Hong Life CalculatorsUnderstanding the sound level vs distance calculator — concept and principle
Sound gets quieter as you move away from its source because the same acoustic power spreads over a larger area. This calculator estimates the sound level at a new distance from a level measured at a known distance, for either a compact point source (a machine, a loudspeaker) or a long line source (a busy road, a railway, a pipeline).
How it is calculated
- Point source: L₂ = L₁ − 20 · log₁₀(r₂ / r₁)
- Line source: L₂ = L₁ − 10 · log₁₀(r₂ / r₁)
L₁ is the level in dB at distance r₁, and L₂ is the predicted level at distance r₂. Both distances must use the same unit (metres here); only their ratio matters. If r₂ is smaller than r₁, the formula gives a higher level.
The principle
A point source in a free field radiates its power W over the surface of a sphere, 4πr², so intensity I = W / (4πr²) falls with the square of distance: the inverse-square law. In decibels, the change is 10 log₁₀(I₂/I₁) = 10 log₁₀(r₁²/r₂²) = −20 log₁₀(r₂/r₁). Each doubling of distance therefore costs about 6.02 dB, and each tenfold increase costs 20 dB. A long, incoherent line source radiates over a cylinder, whose area grows as 2πr per metre of length, so intensity falls only as 1/r: about 3 dB per doubling and 10 dB per tenfold.
Worked example
- Inputs: L₁ = 90 dB at r₁ = 1 m; r₂ = 10 m; point source.
- Distance ratio r₂ / r₁ = 10 / 1 = 10.
- Attenuation = 20 · log₁₀10 = 20 × 1 = 20 dB.
- L₂ = 90 − 20 = 70 dB.
For a line source the same inputs would give 90 − 10 = 80 dB.
| Level at r₁ (dB) | Level at r₂ (dB) |
|---|---|
| 22.5 | 2.5 |
| 45 | 25 |
| 67.5 | 47.5 |
| 90 | 70 |
| 112 | 92.5 |
| 135 | 115 |
| 180 | 160 |
How to read the result
The result is the geometric-spreading level only. In real environments the level at a distance is often lower because of air absorption (significant at high frequencies and long ranges), ground effects, barriers and buildings. It can also be higher than predicted indoors, where reflections create a reverberant field that stops decreasing with distance beyond a certain point.
Common mistakes
- Applying −6 dB per doubling to a road or railway, which behaves closer to −3 dB per doubling.
- Using the formula indoors, where reverberation keeps levels higher far from the source.
- Using a reference measured too close to a large source (near field).
Frequently asked questions
How much quieter is it at twice the distance?
About 6 dB for a point source and about 3 dB for a line source, in free field.
How far must I move to reduce a point source by 10 dB?
The distance must grow by a factor of 10^(10/20) ≈ 3.16.
Sources: ISO 9613-2, Acoustics — Attenuation of sound during propagation outdoors — Part 2: General method of calculation · L. E. Kinsler, A. R. Frey, A. B. Coppens, J. V. Sanders, Fundamentals of Acoustics, Wiley