Distance Attenuation
Calculate how sound pressure level (SPL) decreases with distance using the inverse square law. Free online distance attenuation calculator for acoustics, audio engineering, and physics.
About This Calculator
The Distance Attenuation Calculator helps you determine how sound pressure level (SPL) changes as you move away from a sound source. Based on the inverse square law of physics, this tool is essential for acousticians, audio engineers, sound designers, environmental noise consultants, and physics students who need to predict sound propagation in free-field conditions.
The calculator applies the fundamental sound attenuation formula: SPL₂ = SPL₁ − 20 × log₁₀(R₂ / R₁), where SPL₁ is the known sound pressure level in decibels at a reference distance R₁, and SPL₂ is the predicted level at the new distance R₂. The formula assumes a point source radiating uniformly in all directions with no reflective surfaces or barriers — known as free-field or anechoic conditions. For each doubling of distance, the sound pressure level drops by approximately 6 dB, a relationship known as the inverse square law of sound propagation.
How to Use This Calculator
Enter the sound pressure level measured at the reference distance R₁ (in dB), along with the reference distance R₁ and the target distance R₂ (both in meters). The calculator instantly computes the attenuated sound level SPL₂, the total attenuation in dB, the distance ratio, and categorizes the resulting sound level from Very Faint (below 20 dB) to Pain Threshold (above 120 dB). A step-by-step breakdown shows the intermediate calculations, while interactive bar and pie charts visualize the sound level comparison.
Regional Notes
United States: The US EPA and OSHA regulate workplace noise exposure. OSHA sets a permissible exposure limit of 90 dB over 8 hours with a 5 dB exchange rate. NIOSH recommends 85 dB over 8 hours with a 3 dB exchange rate. The inverse square law is used in environmental noise modeling per ANSI/ASA standards.
United Kingdom: The UK Control of Noise at Work Regulations 2005 set lower exposure action values at 80 dB and upper at 85 dB daily exposure. The inverse square law is applied in environmental noise assessment per BS 4142 and ISO 9613 standards.
India: The Central Pollution Control Board (CPCB) sets ambient noise standards under the Environment (Protection) Rules, 1986. Industrial areas allow 75 dB daytime / 70 dB nighttime, commercial areas 65 dB / 55 dB, residential areas 55 dB / 45 dB, and silence zones 50 dB / 40 dB.
Frequently Asked Questions
How does the distance attenuation calculator work?
The calculator uses the inverse square law formula SPL₂ = SPL₁ − 20 × log₁₀(R₂/R₁). Enter the known sound pressure level at a reference distance, then set a new distance to find the attenuated sound level. The calculator also shows the total attenuation in dB, the distance ratio, and categorizes the resulting sound level (e.g. Loud, Moderate, Quiet).
What is the inverse square law for sound?
The inverse square law states that sound intensity decreases proportionally to the square of the distance from the source. In practice, this means that for every doubling of distance from a point sound source, the sound pressure level drops by approximately 6 dB. This happens because the sound energy spreads over a spherical surface area that increases with the square of the radius.
What is the formula for sound attenuation over distance?
The sound attenuation formula is SPL₂ = SPL₁ − 20 × log₁₀(R₂/R₁), where SPL₁ is the known sound pressure level at distance R₁, and SPL₂ is the sound pressure level at the new distance R₂. The result is in decibels (dB). The factor 20 comes from the relationship between sound pressure and intensity — intensity is proportional to the square of pressure.
Is this calculator free to use?
Yes, the distance attenuation calculator is completely free to use with no registration or account required. You can also share your calculations via the generated URL that saves all input values.
What is the 6 dB rule for distance attenuation?
The 6 dB rule states that whenever the distance from a sound source doubles, the sound pressure level drops by approximately 6 dB. For example, moving from 1 meter to 2 meters away from a source results in a 6 dB reduction. Moving from 2 meters to 4 meters results in another 6 dB drop, for a total reduction of 12 dB from the original position.
What are typical sound pressure levels in daily life?
Typical sound pressure levels include: 0 dB (threshold of hearing), 20-30 dB (whisper, quiet library), 40-60 dB (normal conversation), 60-80 dB (busy traffic, vacuum cleaner), 80-100 dB (lawn mower, motorcycle), 100-120 dB (concert, jackhammer), and 120-140 dB (jet engine at close range, pain threshold). Prolonged exposure above 85 dB can cause hearing damage.
Does the calculator account for air absorption or reflections?
No, this calculator uses the basic inverse square law for a point source in a free field (anechoic conditions). It does not account for air absorption (which affects high frequencies more), reflections off walls, ground effect, barriers, or other environmental factors. For precise acoustic engineering, additional corrections should be applied based on ISO 9613 or other relevant standards.
How much louder is 40 dB compared to 20 dB?
40 dB is 100 times more intense than 20 dB. This is because the decibel scale is logarithmic — an increase of 10 dB corresponds to a tenfold increase in sound intensity, and an increase of 20 dB corresponds to a hundredfold increase. In subjective terms, a 20 dB increase is perceived as approximately 4 times louder by the human ear.