Short answer: The inverse square law says sound intensity falls with the square of the distance from a point source. In decibels, every doubling of distance lowers the level by about 6 dB: 100 dB at 1 m becomes 94 dB at 2 m and 88 dB at 4 m. From a long line source such as a busy road, the level falls only about 3 dB per doubling.
This post explains the “6 dB rule” and the formula behind it, gives a worked table from 1 to 32 metres, shows why roads behave differently from loudspeakers, and covers the situations where the simple rule breaks down: close to the source, indoors and over long distances. You can check it yourself with our free sound decibel meter and a tape measure.
The Inverse Square Law in One Line
A small source radiates sound energy outwards in all directions. At distance r the energy is spread over a sphere with area 4πr², so the intensity is I = P ÷ (4πr²). Double the distance and the same energy covers four times the area, so the intensity drops to a quarter. A quarter of the energy is −6 dB, because 10 × log10(¼) ≈ −6.0. Sound pressure falls in proportion to 1/r, which gives the same −6 dB through the 20 × log10 formula (see sound pressure level and what a decibel is).
The Formula: Level at a New Distance
- Point source, free field: L₂ = L₁ − 20 × log10(r₂ ÷ r₁). About −6 dB per doubling and −20 dB per tenfold distance.
- Line source (long road, railway, pipeline): L₂ = L₁ − 10 × log10(r₂ ÷ r₁). About −3 dB per doubling and −10 dB per tenfold distance, because the energy spreads over a cylinder, not a sphere.
- Plane source (very close to a large wall or panel): hardly any drop with distance until you are far enough away for it to act like a point.
Example: a speaker reads 96 dB at 2 m. At 10 m, L₂ = 96 − 20 × log10(5) = 96 − 14 = 82 dB. The decibel calculator has a distance mode that does this for point and line sources, and the logarithmic decibel scale explains why ratios become subtractions.
Worked Table: 100 dB at 1 Metre
| Distance | Point source (−6 dB per doubling) | Line source (−3 dB per doubling) |
|---|---|---|
| 1 m | 100 dB | 100 dB |
| 2 m | 94 dB | 97 dB |
| 4 m | 88 dB | 94 dB |
| 8 m | 82 dB | 91 dB |
| 16 m | 76 dB | 88 dB |
| 32 m | 70 dB | 85 dB |
The point-source column falls 30 dB over 32 m, which is one-thousandth of the energy. Starting at 100 dB, you reach 70 dB, about the level of a vacuum cleaner, only after moving 32 m away in open space.
Examples: Speaker, Lawn Mower and Road
- Loudspeaker: a party speaker playing 100 dB at 1 m gives roughly 86 dB at 5 m and 80 dB at 10 m outdoors. Indoors the far readings will be higher because of reflections.
- Lawn mower: a petrol mower is typically 85–95 dB at the operator. If it reads 90 dB at 1 m, expect about 72 dB at 8 m and 66 dB at 16 m, so a neighbour 15 m away hears it a little above normal conversation level.
- Busy road: if traffic measures 70 dB at 10 m, a line-source estimate gives about 67 dB at 20 m, 64 dB at 40 m and 60 dB at 100 m. Moving a bedroom from 10 m to 40 m from the road buys only about 6 dB, which is why screens and barriers matter. Over soft ground such as grass, the drop is often greater than 3 dB per doubling.
Why “Twice as Far” Isn’t “Half as Loud”
A 6 dB drop is clearly quieter but doesn’t sound half as loud. The ear judges a 10 dB drop as roughly half as loud, and for a point source that takes about 3.2 times the distance (20 × log10(3.16) = 10). From a line source it takes ten times the distance. Hear the steps with the volume level comparator.
When the Inverse Square Law Doesn’t Apply
- Near field: close to a source that is large compared with the distance, such as a big machine or a wide speaker array, different parts of the source are at different distances and the level doesn’t follow the 6 dB rule. As a rule of thumb, measure at least a few times the largest dimension of the source away, and more than one wavelength for low frequencies.
- Indoors: sound reflects off walls, floor and ceiling. Near the source the direct sound dominates and falls about 6 dB per doubling, but further away the reflected sound takes over and the level settles at a reverberant floor that hardly changes across the room. The distance where direct and reflected sound are equal is called the critical distance; in a small, hard room it can be only a metre or so. This is why room noise levels vary less with position than outdoor levels.
- Ground and barriers: a source sitting on hard ground radiates into a hemisphere, so it reads about 3 dB higher at every distance but still falls 6 dB per doubling. Soft ground, hills, buildings and barriers add extra loss.
- Air absorption: over hundreds of metres, air absorbs high frequencies far more than low ones. Under typical conditions the loss is a few decibels per kilometre at 1 kHz but tens of decibels per kilometre at 8 kHz, depending on temperature and humidity (ISO 9613-1). That is why distant thunder and far-off music sound bass-heavy. Wavelength matters here; work it out with the audio wavelength calculator, and see dB vs Hz for the difference between level and frequency.
- Wind and temperature: sound bends downwind and towards cooler air, so a distant road or event can be much louder on a still, cold night than on a sunny afternoon.
Test the 6 dB Rule Yourself
- Go outside, away from walls, with a steady source such as a portable speaker playing pink noise.
- Measure at 1 m with the meter and write down the average.
- Move to 2 m, then 4 m, keeping the phone at the same height and pointing at the source.
- Each step should read close to 6 dB lower. Indoors you’ll see the drop shrink as the reverberant floor takes over. Our guide on how to measure decibels helps with steady readings.
Distance and Hearing Protection
Distance is the cheapest noise control. Stepping from 1 m to 4 m away from a 100 dB source cuts the level to 88 dB and stretches the NIOSH safe time from 15 minutes to 4 hours. Plan a day’s exposure with the noise exposure calculator and compare levels on the safe noise levels chart. Near loudspeakers at gigs, bass-heavy levels are better judged in dB(C); see dBA vs dBC. For neighbour noise, distance estimates help you judge whether a reading at your window is plausible; see the apartment noise complaint guide.
Frequently Asked Questions
How much does sound decrease with distance?
About 6 dB each time you double the distance from a small source outdoors, and about 3 dB per doubling from a long road or railway. Indoors the drop is smaller.
What is the 6 dB rule?
It is the inverse square law expressed in decibels: doubling the distance from a point source lowers the sound level by 6 dB.
Does the inverse square law apply to sound pressure?
Sound intensity follows 1/r², and sound pressure follows 1/r. Both give the same −6 dB per doubling. Convert pressure to dB with the SPL converter.
How far away do you need to be for sound to halve?
For the energy to halve (−3 dB), about 1.4 times the distance from a point source. For it to sound half as loud (−10 dB), about 3.2 times.
Why does sound carry further at night?
Cooler air near the ground bends sound back down, and there is less background noise to mask it.
Addito is an audio analysis and sound measurement writer specializing in decibel testing, noise level analysis, sound frequency measurement, and audio engineering tools for creators, audio professionals, students, and everyday users. He creates practical content focused on sound measurement, hearing safety, microphone testing, and acoustic analysis tools.