SPL Distance Calculator (Inverse Square Law)
Sound level at any distance from a source — the −6 dB-per-doubling law, hearing-safety bands, and why outdoor PA needs so much power.
The inverse-square law is geometry, not absorption: the same energy spreads over a sphere whose area quadruples per doubling of radius — hence −6 dB. Indoors the law dies at the critical distance, where reflected energy equals direct and the level stops falling; line arrays cheat to −3 dB/doubling by design.
Formula
⚠️ Acoustic estimates from standard formulas — real rooms, drivers and ears vary. For hearing-safety decisions use a calibrated SPL meter and official occupational limits.
Sound level at any distance from a source — the −6 dB-per-doubling law, hearing-safety bands, and why outdoor PA needs so much power.
About SPL Distance Calculator (Inverse Square Law)
Sound spends itself on geometry: every doubling of distance from a point source spreads the same watts over four times the sphere, and the meter reads 6 dB less. This calculator runs the inverse-square law from any reference measurement to any listener distance, grades the result against hearing-safety thresholds, and explains the two places the law breaks — indoors past the critical distance, and under line arrays engineered to defeat it.
How to use SPL Distance Calculator (Inverse Square Law)
- 1Enter — sensible defaults are pre-filled so you see a worked result immediately.
- 2Read the live results: .
- 3Check the "With your numbers" line to see the formula L₂ = L₁ − 20·log₁₀(d₂/d₁) — point source, free field: −6 dB per doubling of distance substituted step by step.
- 4Adjust inputs (or flip the unit toggle) until the scenario matches yours, then copy or share the result.
Why use SPL Distance Calculator (Inverse Square Law)?
- ✓Instant, free and private — every calculation runs in your browser, nothing is uploaded
- ✓Built on the published formula L₂ = L₁ − 20·log₁₀(d₂/d₁) — point source, free field: −6 dB per doubling of distance with sources cited on the page
- ✓The inverse-square law is geometry, not absorption: the same energy spreads over a sphere whose area quadruples per doubling of radius — hence −6 dB. Indoors the law dies at the critical distance, where reflected energy equals direct and the level stops falling; line arrays cheat to −3 dB/doubling by design.
- ✓Switch units, tweak any input and watch every result update live
Frequently asked questions
Why exactly 6 dB per doubling of distance?+
Pure sphere arithmetic: intensity = power ÷ 4πr², so doubling r quarters the intensity, and 10·log₁₀(¼) = −6.02 dB. Nothing is absorbed or 'used up' — at PA frequencies, air absorption adds only ~0.1–1 dB per 100 m (rising sharply above 4 kHz, which is why distant concerts sound dull as well as quiet). The law assumes a free field (no reflections) and a source small relative to the distance — a loudspeaker qualifies beyond a few box-lengths.
Why doesn't the level keep dropping indoors?+
Because rooms recycle sound: beyond the CRITICAL DISTANCE, reflected energy off walls and ceiling exceeds the direct sound, and the level plateaus at the room's reverberant field no matter how far you walk. A live room may have a critical distance of barely 1 m — explaining why turning down a home stereo barely helps the neighbors, why intelligibility (not loudness) collapses at the back of untreated halls, and why acoustic treatment 'makes the room quieter' at the same playback level. Our RT60 tool measures the cause.
What SPL do real events need at the listener — and at the stage?+
Targets: speech reinforcement 70–75 dB at the listener, amplified music 95–105, festival front rows 105+. Run this tool backward and outdoor scale gets scary: delivering 100 dB at 64 m needs 136 dB at 1 m — beyond any single box, hence arrays, delay towers, and the line-array trick of stacking sources so the wavefront expands cylindrically (−3 dB/doubling) instead of spherically over the audience depth. Every doubling of required distance quadruples the amplifier wattage; that's the inverse-square law writing the rental invoice.
How do the safety numbers map to real exposure?+
NIOSH's energy-based ladder: 85 dB(A) is the 8-hour limit, and every +3 dB halves the safe time — 88 for 4 h, 94 for 1 h, 100 for 15 min, 110 for 90 seconds. (OSHA's legal limits are laxer — 90 dB/8 h with 5-dB steps — but NIOSH reflects the hearing science.) Concerts routinely run 100–105 at the mix position: earplugs aren't paranoia, they're arithmetic. Distance is the free hearing protector — this calculator shows that stepping from 2 m to 8 m off the stacks buys 12 dB, a 16× exposure reduction.
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