Sound Intensity Level Calculator

Divide the measured sound intensity I by the reference intensity I₀ = 1e-12 W/m², take the base-10 logarithm, and multiply by ten: L = 10 × log₁₀(I / I₀). For example, an intensity of 0.000001 W/m² gives 10 × log₁₀(1,000,000) = 60 dB, the level of normal conversation.

The sound intensity level is the loudness of a sound on the decibel (dB) scale, measured relative to the threshold of hearing. It compares the physical sound intensity in W/m² to the reference I₀ = 1e-12 W/m² and expresses the ratio logarithmically, so a huge range of intensities fits on one compact scale.

I₀ = 1e-12 W/m² is the threshold of hearing — the faintest sound a healthy human ear can detect at 1 kHz. It is the internationally agreed zero point of the decibel scale, so a sound at exactly I₀ has a level of 0 dB. Everything louder is measured as a positive number of decibels above it.

Useful landmarks are a whisper near 30 dB, normal conversation around 60 dB, busy traffic about 80 dB, and the threshold of pain near 120 dB. Because the scale is logarithmic, each 10 dB step is a tenfold change in intensity, so 80 dB carries a hundred times the intensity of 60 dB.

Human hearing spans an enormous range — from 1e-12 W/m² to over 1 W/m², a factor of a trillion. A logarithmic scale compresses that range so it fits between roughly 0 and 120 dB, and it matches how we perceive loudness: each tenfold rise in intensity adds a fixed 10 dB rather than a number that grows out of control.