The sound attenuation calculator above answers the everyday acoustics question: I know how loud this is here, how loud will it be over there? The dominant mechanism at ordinary distances is not the air absorbing energy but simple geometry — the same acoustic power spread over an ever-larger surface as the wave expands. This page computes that spreading loss for both point and line sources, and adds atmospheric absorption as a separate term you can see rather than a hidden fudge.
Arb Digital builds free physics calculators that separate the mechanisms instead of merging them into one opaque number. Splitting geometric spreading from atmospheric absorption matters because they behave completely differently: spreading loss depends on the ratio of distances and is frequency-independent, while absorption depends on the difference in distances and varies enormously with frequency and humidity.
What This Sound Attenuation Calculator Does
Give it a level and a distance, and a second distance, and it returns the level at the second distance. You can start from a sound pressure level measured with a meter, which is the usual field case, or from a manufacturer's sound power level, which is the usual specification case. The two are different quantities and the tool handles them differently.
The grid separates the loss into its parts: the geometric spreading loss in decibels, the atmospheric absorption in decibels, the total of the two, and how many doublings of distance you have travelled. That last figure is worth reading, because the whole behaviour of sound with distance is easiest to hold in your head as decibels per doubling — 6 for a point source, 3 for a line source, and nothing else in free field.
This is a free-field calculation. It assumes there is nothing between the source and the receiver, no ground effect, no barrier, no reflecting surfaces other than through the directivity factor, and no wind or temperature gradient bending the sound. Every one of those is a real effect that a full environmental noise assessment has to include, and none of them is modelled here.
How to Use It
- Pick the right starting point. A meter reading is a sound pressure level and needs the distance it was taken at. A manufacturer's figure is usually a sound power level, which has no distance attached to it at all.
- Choose the geometry honestly. Point or line is the single most consequential choice on the page. If in doubt, ask whether the source is much shorter or much longer than the distance you care about.
- Set the directivity only in power mode. A machine sitting on a hard floor radiates into a hemisphere rather than a sphere, which raises the level at any distance by 3 dB. In reference mode it cancels out and is ignored.
- Leave absorption at zero unless you have a real coefficient. Air absorption is negligible over tens of metres and significant over kilometres, and it varies by more than an order of magnitude with frequency and humidity.
- Read the doublings figure as a sanity check. Three doublings on a point source should give 18 dB of spreading loss. If your answer disagrees, one of the inputs is not what you thought.
The Formula: How Attenuation With Distance Is Calculated
For a point source radiating into free space, the intensity falls as the inverse square of the distance, because the same power is spread over a sphere whose area grows as r². In level terms that gives L2 = L1 − 20 log10(r2 ÷ r1). OpenStax University Physics Volume 1, section 17.3 on sound intensity, sets out the decibel definition and the inverse-square relationship this rests on.
For a line source the wavefront is a cylinder rather than a sphere, its area grows as r rather than r², and the expression becomes L2 = L1 − 10 log10(r2 ÷ r1). That single change of coefficient is why traffic noise carries so much further than the noise from an individual machine.
Starting from a sound power level instead, the free-field sound pressure level at distance r is Lp = LW + 10 log10(Q ÷ (4πr²)), with r in metres. The 4πr² is the area of the sphere and Q is the directivity factor that accounts for the source radiating into less than the full sphere.
Atmospheric absorption is added as a term proportional to the distance travelled: Aatm = α × (r2 − r1), with α in decibels per unit distance. The coefficients belong to ISO 9613-2, the standard for attenuation of sound during propagation outdoors, and its companion part 1, which is why this page asks you for the value rather than assuming one.
Work the defaults. A level of 100 dB measured at 1 m from a point source, evaluated at 10 m, gives a spreading loss of 20 log10(10) = 20 dB, so the level at 10 m is 80 dB. Ten is 3.32 doublings, and 3.32 × 6 = 19.9 dB, which is the same answer read the other way round.
Point or Line: the Choice That Decides the Answer
A source behaves as a point when you are far enough away that its physical size no longer matters. A rough working rule is that a source acts as a point beyond about twice its largest dimension, and as a line while you are much closer to it than its length. A 300-metre stretch of busy road looks like a line at 20 metres and increasingly like a point at 3 kilometres.
The consequence is large. Start both source types at 70 dB at 10 metres. At 320 metres — five doublings — the point source has fallen to 40 dB and the line source only to 55 dB. That 15 dB gap is the difference between an inaudible background and a level that will keep people awake, and it comes entirely from one dropdown.
Trains are the classic ambiguous case: a line source while one passes, a point source once it has gone. Planning assessments handle that with equivalent continuous levels over a defined period rather than by picking one geometry.
When Atmospheric Absorption Actually Matters
Air converts a small fraction of acoustic energy into heat, and the fraction rises steeply with frequency. It is why a fireworks display a few kilometres away is heard as thuds without the crackle.
Over a hundred metres, absorption at speech frequencies typically amounts to less than a decibel, which is inside the uncertainty of everything else. Over five kilometres it can exceed the geometric spreading loss entirely at high frequencies. The rule of thumb is that below a few hundred metres you can ignore it, and beyond a kilometre you cannot — but the coefficient must come from the standard for your temperature, humidity and frequency band, because a value that is right at 20 °C and 70 per cent humidity can be several times wrong at 5 °C and 20 per cent.
What This Page Does Not Model
Real outdoor propagation includes several effects this calculator leaves out, and all of them can exceed the difference the tool is computing. Ground effect — interference between the direct sound and the sound reflected from the ground — can add or subtract several decibels depending on the surface and the geometry. Barriers, embankments and buildings provide screening that depends on the path difference and the wavelength. Wind and temperature gradients refract sound, which is why the same source is audibly louder downwind and can be almost inaudible upwind at the same distance.
Indoors the whole model changes. Beyond the critical distance in a room, the reverberant field dominates and the level stops falling with distance at all, which is why a workshop can be uniformly loud everywhere rather than quieter in the far corner. Nothing on this page applies inside a reverberant space.
Where the question is about noise exposure rather than propagation, the governing regulation and its measurement method decide, not a spreading calculation. The noise exposure calculator covers dose over time; the applicable occupational health regulation in your jurisdiction sets the limits.
Where This Sits Next to the Other Acoustics Tools
The decibel calculator handles the arithmetic of the decibel scale itself — turning ratios into decibels with the right 10-log or 20-log rule and adding several levels together. It has no concept of distance. This page is about propagation: how one level becomes another over a distance. The sound level converter moves between decibel levels and the linear pressures and intensities they represent, which is the unit side rather than the distance side.
For the wave itself rather than its level, the speed of sound calculator gives the propagation speed in air and other media, the wavelength calculator converts between frequency and wavelength, and the Doppler effect calculator covers the frequency shift from a moving source. A passing vehicle changes both level and pitch, and those are separate effects handled by separate tools.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Treating a road or railway as a point source — a line source loses 3 dB per doubling, not 6, and the two predictions diverge by 3 dB for every doubling of distance.
- Confusing sound power with sound pressure — a sound power level has no distance attached and is typically 8 to 11 dB above the pressure level at one metre. Feeding one in as the other is a large and silent error.
- Applying free-field spreading indoors — past the critical distance in a room the reverberant field dominates and the level barely falls with distance at all.
- Guessing an absorption coefficient — air absorption varies by more than a factor of ten across frequency and humidity, so a guessed value can be worse than using zero.
- Ignoring the ground and the wind — ground effect and refraction routinely move real measurements several decibels from a free-field prediction, in either direction.
Related Free Tools From Arb Digital
Handle the decibel arithmetic with the decibel calculator and unit conversions with the sound level converter. For exposure over a working day, use the noise exposure calculator. On the wave side, the speed of sound calculator, the wavelength calculator and the frequency and period calculator cover propagation speed and wave geometry, and the Doppler effect calculator handles moving sources. Everything Arb Digital publishes is listed on the free online tools hub.
Frequently Asked Questions
Six decibels for a point source in free field, and three decibels for a line source. Those figures come straight from the geometry: a sphere's area grows as the square of the radius while a cylinder's grows only in proportion to it. No other value is correct in free field.
Sound power is a property of the source alone, measured in watts and expressed in decibels relative to one picowatt. Sound pressure is what a microphone measures at a particular place, and it depends on distance and surroundings. A machine has one sound power level and an infinite number of sound pressure levels.
Because it affects both distances by the same amount. Directivity describes the fraction of a sphere the source radiates into, and that fraction is the same at one metre and at a hundred. When you start from a measured level, the directivity is already inside that measurement.
Below a few hundred metres it is usually well under a decibel and lost in the uncertainty of everything else. Beyond a kilometre, and particularly at high frequencies or in dry air, it becomes comparable with or larger than the spreading loss and must be included with a coefficient taken from the standard.
Only very close to the source. Beyond the critical distance in a room the reverberant field takes over and the level becomes roughly uniform, so free-field spreading no longer applies. Room acoustics needs a reverberation-based calculation instead.
Usually because of temperature inversion rather than any change in the source. At night the air near the ground is often cooler than the air above it, which bends sound rays back down towards the surface instead of letting them escape upwards. Lower background noise makes the effect more noticeable still.
No. It predicts a free-field level. Whether a level is acceptable is set by the applicable regulation, planning condition or occupational standard in your jurisdiction, each of which specifies its own measurement position, averaging period and weighting.
This tool is provided for educational and preliminary estimating use. It models free-field spreading only, with no ground effect, barriers, reflections, wind or temperature gradients, and it is not a substitute for a measured noise survey or an environmental noise assessment carried out to the applicable standard.
