Sound Pressure Level Distance Attenuation Calculator

Project how audio decays over distance using the inverse square law. Calculate SPL drop in real time for point sources or line array speaker systems, with psychoacoustic context on perceived loudness.

Source Calibration
Measured level at your known reference point
Distance at which the base SPL was measured
Speaker, subwoofer, or omnidirectional source. Decays 6 dB per doubling of distance.
Attenuation Decay Curve
Enter values to render the decay curve
Reference Point
Target Distance
Logarithmic distance scale - free field propagation model
Projected SPL Telemetry
Distance at which you want the projected SPL
Projected SPL at Target Distance
--
dB SPL
Base SPL -- dB
Total dB Drop --
Distance Ratio --
Decay Model --
Psychoacoustic Context Enter your distances above to see a perceived loudness note.
Key Acoustic Terms Explained
Sound Pressure Level (SPL)
A logarithmic measure of the effective sound pressure relative to a reference pressure of 20 microPascals, the approximate threshold of human hearing. Expressed in decibels (dB SPL).
Decibel (dB)
A dimensionless logarithmic unit expressing the ratio of one quantity to a reference value. For sound, a 3 dB increase represents a doubling of acoustic power, while a 10 dB increase sounds roughly twice as loud to the human ear.
Inverse Square Law
A physical principle stating that the intensity of a point source radiating into a free field decreases in proportion to the square of the distance from the source. In decibel terms, this produces a 6 dB reduction for every doubling of distance.
Point Source
An idealized acoustic source that radiates sound equally in all directions as an expanding sphere. Most practical speakers approximate a point source in their far field. The attenuation formula is L2 = L1 - 20 x log10(d2/d1).
Line Source
A source that radiates sound as an expanding cylinder rather than a sphere. Vertical line arrays of speakers and extended sources like busy highways behave as line sources, attenuating at 3 dB per doubling of distance. Formula: L2 = L1 - 10 x log10(d2/d1).
Free Field
An acoustic environment with no boundaries or reflections, where sound radiates from a source without interference. Anechoic chambers approximate free-field conditions. Outdoors far from surfaces is the closest real-world approximation.
Attenuation
The reduction in the amplitude or intensity of a signal as it travels through a medium or over distance. In acoustics, attenuation results from geometric spreading, atmospheric absorption, barriers, and scattering.
Psychoacoustics
The branch of science studying how humans perceive sound. A key finding is the 10 dB rule: a 10 dB measured increase corresponds to a perceived doubling of loudness. This relationship is nonlinear and frequency-dependent.

The Complete Guide to Sound Pressure Level Distance Attenuation

Whether you are designing a concert sound system, assessing occupational noise exposure, calibrating a home theater, or checking speaker coverage for a worship space, the ability to project how sound pressure level changes with distance is a fundamental audio engineering skill. This guide explains the physics, formulas, and practical limits of SPL distance attenuation calculations.

How to Use This SPL Attenuation Calculator

Start by entering your known Base SPL in decibels. This is the measured or specified sound pressure level at a known distance from your source. Enter that distance in the Reference Distance field. Then enter the distance at which you want to know the level in the Target Distance field. All three fields update the result instantly with no submit button required.

Use the Unit toggle to switch between meters and feet. Because the inverse square law depends only on the ratio of the two distances, the unit does not affect the dB calculation as long as both distances use the same unit. The Acoustic Source Type toggle switches between Point Source (6 dB per doubling, standard speakers and subwoofers) and Line Source (3 dB per doubling, line arrays and highway noise).

The Mathematics Behind the Attenuation Curve

For a point source in a free field, the inverse square law gives the following formula for the projected SPL at distance d2 from a reference measurement at distance d1:

L2 = L1 - 20 x log10(d2 / d1)

For a line source (cylindrical propagation), the formula is:

L2 = L1 - 10 x log10(d2 / d1)

The ratio d2/d1 determines the drop. If d2 is twice d1, log10(2) is approximately 0.301, so the point source drop is 20 x 0.301 = 6.02 dB, and the line source drop is 10 x 0.301 = 3.01 dB. These are the well-known 6 dB and 3 dB per doubling rules. If d2 equals 10 times d1, the point source drop is 20 dB (log10(10) = 1). If d2 equals 100 times d1, the drop is 40 dB.

Point Source vs. Line Source in Practice

A single cabinet speaker, subwoofer, or cluster of speakers whose physical dimensions are small relative to the listening distance behaves as a point source. Large-format vertical line arrays, designed with precise inter-element spacing to control vertical dispersion, exhibit near-cylindrical propagation in their near field and are well modeled by the line source formula. At very large distances (the far field of the array), even a line array eventually transitions toward spherical spreading. The transition distance depends on the array length and wavelength.

For occupational noise assessment, a busy highway with continuous traffic is often modeled as a line source. This has important implications for sound barrier design: reducing highway noise by 6 dB requires quadrupling the distance for a point source, but only requires doubling the distance for a line source.

What This Calculator Does Not Model

This tool calculates ideal free-field geometric spreading only. In real environments, additional factors reduce or increase the apparent level: room reflections and standing waves in enclosed spaces, ground reflection and interference in outdoor settings, atmospheric absorption (which affects high frequencies most severely over long distances), wind and temperature gradients that refract sound, vegetation, barriers, and structures that attenuate or diffract sound, and the directional characteristics (directivity index) of the source. For indoor environments, room acoustics often dominate over direct-field propagation beyond the critical distance of the room.

Frequently Asked Questions

In a free field, a point source radiates sound equally in all directions as an expanding sphere. When you double the distance from the source, the same acoustic energy is spread over four times the surface area (because surface area of a sphere scales with the square of the radius). Because power is divided by four, and the decibel scale is logarithmic, the level drops by 10 x log10(4), which equals approximately 6.02 dB. This is the inverse square law applied to sound: every doubling of distance results in a 6 dB reduction in sound pressure level.
A point source radiates sound as an expanding sphere. Its energy spreads over an area that grows with the square of distance, producing a 6 dB drop per doubling of distance (20 x log10 formula). A line source, such as a vertical line array speaker system or a busy highway, radiates sound as an expanding cylinder. Energy spreads over an area proportional to distance rather than distance squared, so it decays more slowly at only 3 dB per doubling of distance (10 x log10 formula). At very large distances, a line source eventually transitions back toward spherical spreading. In practice, the line source model is most accurate in the near field close to the array, and the point source model applies in the far field.
For a single home theater speaker, the inverse square law predicts that a listener at 2 meters experiences 6 dB less SPL than a listener at 1 meter. For a large concert venue, an engineer might measure 103 dB at 10 meters in front of the stage and use this calculator to predict the level at 80 meters will be approximately 84 dB, a drop of about 18 dB. Line arrays used in large concerts attenuate more slowly (3 dB per doubling), which is why venues favor them for even coverage across long throws. The formula only models free-field propagation and does not account for room reflections, air absorption, or barriers.
Yes. The inverse square law describes geometric spreading only, which is the dominant factor at short distances. At longer distances, atmospheric absorption becomes significant and adds extra attenuation beyond what geometry alone predicts. High frequencies are absorbed most severely. Temperature gradients in the atmosphere cause sound to refract: on a warm day with a cool upper layer, sound bends upward and the level at ground level drops faster than predicted. On a cool night with a warm inversion layer above, sound bends downward and can travel farther than expected. Humidity reduces absorption slightly at mid-to-high frequencies. This calculator models ideal free-field geometric spreading without atmospheric corrections.
The decibel is a physical measure of sound pressure, but perceived loudness follows a different curve. The widely used rule of thumb from psychoacoustic research is that a 10 dB increase in measured level corresponds to a doubling of perceived loudness, and a 10 dB decrease sounds approximately half as loud. This is based on Stevens Power Law and studies using the sone loudness scale. A 3 dB change is at the threshold of noticeable difference for most listeners. A 20 dB drop sounds about one-quarter as loud, and a 30 dB drop sounds about one-eighth as loud. These are approximations because perceived loudness also depends on frequency content, listening environment, and individual hearing.