Sound Intensity and Decibel Calculator
Calculate sound intensity from source power and distance, then convert to decibels using the inverse-square law.
Chart shows dB falloff over distance.
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).
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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