Calculate how much quieter a point sound source becomes as you move away from it. Adjust the sound power level, distance, directivity factor and background noise to see inverse-square distance attenuation (about 6 dB per doubling), the combined level and the signal-to-noise margin update in real time.
Parameters
Sound power level L_W
dB
Total acoustic energy radiated by the source itself
Distance r
m
Distance from the source to the listening point
Background noise level
dB
Ambient background noise with the source switched off
Directivity factor Q
Reflecting-surface effect. Larger when radiating into a smaller space
Results
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Sound pressure level here (dB)
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Level at twice the distance (dB)
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Level at 1 m reference (dB)
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Combined level with noise (dB)
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S/N over background (dB)
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Noise level rating
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Point source, spherical waves, listener — distance attenuation animation
Spherical wavefronts spread out from the point source and dim with distance. A sound-level meter at the listener reads the sound pressure level, and the background-noise floor is shown.
Sound pressure level vs distance (logarithmic distance axis)
Sound pressure level vs directivity factor Q
Theory & Key Formulas
$$L_p=L_W+10\log_{10}\!\frac{Q}{4\pi r^{2}}$$
Sound pressure level L_p of a point source. L_W: sound power level, Q: directivity factor, r: distance. The level drops by about 6 dB for every doubling of distance, and Q accounts for reflecting surfaces such as floors and walls.
Combined level L_sum of the source and the background noise. Because sound energy is added logarithmically, two equal sources together are only +3 dB.
What is the Sound Pressure Level vs Distance Simulator?
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Loudness is given in "so-many dB", right? But this tool shows two things — "sound power level" and "sound pressure level". They are both dB, so what's the difference?
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Good question — confusing these two is the most common mistake in acoustics. Roughly speaking, the sound power level L_W is the "strength of the source itself". Think of a light bulb's wattage: it is a fixed property describing how much acoustic energy the source pours out per second, and it does not change with distance. The sound pressure level L_p, on the other hand, is "the loudness your ear or a microphone actually feels at one place", and that changes a lot with distance. So if someone says "an 85 dB machine", it means something completely different depending on whether that is the power level or the pressure level at some number of metres.
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I see. So if the source is the same, why does the pressure drop with distance? What's the mechanism?
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That is the inverse-square law. A point source radiates a fixed amount of energy onto a spherical wave that expands like a balloon. When the distance doubles, the surface area of that sphere grows by 2 squared, so it is 4 times larger. The same energy spreads thinly over 4 times the area, so the energy per square metre — the intensity — drops to one quarter. In decibels that is 10·log10(1/4) ≈ −6 dB. So the sound pressure level falls by about 6 dB every time the distance doubles. Move the "distance" slider on the left and you will see that constant slope in the chart below.
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6 dB per doubling is a beautifully clean rule. But changing the "directivity factor Q" shifts the level even at the same distance. What is that?
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Q is "how much the surroundings concentrate the source's sound into a narrower direction". In open air the sound spreads in all directions (a full sphere), so Q=1. But place the source on a hard floor and the sound that would have gone down is reflected upward, packing the same power into half the space (a hemisphere). The level rises about 3 dB and Q=2. Against a wall-floor edge it is a quarter-space, Q=4, about 6 dB up. In a three-surface room corner it is one eighth, Q=8, about 9 dB up. The same speaker sounding different on a desk versus in a room corner is exactly this effect.
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I'm also curious about the "combined level with background noise" and "S/N". Isn't adding two sounds just plain addition?
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That is the decibel trap. Because dB is logarithmic, 60 dB + 60 dB is not 120 dB. You add the energy first, then convert back to a logarithm, so two equal sounds together give only +3 dB — 63 dB. So the "combined level" of the source pressure and the background noise is, when one is 10 dB or more above the other, almost equal to the louder one. Conversely, if the source is quieter than the background noise, that sound is buried and inaudible. That difference is the S/N (signal-to-noise ratio), and for alarm design and noise measurement you always check whether the S/N is sufficient.
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Does the inverse-square law hold everywhere?
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Be careful there. The inverse-square law holds cleanly only for a "point source" seen in an outdoor "free field". Very close to a large source, indoors where reflections build up a reverberant field, or along a line source such as a busy motorway, the attenuation with distance is slower. A straight line of road noise, for example, drops only about 3 dB per doubling of distance. This tool uses the point-source model, so keep that assumption in mind when you use it.
Frequently Asked Questions
The sound power level L_W is the total acoustic energy a source radiates per second — a fixed property of the source itself, like a light bulb's wattage. It does not change with distance. The sound pressure level L_p is what a listener or microphone actually receives at a particular point, and it depends strongly on distance. The link between them is the inverse-square law: for a point source, L_p = L_W + 10log10(Q/(4πr²)). Confusing the two is one of the most common mistakes in acoustics.
A point source radiates a fixed acoustic power over an ever-expanding spherical wavefront. The area of that sphere grows with the square of the distance, so the energy passing through each square metre — the intensity — falls with the square of the distance. On the logarithmic decibel scale this becomes the simple form 10·log10(1/4) ≈ −6.0 dB, so the sound pressure level drops by about 6 dB every time the distance doubles. This is inverse-square distance attenuation.
The directivity factor Q describes how much the surroundings concentrate the radiated sound into a smaller space. In free space (radiating in all directions) Q=1; on a hard floor (half-space) Q=2, about 3 dB louder than free space; at a wall-floor edge Q=4, about 6 dB louder; in a three-surface corner Q=8, about 9 dB louder. The same source produces a different level at the listener depending on where it is placed, so choose Q to match the installation.
However quiet a source is, it cannot be heard if it is below the background noise. When you add two sound levels you must add their energy logarithmically, so two equal sources together are only 3 dB louder than one. If the S/N (the difference between the source and the background noise) is 10 dB or more the source dominates; near 0 dB it is almost buried in the background. For noise measurement and alarm design, both the combined level and the S/N must be checked.
Real-World Applications
Factory and plant noise control: The sound power level of a machine is measured from manufacturer data or tests such as ISO 3744. Engineers then predict the sound pressure level at the site boundary or the operator position using the inverse-square law. If a boundary limit (say 55 dB during the day) is likely to be exceeded, options such as moving the source farther away, adding a noise barrier or switching to a low-noise model can be assessed quantitatively from the distance attenuation.
Environmental noise assessment: For roads, railways, wind farms and outdoor events, predicting the distance attenuation from the source to nearby homes is central to the planning. A point source (such as a substation transformer) drops 6 dB per doubling of distance, while a line source (a road) drops only about 3 dB, so the choice of source model strongly affects the result.
Alarm and signal-sound design: Fire alarms, station announcements and vehicle back-up alarms must provide a sufficient S/N over the background noise (typically 15 dB or more) even at the farthest listening point. Calculating the combined level and S/N from source power, distance and background noise — as this tool does — lets you size the required source output and speaker layout.
Audio and public-address design: When designing speakers for a hall or an outdoor venue, the difference in sound pressure level between the front and back rows (coverage) is estimated from the inverse-square law. A single speaker creates too large a near-far difference, so multiple units are distributed and the combined level at each listening point is evened out. The directivity-factor idea is also used to correct for wall-side or corner placement.
Common Misconceptions and Pitfalls
The biggest misconception is that "the inverse-square law applies to any sound as-is". The 6 dB drop per doubling holds only for an idealized point source in an outdoor free field. Indoors, reflections from walls, ceiling and floor pile up into a reverberant field, and beyond a certain distance (the reverberation radius) the level barely falls with distance. Line sources such as roads and railways drop only about 3 dB per doubling, and area sources fall even more slowly — the attenuation law itself changes. Identifying the source type and the sound field (free field or reverberant field) first is a prerequisite for prediction accuracy.
Next, treating the sound power level and the sound pressure level as the same thing. If a catalogue simply says "85 dB", the result of converting it to another location differs by more than 10 dB depending on whether that is the sound power level, the sound pressure level at 1 m, or the value at the machine surface. The power level L_W is a property of the source and is distance-independent, but the sound pressure level L_p is always a quantity that comes with a "where was it measured". Always check the definition and the measurement conditions, not just the number.
Finally, the assumption that "decibels can be added and subtracted like ordinary numbers". Decibels are logarithmic quantities, so 60 dB + 60 dB is not 120 dB but about 63 dB. Conversely, if two sources differ by 10 dB or more, the combined level is almost the same as the louder one and the quieter one can be ignored. When a source is quieter than the background noise, that sound is buried and not heard at all. When adding or subtracting levels, the rule is always to convert back to energy (10^(L/10)) first and then calculate.