What is the inverse square law for sound?

The inverse square law states that sound intensity decreases with the square of the distance from the source. In decibels, this means SPL drops by 6 dB each time the distance doubles. At 2 meters, the level is 6 dB lower than at 1 meter. At 4 meters, it is 12 dB lower. This applies to point sources in free-field conditions without reflections.

Why does sound lose 6 dB per doubling of distance?

As sound radiates from a point source, it spreads over an expanding spherical surface. When distance doubles, the surface area quadruples (area = 4*pi*r^2). The same acoustic power spread over four times the area means one-quarter the intensity. In decibels: 10*log10(1/4) = -6.02 dB, which rounds to 6 dB.

Does the inverse square law apply indoors?

Only partially. Near the source (direct field), the inverse square law applies. Beyond the critical distance, reflected sound dominates and level decreases much more slowly (approximately 0 dB change in a diffuse field). The critical distance depends on room absorption and source directivity. In highly reverberant spaces, it can be as short as 2-3 meters.

What is atmospheric absorption and when does it matter?

Air absorbs sound energy, with absorption increasing dramatically at high frequencies. At 20 degrees C and 50% humidity, absorption at 1 kHz is about 0.005 dB/m, but at 8 kHz it reaches 0.05 dB/m. Over 100 meters, this means 5 dB of extra loss at 8 kHz beyond inverse square law predictions. ISO 9613-1 provides the reference calculation.

How does directivity factor affect SPL prediction?

A source on a reflective surface (ground, wall) radiates into a smaller solid angle, concentrating energy. Q=2 (hemisphere) adds 3 dB compared to Q=1 (full sphere). Q=4 (quarter-space, at a wall-floor junction) adds 6 dB. Q=8 (corner) adds 9 dB. Speaker directivity (horn pattern) further focuses energy, making the effective Q much higher on-axis.

How do I calculate how far a speaker can throw?

Use the formula: max_distance = ref_distance * 10^((SPL_ref - target_SPL)/20). If a speaker produces 130 dB at 1 meter and you need 90 dB at the audience: distance = 1 * 10^((130-90)/20) = 100 meters (free-field). Account for atmospheric absorption and audience absorption for real-world results.

What is critical distance in a room?

Critical distance is where the direct sound level equals the reverberant sound level. Beyond this distance, increasing amplifier power does not significantly increase perceived level because reverberant energy dominates. Critical distance = 0.057 * sqrt(Q * room_constant), where room_constant depends on room volume and absorption.

How does the inverse square law apply to noise regulations?

Environmental noise regulations specify limits at the property boundary or receiver location. The inverse square law predicts noise levels at these distances from the source. For compliance calculations per ISO 9613-2, atmospheric absorption, ground effect, barrier attenuation, and meteorological corrections modify the basic inverse square law prediction.

What is the inverse square law for sound?

The inverse square law states that sound intensity decreases with the square of the distance from the source. In decibels, this means SPL drops by 6 dB each time the distance doubles. At 2 meters, the level is 6 dB lower than at 1 meter. At 4 meters, it is 12 dB lower. This applies to point sources in free-field conditions without reflections.

Why does sound lose 6 dB per doubling of distance?

As sound radiates from a point source, it spreads over an expanding spherical surface. When distance doubles, the surface area quadruples (area = 4*pi*r^2). The same acoustic power spread over four times the area means one-quarter the intensity. In decibels: 10*log10(1/4) = -6.02 dB, which rounds to 6 dB.

Does the inverse square law apply indoors?

Only partially. Near the source (direct field), the inverse square law applies. Beyond the critical distance, reflected sound dominates and level decreases much more slowly (approximately 0 dB change in a diffuse field). The critical distance depends on room absorption and source directivity. In highly reverberant spaces, it can be as short as 2-3 meters.

What is atmospheric absorption and when does it matter?

Air absorbs sound energy, with absorption increasing dramatically at high frequencies. At 20 degrees C and 50% humidity, absorption at 1 kHz is about 0.005 dB/m, but at 8 kHz it reaches 0.05 dB/m. Over 100 meters, this means 5 dB of extra loss at 8 kHz beyond inverse square law predictions. ISO 9613-1 provides the reference calculation.

How does directivity factor affect SPL prediction?

A source on a reflective surface (ground, wall) radiates into a smaller solid angle, concentrating energy. Q=2 (hemisphere) adds 3 dB compared to Q=1 (full sphere). Q=4 (quarter-space, at a wall-floor junction) adds 6 dB. Q=8 (corner) adds 9 dB. Speaker directivity (horn pattern) further focuses energy, making the effective Q much higher on-axis.

How do I calculate how far a speaker can throw?

Use the formula: max_distance = ref_distance * 10^((SPL_ref - target_SPL)/20). If a speaker produces 130 dB at 1 meter and you need 90 dB at the audience: distance = 1 * 10^((130-90)/20) = 100 meters (free-field). Account for atmospheric absorption and audience absorption for real-world results.

What is critical distance in a room?

Critical distance is where the direct sound level equals the reverberant sound level. Beyond this distance, increasing amplifier power does not significantly increase perceived level because reverberant energy dominates. Critical distance = 0.057 * sqrt(Q * room_constant), where room_constant depends on room volume and absorption.

How does the inverse square law apply to noise regulations?

Environmental noise regulations specify limits at the property boundary or receiver location. The inverse square law predicts noise levels at these distances from the source. For compliance calculations per ISO 9613-2, atmospheric absorption, ground effect, barrier attenuation, and meteorological corrections modify the basic inverse square law prediction.

Inverse Square Law Calculator for Sound

The inverse square law states that sound pressure level decreases by 6 dB for each doubling of distance from a point source in free-field conditions. SonaVyx calculates SPL at any distance given a reference measurement, accounts for atmospheric absorption at high frequencies per ISO 9613-1, and corrects for directivity factor to provide accurate level predictions for sound system design and noise assessment.

Try It Now

Measure actual SPL at your position to verify the calculation.

Open Tool

Technical Specifications

Parameter	Value	Standard
Basic Rule	-6 dB per doubling of distance	Free-field point source
Formula	SPL2 = SPL1 - 20*log10(d2/d1)	ISO 9613-2
Atmospheric Absorption	Per ISO 9613-1 (temp, humidity)	Significant above 2 kHz
Directivity Factor	Q = 1 (free) to Q = 8 (corner)	Half-space, quarter-space
Distance Range	0.1 m to 10 km	Near field to far field
Temperature	-20 C to +50 C	ISO 9613-1 Table 1
Humidity	10% to 100% RH	ISO 9613-1 Table 1

How to Calculate SPL at Distance

Enter Reference SPL

Input the known sound pressure level at a reference distance. Loudspeaker specifications typically list sensitivity at 1 meter with 1 watt (or 2.83V) input. If you have a measurement at any distance, enter that value and distance as your reference.

Set Target Distance

Enter the distance at which you want to know the SPL. For concert venues, this might be 30-100 meters. For environmental noise assessment, distances can extend to several kilometers. The calculator handles both short and long ranges.

Adjust for Environment

Select the directivity factor: Q=1 for suspended in free air, Q=2 for on a large surface (ground), Q=4 for at a wall-floor junction, Q=8 for in a corner. Directivity factor adds up to 9 dB at Q=8 compared to free-field.

Include Atmospheric Absorption

For distances beyond 50 meters, atmospheric absorption becomes significant especially above 2 kHz. Enter temperature and humidity for per-frequency absorption calculation per ISO 9613-1. At 8 kHz in dry conditions, absorption can reach 0.1 dB per meter.

Understanding Sound Propagation

Sound propagation in the real world involves more than just the inverse square law. While the 6 dB per doubling rule is fundamental, actual sound levels at distance depend on source directivity, ground absorption, atmospheric conditions, barriers, and wind and temperature gradients. For accurate predictions beyond 100 meters, ISO 9613-2 provides a comprehensive calculation method incorporating all these factors.

Atmospheric Absorption by Frequency

Air absorbs sound through viscous and thermal losses and molecular relaxation of oxygen and nitrogen. The absorption coefficient in dB/meter depends on frequency, temperature, humidity, and barometric pressure. At 1 kHz, absorption is typically 0.005 dB/m. At 4 kHz, it rises to 0.02 dB/m. At 8 kHz, it reaches 0.05 dB/m in standard conditions. Over long distances, this dramatically reduces high-frequency content, which is why distant thunder sounds only like a low rumble.

Practical Applications

Sound system designers use inverse square law calculations to determine how much SPL a speaker system needs to produce to achieve the target level at the farthest audience position. Environmental consultants use it to predict noise levels at nearby residences from industrial sources. Event planners use it to ensure compliance with local noise ordinances at property boundaries. In all cases, the calculation starts with a known source level and predicts the received level at the distance of interest.

SPL Calculator Comparison

Feature	SonaVyx	Smaart v9	REW	OSM
SPL distance calculation	Yes	No	No	No
Atmospheric absorption	Yes (ISO 9613-1)	No	No	No
Directivity factor	Q=1/2/4/8	No	No	No
Multi-frequency	Yes (per octave band)	N/A	N/A	N/A
Browser-based	Yes	No	No	No
Price	Free	$898	Free	Free

Frequently Asked Questions

Related Tools & Resources

SPL Meter

Measure actual sound pressure levels

Noise Dose Calculator

Calculate occupational noise exposure

Cable Loss Calculator

Calculate electrical signal loss in cables

SPL (Glossary)

Sound Pressure Level definition and reference

Standards References

ISO 9613-1:1993 — Attenuation of sound during propagation outdoors: Calculation of atmospheric absorption
ISO 9613-2:1996 — Attenuation of sound during propagation outdoors: General method of calculation
IEC 61672-1:2013 — Sound level meters: Specifications (SPL measurement reference)
ANSI S1.26-2014 — Calculation of the absorption of sound by the atmosphere