Sound Distance Attenuation Calculator
Enter the sound level at a reference distance and a new distance. The calculator gives the level there, for a point source in a free field, where each doubling of distance lowers the level by about 6.02 dB.
The assumptions: a point source in a free field
This calculator is limited to these conditions:
- A point source: a source that spreads sound out in a sphere from a single point.
- A free field: a space without reflections from walls, floors or ceilings.
It does not account for the behavior of a line source (a line array), reflections from walls or floors, reverberation, absorption of sound by the air, wind or the effect of the ground. In a real room or outdoors, these make the level different from the result here.
How it is calculated
For a point source in a free field, the sound level falls as the distance grows (the inverse square law).
- Change in level (dB) = −20 × log10(new distance ÷ reference distance)
- Level at the new distance (dB) = reference level + change
Doubling the distance lowers the level by about 6.02 dB. Ten times the distance lowers it by 20 dB. Halving the distance raises it by about 6.02 dB.
Distance ratio and change
| Distance ratio (new ÷ reference) | Change |
|---|---|
| 0.5 × (half) | +6.02 dB |
| 2 × | −6.02 dB |
| 3 × | −9.54 dB |
| 4 × | −12.04 dB |
| 5 × | −13.98 dB |
| 10 × | −20.00 dB |
| 100 × | −40.00 dB |
Examples
- A sound of 100 dB at 1 m: about 93.98 dB at 2 m, and 80 dB at 10 m.
- A sound of 90 dB at 2 m: about 77.96 dB at 8 m (4 times the distance, −12.04 dB), and about 96.02 dB at 1 m (half the distance).
Things to know
- The sound level can be from −999 to 999 dB, with decimals. Negative values are accepted.
- The distances must be greater than 0 and can have decimals (up to 9 digits before the decimal point and 6 decimal places). Use the same unit for both.
- The result is rounded half up to 0 to 2 decimal places (1 by default). Because the calculation uses a logarithm, it uses ordinary floating-point arithmetic, rounded to a fixed number of decimal places.
- For acoustic design or anything involving safety, confirm with measurements or dedicated simulation software.
- To add the levels of several sources, use the Decibel Addition Calculator.
Frequently asked questions
How many dB does the level fall when the distance doubles?
For a point source in a free field, about 6.02 dB.
Does this hold indoors too?
No. A room has reflections from the walls, floor and ceiling and has reverberation, so the level can fall off by less than this formula says. This calculator is for a free field without reflections.
Can I use it for a line array speaker?
A line array (line source) spreads sound differently from a point source. Over some range the level falls off by less than for a point source when the distance doubles, so it is not covered here.
Does the reference distance have to be 1 m?
No. Only the ratio of the distances matters, so going from 2 m to 8 m or from 1 m to 4 m gives the same change (−12.04 dB).