Intensidade Sonora c/ Distância
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
I ∝ 1/r²
About this calculator
The Sound Intensity with Distance Calculator determines how sound intensity decreases as it propagates through air. Sound intensity I is the power transmitted per unit area, measured in W/m². Under ideal conditions, without obstacles or absorption, intensity decreases with the square of the distance: I₂ = I₁ × (r₁/r₂)², where I₁ is the intensity at distance r₁ and I₂ is the intensity at distance r₂. This relationship comes from spherical geometry, as sound energy spreads over an increasing area.
Usage is straightforward: enter a known intensity and its distance, then provide the new distance to calculate the new intensity. The tool can also compute the initial intensity if you have the final intensity and both distances. The formula I ∝ 1/r² is valid for point sources in free field, without reflections. Example applications include: estimating loudspeaker volume at different distances, calculating noise exposure in open environments, or sizing sound systems.
Practical cases: a sound engineer can predict sound pressure levels (SPL) at different points in an arena; a safety technician can evaluate noise reduction when moving away from machinery; a musician can position stage monitors to avoid feedback. Caveats: the formula assumes spherical propagation without obstacles, atmospheric absorption, or interference. In enclosed spaces, reflections and reverberation alter behavior. Also, intensity does not account for source directivity; directional sources may have different patterns.
Frequently asked questions
Does the calculator work for any type of sound?
Yes, as long as the source is approximately point-like and the environment is free of obstacles. The formula I ∝ 1/r² is a valid approximation for spherical waves.
Can I use this calculator to measure sound pressure level in decibels?
Not directly. The calculator works with intensity in W/m². To convert intensity to decibels, use SPL = 10 log(I/I₀), where I₀ = 10⁻¹² W/m².
What happens if the distance doubles?
The intensity drops to one quarter of the original value, since (1/2)² = 1/4. This corresponds to a 6 dB reduction in sound pressure level.
Is the formula valid in enclosed rooms?
Not exactly. In enclosed spaces, reflections and reverberation cause intensity to deviate from the inverse square law. The calculator is more accurate for open fields or anechoic chambers.
How does air absorption affect the calculation?
Atmospheric absorption attenuates sound further, especially at high frequencies and long distances. For very long distances, the simple formula underestimates the loss.