Sound Pressure Level Distance Calculator — Inverse Square Law & Speaker SPL
Sound source and distance
Use the manufacturer's 1 W/1 m rating.
Your values stay in this browser. Nothing is uploaded or stored.
Estimated level
What this means
Moving from 1.00 m to 4.00 m reduces the ideal free-field level by 12.04 dB.
The selected 85.00 dB target occurs at about 5.62 m in the same ideal model.
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How to use the SPL distance calculator
- Choose a starting point. Select a known sound-level measurement, or use a loudspeaker's sensitivity and the electrical power delivered to one speaker.
- Choose metres or feet. Changing units converts the distances already entered without changing their physical length.
- Enter the listening distance. Measure from the acoustic centre of the source to the listener or microphone.
- Set a target if useful. The calculator finds the ideal distance at which that target level would occur.
- Check the result in the real space. Use a calibrated sound-level meter when level or hearing exposure matters.
Speaker mode models one speaker. Do not enter total system power for multiple boxes unless the manufacturer provides a matching system sensitivity specification.
Inverse square law and speaker SPL formulas
For a point source radiating into a reflection-free free field, the level at a new distance is:
L₂ = L₁ + 20 × log₁₀(r₁ ÷ r₂)
- L₁ is the known SPL at reference distance r₁.
- L₂ is the estimated SPL at new distance r₂.
- Doubling distance gives
20 × log₁₀(1 ÷ 2) = −6.02 dB. - Halving distance gives a
+6.02 dBchange.
Speaker mode first estimates the 1 metre level from the manufacturer's 1 W/1 m sensitivity:
L₁m = sensitivity + 10 × log₁₀(power in watts)
Ldistance = L₁m − 20 × log₁₀(distance in metres)
Each doubling of electrical power adds an ideal 3.01 dB. Maintaining the same ideal SPL at twice the distance therefore requires four times the power. Real loudspeakers can produce less because of power compression, voltage limiting, excursion limits, frequency response, and amplifier clipping.
Formula references: OSHA Technical Manual — sound fields and SPL at distance, JBL Professional — inverse square law and amplifier power calculators, and UC San Diego — sound pressure level definition.
Quick distance-loss reference
| Distance multiple | Ideal level change | Pressure ratio | Power needed to restore level |
|---|---|---|---|
| 0.5× | +6.02 dB | 2.000× | 0.25× |
| 2× | −6.02 dB | 0.500× | 4× |
| 4× | −12.04 dB | 0.250× | 16× |
| 10× | −20.00 dB | 0.100× | 100× |
When the inverse square law works—and when it does not
The inverse square law describes geometric spreading from a compact point source in a free field. Outdoors, away from reflecting surfaces, it can be a useful first estimate. It also provides a quick sanity check for loudspeaker throw, microphone placement, equipment noise, and measurement planning.
Indoors, reflected energy builds a reverberant field. Beyond a room's critical distance, moving farther from the speaker may reduce the direct sound while the reflected field changes much less. Floors, walls, ceilings, audience areas, and barriers can all change the result. Line arrays and distributed sources also follow different distance behaviour over parts of their coverage.
Very close to a large source, the source cannot be treated as a point and small position changes may produce irregular readings. At low frequencies, room modes can create peaks and nulls that are much larger than the smooth distance loss predicted here. Use the Room Mode Calculator to identify ideal axial resonance frequencies, then measure the real response.
Acoustic model and hearing-safety limits
This is an engineering estimate, not a loudspeaker guarantee or hearing-safety assessment. It assumes one point source, free-field propagation, far-field behaviour, and no air absorption, barriers, reflections, directivity change, power compression, clipping, or frequency-dependent limits.
dB SPL and dBA are not interchangeable. Hearing risk depends on measured A-weighted level, exposure duration, repetition, impulse content, spectrum, and personal factors. NIOSH identifies 85 dBA averaged over an eight-hour workday as its occupational recommended exposure limit; louder levels require shorter exposure under its criteria. See NIOSH guidance on noise-induced hearing loss. Use a calibrated meter and qualified guidance for compliance, system commissioning, or exposure decisions.
Sound pressure level distance calculator FAQ
What is the inverse square law for sound?
For an ideal point source in a free field, intensity is inversely proportional to distance squared. Because sound-pressure level is logarithmic, the practical distance equation uses 20 × log₁₀(r₁ ÷ r₂).
How much does SPL fall when distance doubles?
About 6.02 dB in the ideal model. Doubling from 1 m to 2 m produces the same change as doubling from 10 m to 20 m.
Why does speaker power use 10 log while distance uses 20 log?
Electrical power is a power ratio, so its decibel change uses 10 × log₁₀(P₂ ÷ P₁). Sound pressure is an amplitude quantity, so its ratio uses 20 log. Pressure itself falls in proportion to 1/distance for an ideal spherical wave.
Can I calculate two or more speakers?
Not reliably from speaker count alone. The combined level depends on spacing, phase, signal correlation, directivity, listener position, and frequency. Speaker mode intentionally estimates one loudspeaker.
Why does my sound-level meter show a different result?
The meter includes the real environment: reflections, room modes, background noise, speaker directivity, frequency response, and near-field behaviour. The calculator includes none of those effects.
Does the target distance mark a safe listening position?
No. It is only the distance where the ideal model reaches the entered target SPL. It does not calculate exposure dose or confirm safety.
Does this page upload my data?
No. All calculations and report generation run locally in your browser.