How sound spreads
A small source in open air radiates its energy over a growing sphere. The area of a sphere grows with the square of its radius, so the intensity drops with the square of distance: the inverse square law. On the decibel scale, that is about 6 dB less each time the distance doubles.
A long, busy road or a railway behaves like a line source. Its energy spreads over a cylinder instead, and the level drops about 3 dB per doubling of distance.
The formulas
- Point source: L2 = L1 − 20 × log10(r2 ÷ r1)
- Line source: L2 = L1 − 10 × log10(r2 ÷ r1)
The calculator also gives the change per doubling of distance and the ratio of sound intensities.
Worked example
A chainsaw measures 100 dB at 3 m (10 ft). At 30 m (100 ft):
- r2 ÷ r1 = 10.
- L2 = 100 − 20 × log10(10) = 100 − 20 = 80 dB.
- The intensity is 100 times lower (0.01).
For a highway that measures 75 dB at 15 m, the level at 120 m (three doublings) would be about 75 − 9 = 66 dB.
Point source, distance doubling
| Distance | Level |
|---|---|
| 1 m | 100 dB |
| 2 m | 94 dB |
| 4 m | 88 dB |
| 8 m | 82 dB |
| 16 m | 76 dB |
| 32 m | 70 dB |
Practical uses
- Hearing protection: stepping back from a machine is often the cheapest way to cut exposure. Doubling your distance from a point source cuts the level by 6 dB, and the safe exposure time roughly quadruples under NIOSH’s 3 dB exchange rate.
- Neighbor noise: estimate how loud a generator, heat pump or pool pump will be at the property line. Many local noise ordinances set limits around 55 to 65 dBA during the day and 45 to 55 dBA at night at the property line.
- Events and speakers: plan the mixing position and audience distance.
Real-world corrections
The free-field formula is a starting point. In practice:
- Air absorption removes high frequencies over hundreds of meters.
- Ground effect: soft ground such as grass absorbs sound, hard surfaces reflect it.
- Barriers such as walls, buildings and earth berms can cut 5 to 15 dB if they block the line of sight.
- Wind and temperature: sound carries farther downwind and on calm nights with temperature inversions.
- Indoors, reflections stop the level from falling beyond a certain distance from the source.