Distance Attenuation Calculator
How loud is it over there? Enter the sound pressure level measured at a reference distance and get the SPL at any target distance — using the inverse square law for point sources, or the 3 dB rule for line sources like traffic.
Free · 100% in-browser · no sign-up · no data leaves your deviceSound level drop over distance
Point source (speaker, machine): L2 = L1 − 20·log10(d2/d1)
Line source (highway traffic): L2 = L1 − 10·log10(d2/d1)
Results appear here after you press Calculate.
| Distance multiple | Distance | Point source SPL | Line source SPL |
|---|
How distance attenuation works
Sound leaving a small source spreads over the surface of an ever-expanding sphere. Since a sphere's surface area grows with the square of its radius (4πr²), the acoustic intensity — power per unit area — falls with the square of the distance. That is the inverse square law: double the distance, quarter the intensity. Converted to decibels, that quarter-intensity step is exactly 20·log10(2) ≈ 6.02 dB, the familiar "6 dB per doubling of distance" rule for sound pressure level.
A line source — a long stream of traffic, a production line, a long exhaust duct — spreads its energy over a cylinder instead of a sphere, so intensity falls only as 1/d. In decibels that is 10·log10, or about 3 dB per doubling. This calculator covers both models, and can even work backwards: give it a target SPL and it solves for the distance you need.
Distance vs. decibels: what each step costs you
Starting from a 100 dB source, here is the SPL at each distance multiple in an ideal free field. Bookmark this pattern: point sources shed 6 dB per doubling, line sources shed 3 dB.
| Distance multiple | Drop (point source) | SPL, 100 dB point source | Drop (line source) | SPL, 100 dB line source |
|---|---|---|---|---|
| 1× | 0 dB | 100.0 dB | 0 dB | 100.0 dB |
| 2× | −6.02 dB | 94.0 dB | −3.01 dB | 97.0 dB |
| 4× | −12.04 dB | 88.0 dB | −6.02 dB | 94.0 dB |
| 8× | −18.06 dB | 81.9 dB | −9.03 dB | 91.0 dB |
| 16× | −24.08 dB | 75.9 dB | −12.04 dB | 88.0 dB |
| 32× | −30.10 dB | 69.9 dB | −15.05 dB | 85.0 dB |
| 64× | −36.12 dB | 63.9 dB | −18.06 dB | 81.9 dB |
Typical source levels (at 1 m unless noted)
| Source | Typical SPL | What it drops to at 10 m (point source) |
|---|---|---|
| Threshold of hearing | 0 dB | −20 dB (inaudible) |
| Normal conversation | 60 dB | 40 dB (quiet library) |
| Vacuum cleaner | 70 dB | 50 dB |
| Diesel truck at 15 m (spec distance) | 85 dB | ≈ 88.5 dB at 10 m (closer → louder) |
| Lawnmower | 90 dB | 70 dB |
| Chainsaw | 110 dB | 90 dB |
| Rock concert speaker | 120 dB | 100 dB |
| Threshold of pain | 130 dB | 110 dB |
| Jet takeoff (at 30 m) | 140 dB | ≈ 149.5 dB at 10 m (closer → louder) |
Values are typical free-field estimates for steady sources; real measurements vary with environment and frequency content. Rows marked "closer → louder" show the formula also working in reverse when the target is nearer than the reference distance.
Practical rules of thumb
- 6 dB per doubling — a loudspeaker 2× farther away reads 6 dB lower; 10× farther reads 20 dB lower.
- 3 dB per doubling — road traffic behaves as a line source; it takes 10× the distance to lose 10 dB.
- 10 dB ≈ half as loud — perceived loudness halves roughly every 10 dB, so making something sound "half as loud" needs 3.16× the distance (point source).
- Outdoors beats the formula rarely — ground reflection, wind, and temperature gradients mean measured drop is often a little less than the ideal 6 dB; treat the result as a best-case estimate.
- Indoors, the rule breaks down — beyond a room's critical distance, reverberation holds the level nearly constant no matter how far you stand.
Distance attenuation FAQs
What is the distance attenuation formula?
For a point source in a free field: L2 = L1 − 20·log10(d2/d1), where L1 is the SPL at reference distance d1 and L2 is the SPL at target distance d2. Example: 94 dB at 1 m → 94 − 20·log10(2) ≈ 88 dB at 2 m. The calculator above applies this formula (and the 10·log10 line-source variant) automatically.
How many dB are lost each time the distance doubles?
About 6.02 dB for a point source — the "6 dB per doubling" rule from 20·log10(2). A line source such as highway traffic loses about 3.01 dB per doubling (10·log10(2)). So a speaker at 4 m instead of 2 m drops 6 dB, while a busy road drops only ~3 dB over the same step.
What is the inverse square law in acoustics?
Sound intensity from a point source falls with the square of the distance (I ∝ 1/d²) because the energy spreads over a sphere of area 4πr². Doubling the distance quarters the intensity, which in decibels is the 6 dB-per-doubling rule for sound pressure level.
Why does the formula use 20·log10 instead of 10·log10?
The decibel is defined for power-like quantities as 10·log10(P2/P1). Sound intensity is power-like, but SPL is defined from pressure, and intensity is proportional to pressure squared — substituting gives 10·log10(p2²/p1²) = 20·log10(p2/p1). Line sources spread cylindrically, so intensity falls as 1/d and the 10·log10 form applies there.
How do I calculate SPL at a distance? (worked example)
Take a 90 dB lawnmower measured at 1 m; at 8 m: L2 = 90 − 20·log10(8) = 90 − 18.06 ≈ 71.9 dB. Shortcut: 1→2→4→8 m is three doublings at 6 dB each, so 90 − 18 = 72 dB. Enter your own numbers in the calculator for an exact value.
What is the difference between a point source and a line source?
A point source radiates from one small spot — a loudspeaker, chainsaw, or gunshot — and attenuates at 20·log10 (6 dB per doubling). A line source radiates along a long line — highway traffic, a production line — and attenuates at 10·log10 (3 dB per doubling) because energy spreads over a cylinder, not a sphere. This calculator has a mode for each.
How far away do I need to be for a 10 dB drop?
For a point source, a 10 dB drop needs 10^(10/20) ≈ 3.16× the reference distance — a 94 dB speaker at 1 m reads ~84 dB at 3.16 m. For a line source it needs 10× the distance. Since ~10 dB is perceived as half the loudness, you must go surprisingly far to make something sound half as loud.
What is the reference for dB SPL?
SPL is referenced to 20 micropascals (20 µPa): SPL = 20·log10(p / 20 µPa), the average threshold of hearing at 1 kHz. That is why 0 dB SPL means "barely audible," not silence — and why every input and output here is dB SPL (re 20 µPa).
Can I use feet or other units instead of meters?
Yes. The formula only uses the ratio d2/d1, so any consistent length unit works — meters, feet, inches, kilometers — because the units cancel. The calculator's m/ft switch even lets you mix units between reference and target distances.
What if the target is closer than the reference distance?
The formula works both ways: moving closer raises the level. Halving the distance adds ~6.02 dB for a point source — 94 dB measured at 2 m becomes 100 dB at 1 m — and ~3.01 dB for a line source. This is how you estimate near-field levels from a loudspeaker datasheet rated at 1 m.
Why does real-world sound sometimes drop less than 6 dB per doubling?
The 6 dB rule assumes a point source in a free field. Outdoors, ground reflections add energy back, temperature gradients and wind refract sound up or down, long sources behave as line sources (~3 dB per doubling), and air absorption steals extra high frequencies. Measured values therefore often differ from the ideal calculation.
Does distance attenuation work indoors?
Only approximately, and only near the source. Indoors, reflections from walls, floor, and ceiling build a reverberant field that stays roughly constant with distance. Direct sound still follows the inverse square law, but beyond the room's critical distance the reverberant sound dominates and the level stops falling. This calculator is most accurate outdoors or in anechoic spaces.
At what distance does a 110 dB speaker drop to 70 dB?
A 40 dB drop for a point source needs a distance ratio of 10^(40/20) = 100×: a speaker rated 110 dB at 1 m falls to ~70 dB (conversation level) at 100 m in free field. Use the calculator's "Distance for target SPL" tab to solve this for any levels.
What is geometric spreading loss?
Geometric spreading (divergence) loss is the level drop caused purely by wavefronts spreading over a larger area — a sphere's 4πr² for point sources, a cylinder for line sources. It is frequency-independent and is exactly what this calculator computes; it excludes air absorption, ground effects, wind, and barriers.
Can this calculator find the distance for a target noise level?
Yes — switch to the "Distance for target SPL" tab. Enter the known SPL and its reference distance, then the target SPL (e.g. a 55 dB neighborhood limit). It solves d = d1 × 10^((L1 − Ltarget)/20) for point sources, e.g. how far a 100 dB generator must sit to read 55 dB at the property line.
What are the limits of this calculation?
Four limits: (1) far field only — the source must be much smaller than the distance and the wavelength, so very close distances to large speakers are unreliable; (2) free field — no walls, ground reflection, wind, or temperature gradients; (3) no air absorption, which matters for high frequencies over long distances; (4) steady broadband sources — tonal or impulsive sounds need extra corrections. For regulatory noise work, treat results as a first-order estimate.
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