Sound Intensity and Decibel Calculator

Sound intensity and decibels

Sound intensity is the sound energy passing through unit area per unit time, measured in W/m². The ear copes with an enormous range: the faintest audible sound and a painful one differ by a factor of a trillion. Intensity is therefore quoted on a logarithmic scale, in decibels:

L = 10 × log₁₀(I / I₀)

The reference value is I₀ = 10⁻¹² W/m². 0 dB is that threshold, not silence.

Reading decibels

• Every 10 dB step is a tenfold increase in intensity. 20 dB is a factor of 100 and 30 dB a factor of 1000.
• Doubling the intensity adds about 3 dB.
• Going back: I = I₀ × 10^(L / 10)

Fall off with distance

In the open, sound from a point source spreads over a sphere: I = P / (4 × π × r²). Doubling the distance cuts the intensity to a quarter and the level by about 6 dB. Ten times the distance lowers the level by 20 dB.

Why decibels do not simply add

Two machines at 80 dB each do not make 160 dB. What adds is intensity: two equal sources double it, and the level becomes 83 dB. If one level is 10 dB or more above the other, the weaker source adds less than half a decibel.

Example

At 10 m from a source radiating 1 W of sound power the intensity is 1 / (4 × π × 100) = 7.96 × 10⁻⁴ W/m² and the level is 10 × log(7.96 × 10⁸) = 89 dB.

Limits

The distance and power modes are for a point source in the open with no reflections. Indoors, reflections raise the level. The result is in unweighted decibels, not the dB(A) used in noise measurements. The tool does not assess hearing safety or compliance with noise regulations.