How this instrument works
Sound leaving a small source spreads across an expanding sphere. Power crossing that sphere stays fixed, so intensity dilutes as surface area grows — 4πd² at distance d. Double d and every square metre collects one quarter as much — 6.02 dB down. Pressure, which a microphone actually senses, falls as 1⁄d rather than 1⁄d², and 20·log₁₀ of a pressure ratio matches 10·log₁₀ of an intensity ratio exactly. Both routes land on identical numbers.
Kepler stated this geometry for light in 1604, in Ad Vitellionem Paralipomena, reasoning purely from how a sphere's area grows; Bullialdus applied identical logic to gravity in 1645. Acousticians inherited it unchanged, since spreading cares nothing about what happens to be spreading. Loudspeaker datasheets still encode that inheritance — sensitivity is quoted at one metre, and every distance figure you meet afterwards is a correction applied outward from that metre.
Three assumptions hold this formula up, and real sites break all three. A source only looks like a point beyond roughly twice its largest dimension, so a 3-metre line array measured at 2 metres obeys nothing so tidy. A genuinely long source — motorway traffic, a pipeline, a queue of idling trucks — radiates cylindrically and sheds nearer 3 dB per doubling. Indoors, reflected energy eventually outweighs direct sound, and past critical distance walking further changes almost nothing. Outdoors across long spans, air absorption stacks on top of spreading: ISO 9613-2 tabulates roughly 3.7 dB per kilometre at 1 kHz and 33 dB per kilometre at 4 kHz for 10 °C and 70% humidity, which is why distant thunder arrives as a rumble with its edges filed off.
- Enter Reference distance — wherever your known level was measured. Speaker and machinery specs almost always cite 1 m.
- Enter New distance — wherever you now want that level. Units switch between cm, m and km; both fields convert to metres before dividing.
- Read Level change (dB). Positive means loss, so subtract it from your known level to get the figure at your new spot.
- Moving closer instead? Put the smaller figure in New distance and the result turns negative — level gained, not lost.
Worked example — one metre out to two
A studio monitor's datasheet quotes 88 dB SPL for one watt at 1 metre, and your chair sits 2 metres back. Enter Reference distance 1 m and New distance 2 m. Level change (dB) returns 20 × log₁₀(2 ⁄ 1) = 20 × 0.301029995664 = 6.02059991328 dB, displayed as 6.020600 at six-figure precision. That monitor reaches your ears at roughly 82 dB.
Six decibels, not three — and that gap trips people constantly. Halving intensity costs 3.01 dB, but stepping from 1 m to 2 m quadruples sphere area, so each square metre receives one quarter of its former share, and that quarter reads 6.02 dB down. Sound engineers carry this as reflex: another doubling, another 6 dB gone. Ten metres out from that same monitor, loss reaches exactly 20 dB, leaving 68 dB — quiet enough to hold a conversation over.
Questions
Why is Level change positive when sound gets quieter?
Because this field reports loss, and losses are counted positive. Going from 1 m to 2 m returns 6.02, meaning 6.02 dB quieter. Swap the entries — 2 m back in to 1 m — and it returns −6.02, meaning louder. Subtract whatever appears here from your known level and sign handles direction for you.
Why 20·log rather than 10·log for distances?
Because distance acts on pressure, and pressure is an amplitude quantity. Sound pressure weakens as 1⁄d while intensity weakens as 1⁄d², and 10·log₁₀(d₂²⁄d₁²) is algebraically identical to 20·log₁₀(d₂⁄d₁). Whichever your meter reports, decibels come out the same. Neither factor is a matter of taste here — geometry fixes both.
Does this hold for radio, light or radiation dose?
Yes, for anything radiating from a compact source into open space. Free-space path loss for antennas carries exactly this 20·log₁₀ term, so doubling a link's range costs 6 dB of received power. Radiation protection runs it in reverse: step twice as far from a sealed source and dose rate quarters. Illuminance from a lamp behaves identically. What differs between these fields is whatever intervenes along the path — atmosphere, cable, shielding — never spreading itself.
How far outdoors can I trust the answer?
Out to a few hundred metres it usually lands within a decibel or two. Past that, expect this instrument to overpredict loudness at long range, because air absorption removes high frequencies that pure geometry keeps. Ground reflection, wind gradients and temperature inversions push the other way and can carry sound much further than spreading alone suggests — downwind on a still night especially, where refraction bends energy back toward ground level. ISO 9613-2 exists to add those terms for environmental noise assessment.
Why does backing away indoors barely help?
Because rooms hand energy back to you. Direct sound obeys 6 dB per doubling, but reflected sound fills a space at roughly constant level, and beyond critical distance — where direct and reverberant fields match — total level flattens out. In a small hard-surfaced room that boundary can sit under 2 metres. Measure a machine indoors and you are largely measuring its room, which is why acoustic labs use anechoic chambers or take readings very close in.
What actually counts as a point source?
Anything small compared with your measuring distance; one working rule puts that boundary near twice its largest dimension. A 60 cm subwoofer measured at 5 metres qualifies. A 3-metre line array at 2 metres does not, and neither does a motorway, which behaves as a line source and loses closer to 3 dB per doubling. Inside that boundary lies the near field, where pressure and particle velocity fall out of step and no single exponent describes decay.