About Sound Level Distance Calculator (Attenuation, Lw → Lp & dB Addition)
The sound level distance calculator applies the classic free-field relations found in Beranek and underlying ISO 9613-2 geometric divergence. In attenuation mode it projects a known level L1 at distance r1 to any other distance r2: a point source spreads spherically and loses 20 log10(r2/r1) decibels — 6 dB per doubling of distance — while a line source such as a busy road spreads cylindrically and loses 10 log10(r2/r1), only 3 dB per doubling. Moving closer is handled honestly: r2 smaller than r1 returns a genuine positive gain.
Power-to-pressure mode converts a sound power level Lw from a fan, pump, or equipment datasheet into the sound pressure level Lp heard at distance r, using Lp = Lw + 10 log10(Q/(4πr²)) with a directivity factor Q of 1 in free space, 2 on a hard surface, 4 at a wall-floor edge, or 8 in a corner. Combine mode adds up to twenty incoherent source levels energetically — two equal sources are 3 dB louder than one, never twice the number — and reports how far the total sits above the loudest single source.
How It Works
- Pick a mode: distance attenuation, sound power to sound pressure, or combining levels.
- Attenuation: enter the known level L1 at reference distance r1, the target distance r2, and choose point (spherical, −6 dB per doubling) or line (cylindrical, −3 dB per doubling) spreading. The chart traces the level from r1 out to 10·r1 for both source types.
- Power to pressure: enter the sound power level Lw from the equipment datasheet, the listening distance r, and where the source sits — free space (Q = 1), on a hard surface (Q = 2), at a wall-floor edge (Q = 4), or in a corner (Q = 8).
- Combining: enter each incoherent source level (up to 20 rows); the tool sums the energies, 10^(Li/10), and reports the combined level plus its increase above the loudest single source.
- Distances accept meters or feet (converted at exactly 0.3048 m/ft); levels are capped to 0–200 dB and distances to 10 km, mirrored by every input field.
Worked Example
A compressor measures 85 dB at 2 m. At 8 m the distance ratio is 4, so a point source loses 20 log10(4) = 12.04 dB, leaving 72.96 dB — the inverse square law at work. If the noise came instead from a long line of traffic (a line source), the loss over the same ratio is only 10 log10(4) = 6.02 dB, leaving 78.98 dB. Walking back in from 8 m to 2 m reverses the point-source change as an honest +12.04 dB gain, back to 97.04 dB from an 85 dB reading at 8 m. And two such 85 dB compressors side by side combine energetically to 85 + 10 log10(2) = 88.01 dB, 3 dB above the loudest — not 170 dB.
Formulas
- Point-source distance attenuation (spherical spreading)
L2 = L1 − 20 · log10(r2 / r1)- Line-source distance attenuation (cylindrical spreading)
L2 = L1 − 10 · log10(r2 / r1)- Sound power to sound pressure (free field with directivity)
Lp = Lw + 10 · log10( Q / (4π · r²) )- Energetic (incoherent) addition of levels
L = 10 · log10( Σ 10^(Li/10) )
Standards & References
- Beranek, "Acoustics" — free-field spherical/cylindrical spreading and directivity
- ISO 9613-2 — geometric divergence term Adiv (free-field basis of outdoor attenuation)
Frequently Asked Questions
How much quieter does a sound get when I double my distance from it?
A compact (point) source in the free field loses 6 dB per doubling of distance — the inverse square law, 20 log10(r2/r1). A long line source such as a steady stream of traffic or a pipeline loses only 3 dB per doubling (10 log10), because the sound spreads cylindrically instead of spherically. Going from 2 m to 8 m therefore costs 12 dB for a point source but just 6 dB for a line source.
What is the difference between sound power level (Lw) and sound pressure level (Lp)?
Sound power level describes the total acoustic energy a source emits (dB re 1 picowatt) and is a property of the machine alone — it is what fan and pump datasheets quote. Sound pressure level is what a meter reads at a specific location (dB re 20 µPa) and depends on distance and surroundings. In the free field they connect through Lp = Lw + 10 log10(Q/(4πr²)): at 10 m on a hard surface (Q = 2), a 100 dB Lw source produces about 72 dB Lp.
What does the directivity factor Q mean and which value should I choose?
Q describes how nearby hard surfaces concentrate the radiated sound. A source hanging in free space radiates over a full sphere (Q = 1); sitting on a hard floor or against a wall it radiates into a half sphere (Q = 2, +3 dB); at a wall-floor edge into a quarter sphere (Q = 4, +6 dB); and in a corner where three surfaces meet into an eighth sphere (Q = 8, +9 dB). Most floor-mounted equipment outdoors or in large rooms is Q = 2.
Why do two 80 dB machines make 83 dB and not 160 dB?
Decibels are logarithmic, so incoherent sources add by energy, not by level: L = 10 log10(10^8 + 10^8) = 83.01 dB. Doubling the number of equal sources always adds 3.01 dB, and ten equal sources add exactly 10 dB. A source more than about 10 dB quieter than the loudest changes the total by less than 0.5 dB, which is why the tool also reports how far the combined level sits above the loudest single source.
Can I use this calculator to find the level closer to the source than my measurement?
Yes — the attenuation mode accepts r2 smaller than r1 and reports the resulting increase as an honest positive gain, e.g. a level of 85 dB measured at 8 m projects to 97 dB at 2 m for a point source. Bear in mind the free-field equations assume you stay outside the near field, roughly a source dimension or a wavelength away; projected levels very close to a large machine overstate what a meter would read.
How accurate are these free-field equations in real rooms and outdoors?
They are exact for geometric spreading alone, which dominates over the first few tens of meters. Outdoors over longer ranges, ISO 9613-2 adds terms for air absorption, ground effect, and barriers, all of which increase the attenuation beyond the divergence term computed here. Indoors, the reverberant field sets a floor: beyond the room radius the level stops falling with distance, so pair this tool with a reverberation-time check for room predictions.