer comes back in that unit.
Sources
Checked
- Sengpielaudio: Damping of sound level (attenuation) with distance
- HyperPhysics: Inverse Square Law, Sound
Runs entirely in your browser. Nothing you type is sent or stored.
Scope
Estimate for a free-field point source. It ignores reflections, absorption, wind and source directivity. Not a noise-impact assessment. Hearing safety guidance, not medical or occupational-health advice. These are published limits and rules of thumb applied as arithmetic, not a noise survey. Measure real levels with a sound level meter or dosimeter, follow the rules that apply to your workplace, and see an audiologist if you have ringing, muffled hearing or hearing loss.