Sound Intensity (I = P/A)

I = \frac{P}{A}

Worked example: 100 W over 50 m^2 → I = 2 W/m^2 — press Try an example to run it live, then adjust anything.

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Sound Intensity (I = P/A) explained

Intensity measures how concentrated a sound's energy is: the acoustic power crossing each square meter of surface. A rock band's loudspeaker stack might radiate 100 W of acoustic power; spread that over the 50 m² face of a mosh pit and the crowd absorbs 2 W/m² — painfully loud, about 123 dB. The same 100 W spread across a 5000 m² festival field ten times farther back drops to a comfortable 0.02 W/m².

What makes hearing remarkable is the range this formula spans. The faintest sound a healthy ear detects carries about 10⁻¹² W/m² — a millionth of a millionth of a watt per square meter — while the threshold of pain sits near 1 W/m², a trillion times greater. A whisper delivering 10⁻¹⁰ W to your 60 mm² eardrum is moving it a distance smaller than the diameter of a hydrogen atom.

Sound Intensity (I = P/A) formula

I = \frac{P}{A}

Where

$I$ = Sound intensity (W/m²)
$P$ = Acoustic power (W)
$A$ = Area (m²)

Missing one of these? Work it out first, then come back

Sound intensity — Inverse-Square Law for Sound, Decibel Sound Level
Acoustic power — Inverse-Square Law for Sound, Power (P = W/t)
Area — Pressure (P = F/A), Area of a Circle

Part of these formula sets

Sound intensity and decibels

4 formulasSound power spread over area, how it falls with distance, and why the ear's response forces a logarithmic scale.

From acoustic watts to a decibel reading

4 formulasA source rated in watts, turned into the decibels a specification is written in: intensity, the spread with distance, then a second machine.