Decibel Distance Calculator
A speaker that measures 90 dB where you are standing will not measure 90 dB at the back of the field, and the difference is not a guess. Sound from a point source spreads over the surface of an expanding sphere, so the level at any new distance follows one short formula.
Enter the level you measured, the distance you measured it at, and the distance you care about. The calculator returns the estimated sound pressure level there, the size of the drop, and how many doublings of distance that move represents.
Free-field estimate for a point source: no reflections, barriers, ground absorption or air absorption. Indoors and over long outdoor distances, real levels differ.
Quick Answer
Key takeaways
- Doubling the distance from a point source costs about 6.02 dB; ten times the distance costs exactly 20 dB.
- Only the ratio of the distances matters, so feet and metres both work, provided both distances share one unit.
- The formula is a free-field estimate. Walls, ground and air absorption all bend the real number away from it, usually upward indoors.
- Distance is the cheapest noise control there is: the worked example sheds nearly 14 dB by moving from 2 m to 10 m, with no barrier and no enclosure.
- Quick Answer
- How to use the decibel distance calculator
- The inverse square law, and why the factor is 20 not 10
- Worked example: 90 dB at 2 metres, heard at 10 metres
- Point source or line source: the 6 dB and 3 dB rules side by side
- Finding the distance instead: the same formula backwards
- What competing calculators miss
- Frequently Asked Questions
- Add This Calculator to Your Website
- References
How to use the decibel distance calculator
You need one honest measurement to start: a sound level and the distance from the source at which you took it. A phone app reading is fine for planning work, as long as you note the distance properly, because the whole calculation hangs off that pair. Enter the level, then the initial distance, then the new distance, and press Calculate.
Read the change figure as carefully as the headline. A result of 76.02 dB with a change of -13.98 dB tells you what the move bought you, which is the number a noise plan actually needs. The verdict line then puts the new level in context, flagging the 85 dBA region where, according to NIOSH guidance, repeated 8-hour exposure becomes a hearing risk. If the answer is still too loud, work backwards: try doubling the new distance and watch another 6 dB come off, which is the fastest way to find the separation a layout needs.
The inverse square law, and why the factor is 20 not 10
A point source radiates sound power in every direction, and that power spreads over a sphere whose area grows with the square of the radius. Double the distance and the same power covers four times the area, so the intensity at any point falls to a quarter. Sound pressure, the quantity a meter reads, falls more gently, in simple proportion to 1 / distance.
The factor of 20 confuses people because decibels of intensity use 10 × log. Both are correct, and they agree: intensity ratios take 10 × log10, pressure ratios take 20 × log10, and since intensity is proportional to pressure squared, 10 × log of the intensity ratio and 20 × log of the pressure ratio are the same number. The Engineering ToolBox statement of the inverse square law for sound propagation uses the identical 20 log form, as does every acoustics text that starts from a measured level at a measured distance. One boundary matters: this describes a point source. A long road or a production line behaves closer to a line source, losing about 3 dB per doubling instead, and no setting in this tool pretends otherwise.
Worked example: 90 dB at 2 metres, heard at 10 metres
The calculator is pre-filled with this case, and every figure below is what it returns, to two decimal places, exactly as the tool formats it.
| Step | Working | Result |
|---|---|---|
| Distance ratio | D1 / D2 = 2 / 10 | 0.2 |
| Level change | 20 × log10(0.2) = 20 × (-0.69897) | -13.98 dB |
| New level | 90 + (-13.98) | 76.02 dB |
| Doublings in the move | log2(10 / 2) | 2.32 |
Sanity-check it the rough way: 2.32 doublings at about 6 dB each is about 14 dB, and the exact answer is 13.98 dB. The small gap is the difference between the 6 dB rule of thumb and the exact 6.02 dB per doubling, and it grows with distance, which is why the calculator exists instead of the rule.
Each row is the same 90 dB source heard one doubling further away, computed with this tool. Notice what the bars cannot show: the decibel scale is logarithmic, so the step from 90 to 84 dB removes three quarters of the sound intensity even though the bar barely shortens. The bar chart shows the meter reading; the energy story underneath it is far steeper.
Point source or line source: the 6 dB and 3 dB rules side by side
The single most common misuse of this formula is applying it to a source that is not a point. The comparison below is the honest version of the choice.
Point source: this calculator
- Examples: one speaker, one machine, one dog, one generator.
- Intensity falls as 1 / distance squared.
- Level drops about 6.02 dB per doubling, 20 dB per tenfold distance.
- Use this tool when the source is small compared with the distances involved.
Line source: different rule
- Examples: a busy road, a railway, a long conveyor or production line.
- Intensity falls as 1 / distance, because the wavefront is a cylinder, not a sphere.
- Level drops about 3.01 dB per doubling.
- This tool will overstate the drop for line sources, so treat roadside estimates from it as optimistic.
Real sources sit between the ideals at some distances and match one of them at others: a PA stack is a point source across a field and something messier in the first metre. If your measured drop per doubling comes out near 3 dB rather than 6, believe the measurement and model the source as a line.
Finding the distance instead: the same formula backwards
Half the real questions run the other way: the limit is fixed, a wedding venue boundary, a property line, a workstation, and the unknown is how far away the source has to sit. Rearranged, D2 = D1 × 10((L1 – L2) / 20). A 13.98 dB reduction needs 100.699 ≈ 5 times the distance, which is exactly the worked example read in reverse: 2 m becomes 10 m. The 10-to-a-power step is where people slip, and working it through an exponential form calculator once makes the pattern stick. Then confirm the candidate distance in this calculator, because the forward check catches slipped exponents that the rearranged formula hides.
Context for picking a target: OSHA’s enforceable permissible exposure limit is 90 dBA over 8 hours, and its action level, where a hearing conservation programme starts, is 85 dBA. The result at a worker’s position, not at the machine, is the number those limits judge, which is precisely the number this tool estimates.
What competing calculators miss
Six distance-attenuation tools were reviewed against the worked example. All of them use the same core formula; they part company on the extras and on honesty about the model.
Miss 1: silent extra physics. One reviewed calculator folds an atmospheric absorption term into its headline result and reports 69.96 dB for a case the pure inverse square law puts at 70.00 dB, without making clear that two different effects are being quoted as one number. Air absorption is real, but it depends on frequency, temperature and humidity; a single blended figure hides all three. This page models geometric spreading only and says so.
Miss 2: wrong-formula examples. One audio distance page gives the at-distance formula as Ld = Ls – 20 log10(d), which quietly assumes the reference distance is 1 unit and returns nonsense for a measurement taken anywhere else, then computes a factory example at 2 km that does not follow from its own formula. Starting from a measured level at a measured distance, as this tool does, is the version that survives contact with real measurements.
Miss 3: no way back. Most tools answer only the forward question. The distance-for-a-target-level rearrangement above, with the 5× check against the worked example, covers the layout and compliance questions people actually bring to this search.
Miss 4: no source-type warning. Tools that never mention line sources invite a 6 dB-per-doubling estimate for highway noise, which overstates the benefit of moving away by a factor of two in decibel terms. The point-versus-line comparison is on this page because the error is common and expensive.
Frequently Asked Questions
L2 = L1 + 20 × log10(D1 / D2). Take the ratio of the two distances, take its base-10 logarithm, multiply by 20, and add it to the known level. Moving further away makes the ratio smaller than 1, its logarithm negative, and the level drops.
About 6.02 dB for a point source in a free field. Doubling the distance quarters the intensity, and 20 × log10(1/2) = -6.02. Ten times the distance costs exactly 20 dB, which is the fastest mental check: 90 dB at 1 m is 70 dB at 10 m.
The level rises by the same rule. Halving the distance adds about 6.02 dB, and moving from 10 m to 1 m adds the full 20 dB. This is why a measurement taken a step too close can read several decibels high without anything about the source changing.
Yes, as long as both distances use the same unit. The formula only ever sees the ratio D1 / D2, so feet, metres or yards all give the same decibel change. Mixing units, metres for one distance and feet for the other, is the one input error that silently wrecks the result.
The level does not change. The ratio is 1, log10(1) is 0, and the correction term vanishes. It is a useful sanity check: any distance calculator that changes the level at equal distances has a bug.
Only as a rough guide. The formula assumes a free field: open space, no walls, floor or ceiling sending reflections back. Indoors, reflected energy adds to the direct sound, levels fall off more slowly than 6 dB per doubling once you are away from the source, and a room measurement will usually read higher than this prediction.
Rearrange the formula: D2 = D1 × 10((L1 – L2) / 20). To drop from 90 dB to 76.02 dB you need 10(13.98 / 20) ≈ 5 times the starting distance. In practice, enter a candidate distance in this calculator and adjust until the result matches your target.
A sound pressure level, the quantity a sound level meter reads at a position. Sound power level is a property of the source itself and does not change with distance. The factor is 20, not 10, because pressure falls as 1 / distance while intensity, its square, falls as 1 / distance squared, and the two statements are the same physics.
Add This Calculator to Your Website
References
- Engineering ToolBox, “Sound Propagation: the Inverse Square Law,” the 20 log distance relation and the 6 dB per doubling rule used by this calculator, with a worked rifle-shot example. Engineering ToolBox: Inverse Square Law, sound propagation. Accessed October 2026.
- Occupational Safety and Health Administration, standard 29 CFR 1910.95, “Occupational Noise Exposure,” Table G-16 permissible noise exposures: 90 dBA for 8 hours, action level 85 dBA. OSHA: 1910.95 Occupational Noise Exposure. Accessed October 2026.
- National Institute for Occupational Safety and Health (CDC), “Understand Noise Exposure,” the recommended exposure limit of 85 dBA over an 8-hour shift behind the verdict line in this calculator. NIOSH: Understand Noise Exposure. Accessed October 2026.
- National Institute for Occupational Safety and Health (CDC), “About Occupational Hearing Loss,” A-weighted decibel definitions and when noise counts as hazardous. NIOSH: About Occupational Hearing Loss. Accessed October 2026.
- National Institute of Standards and Technology and the BIPM SI Brochure tradition for the decibel as a logarithmic unit, 10 log for power ratios and 20 log for field (pressure) ratios. NIST: SI Units. Accessed October 2026.
- Everest, F. A. and Pohlmann, K. C., “Master Handbook of Acoustics,” McGraw-Hill, chapters on sound propagation outdoors and the inverse square law in free fields. McGraw Hill: Master Handbook of Acoustics. Accessed October 2026.