Sound Intensity and Decibel Calculator
Calculate sound intensity from source power and distance, then convert to decibels.
Based on the inverse-square law.
Chart shows how dB drops with distance from the source.
Sound intensity I is the power passing through a unit area, measured in watts per square meter. For a point source radiating uniformly in all directions, intensity at distance r is:
I = P / (4 * pi * r^2)
The denominator is the surface area of a sphere. Power spreads over a larger shell as you move away, so doubling the distance reduces intensity to one-quarter. This is the inverse-square law.
Decibels convert intensity to a logarithmic scale that better matches how humans perceive loudness:
dB = 10 * log10(I / I0)
where I0 = 10^-12 W/m^2 is the threshold of human hearing (0 dB by definition). A whisper (10^-11 W/m^2) is 10 dB. Normal conversation sits around 60 dB. A rock concert peaks at 110-120 dB. A jet engine at close range: 140 dB.
Key fact: every 10 dB increase sounds roughly twice as loud to the human ear, but it represents a 10x increase in acoustic intensity. A 3 dB increase – the common spec for amplifier power doubles – is the just-noticeable difference in loudness.
OSHA limits unprotected occupational exposure to 90 dB for 8 hours per day. Above 85 dB sustained, hearing damage accumulates. Above 140 dB, a single exposure can cause permanent damage.
The chart shows how dB level drops with increasing distance from the source, confirming the -6 dB per distance-doubling rule (since intensity quarters and log of 1/4 = -6.02 dB).