Inverse Square Law / SPL Calculator

Free inverse square law and SPL calculator for live sound engineers, AV technicians, and system designers who need to predict sound pressure levels at various distances from loudspeakers. Enter the SPL at a reference distance (typically the manufacturer's 1-meter sensitivity rating), and the calculator returns the expected SPL at any target distance using the inverse square law (6 dB loss per doubling of distance in free field). It also handles multiple source addition (coherent and incoherent summing) and coverage angle calculations for aiming loudspeakers at audience areas.

Understanding sound propagation is fundamental to every live event audio system design. A loudspeaker rated at 130 dB SPL at 1 meter delivers only 110 dB at 10 meters (a 20 dB loss), and only 104 dB at 20 meters. This inverse square relationship means that the farthest listener in a venue hears significantly less level than the closest listener unless the system is designed to compensate. Line arrays reduce the rate of loss from 6 dB per doubling to approximately 3 dB per doubling (cylindrical spreading), which is why they dominate large-venue and outdoor event sound reinforcement.

The calculator also performs SPL addition for multiple sources: two identical loudspeakers produce 3 dB more than one (incoherent addition), while two coherent sources (same signal, same phase) produce up to 6 dB more. These calculations are essential for determining delay speaker levels, subwoofer array output, and coverage overlap zones.

Pro Tip: When using the inverse square law to predict outdoor concert levels, remember that real-world conditions cause additional losses beyond the free-field prediction: wind, temperature gradients, humidity (especially above 4 kHz), ground reflections, and audience absorption all affect the actual SPL. Budget an extra 3-6 dB of headroom above what the inverse square law predicts for the farthest listener position.

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How It Works

Enter Source SPL and Reference Distance

Input the loudspeaker sensitivity or maximum SPL at the reference distance (typically 1 meter). This value is found in the loudspeaker manufacturer's specification sheet. For passive speakers, use the sensitivity plus the amplifier headroom.
Enter Target Distance

Input the distance from the loudspeaker to the listener position in feet or meters. For front-of-house mix position, this is typically 60-100 feet in medium venues. For the farthest seat, it may be 200+ feet in large outdoor events.
Configure Multiple Sources (Optional)

If using multiple loudspeakers, enter the number of sources and select coherent (same signal, same phase) or incoherent (uncorrelated signals) summing. Coherent sources add 6 dB per doubling, incoherent add 3 dB per doubling.
Review SPL at Distance

Check the predicted SPL at the target distance, the total loss from the reference distance, and the SPL from combined sources if applicable. Compare against target SPL for the venue (typically 95-105 dBA for live music, 85-90 dBA for corporate speech).

Built For

Live sound engineers predicting front-of-house and last-row SPL levels during system design for concerts and festivals
AV technicians calculating delay speaker levels and timing for conference rooms and houses of worship
System designers determining how many loudspeakers are needed to achieve a target SPL across a venue
Noise consultants predicting sound levels at property boundaries for event permit applications

Features & Capabilities

Inverse Square Law Calculator

Calculates SPL at any distance using the standard inverse square law: SPL2 = SPL1 - 20*log10(D2/D1). Shows the loss in dB and the resulting SPL at the target distance. Works in both feet and meters.

Multiple Source SPL Addition

Adds SPL from multiple sources using logarithmic addition: incoherent (random phase) sources add as 10*log10(N) dB for N identical sources, coherent (same phase) sources add as 20*log10(N). Shows the combined SPL and the gain over a single source.

Point Source vs Line Array

Compares SPL loss over distance for point sources (6 dB per doubling) versus line arrays (approximately 3 dB per doubling in the near field). Shows the practical range where line array behavior transitions to point source behavior.

Target SPL Reference Table

Includes reference SPL targets for common applications: rock/pop concert (100-110 dBA), corporate speech (85-90 dBA), house of worship (90-95 dBA), outdoor festival (95-105 dBA), and cinema (85 dBC peak for dialogue, 105 dBC for effects).

Frequently Asked Questions

How much does sound level drop with distance?

For a point source in free field (outdoors, no reflections), SPL drops 6 dB every time the distance doubles. So if a speaker produces 100 dB at 10 feet, it produces 94 dB at 20 feet, 88 dB at 40 feet, and 82 dB at 80 feet. Indoors, reflections from walls, ceiling, and floor reduce the apparent loss — in a reverberant room, SPL may only drop 3-4 dB per doubling beyond the critical distance.

What is the difference between coherent and incoherent SPL addition?

Coherent addition occurs when sources produce the same signal at the same phase — the pressure waves add constructively, giving up to 6 dB increase for two sources. This happens with two loudspeakers playing the same mono signal at equal distances from the listener. Incoherent addition occurs when sources produce uncorrelated signals (different content, different arrival times, or random phase) — only the power adds, giving 3 dB increase for two sources. Real-world scenarios are usually somewhere between these extremes.

What SPL level is needed for a live music event?

Typical target levels for live music at the front-of-house mix position are 95-105 dBA for amplified rock and pop, with peaks to 110-115 dBA. Corporate speech reinforcement targets 85-90 dBA. House of worship typically targets 90-95 dBA. Local noise ordinances may limit the SPL at the property boundary to 70-85 dBA depending on the jurisdiction, time of day, and zoning. Always check permit requirements before specifying system output.

How does humidity affect sound propagation?

Air absorption increases with frequency and varies with humidity and temperature. At 50% relative humidity and 68 F, absorption at 1 kHz is negligible (about 0.5 dB per 100 meters), but at 8 kHz it reaches 4-5 dB per 100 meters, and at 16 kHz it can exceed 10 dB per 100 meters. For outdoor events with throw distances over 100 feet, high-frequency loss from air absorption is significant and must be compensated with EQ or speaker selection. Very dry air (below 20% RH) has higher absorption than moderate humidity.

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