Distance Attenuation Calculator

The distance attenuation calculator finds how the sound level in dB decreases with distance from the sound source.

Attenuation over that distance12.041 dB20log₁₀ of the distance ratio

Sound pressure level85 dBas entered, against the 20 µPa reference

Sound pressure355.6559 mPa85 dB against the 20 µPa reference, using the AMPLITUDE factor of 20

Sound intensity0.0003162 W/m²against 1 pW/m², using the POWER factor of 10 — the two references are chosen so a plane wave in air gives nearly the same number, which is why they get confused

Pressure as a multiple of the threshold1.778e+4×

Intensity as a multiple3.162e+8×the square of the pressure ratio

Level at the new distance72.959 dBat 4 m, which is 12.041 dB quieter than at 1 m — free-field spreading gives 6 dB per doubling of distance

Distance for a 10 dB drop3.162 mabout 3.16× further — a halving of perceived loudness

Sound power of the source3.9738 mWif it radiates equally in all directions — a surprisingly small figure, since even a shout is well under a watt

Against a whisper55 dB3.16e+5× the intensity of 30 dB

Against normal conversation25 dB316× the intensity of 60 dB

Against a busy road5 dB3.16× the intensity of 80 dB

Against a chainsaw-25 dB0.00316× the intensity of 110 dB

Against the pain threshold-45 dB3.16e-5× the intensity of 130 dB

Maximum daily exposure8 hoursfrom the 8 hours permitted at 85 dB, halving for every 3 dB above it

Hearing damage riskabove the 85 dB action levelhearing protection is required at this level for anything beyond the exposure time above

The 3 dB exchange rate3 dB halves the timebecause 3 dB is twice the power — so 88 dB permits 4 hours, 91 dB permits 2, and 94 dB just 1. Some jurisdictions use a 5 dB rate, which is more permissive and not physically motivated

The formula

SPL = 20log₁₀(p/20µPa); L_I = 10log₁₀(I/1pW·m⁻²)

Two references, two factors

Sound pressure level uses 20 µPa as its reference and the amplitude factor of 20; sound intensity level uses 1 pW/m² and the power factor of 10. The two references were chosen so that a plane wave in air gives almost the same number on both scales, which is convenient and also why the distinction is so often missed — the error only shows up in unusual media or near-field conditions.

Incoherent sources add in power, so two identical machines produce 3 dB more than one, not 6 dB and certainly not twice the loudness. Ten machines add 10 dB, which is roughly what listeners judge as twice as loud. Halving the noise from a plant therefore means removing half the total sound power, not half the machines' decibel readings.

In a free field the level falls 6 dB per doubling of distance, because intensity follows the inverse square law while the decibel scale for pressure carries the factor of 20. Real rooms fall off far more slowly once reverberation dominates, so the 6 dB rule applies outdoors or in an anechoic chamber, not in an office.

Exposure limits use a 3 dB exchange rate: every 3 dB doubles the power, so the permitted daily exposure halves. Eight hours at 85 dB becomes four at 88 and one at 94.