Last updated: 2026-06-16

Sound intensity level

Sound intensity level is a logarithmic measure of acoustic power per unit area, expressed in decibels (dB). The decibel scale was chosen because human hearing responds roughly logarithmically to stimulus: a tenfold increase in physical intensity is perceived as approximately the same step in loudness regardless of starting level. The formula is

where $I$ is the acoustic intensity in watts per square metre and $I_0 = 1\times10^{-12}\ \text{W/m}^2$ is the internationally agreed reference intensity, approximately the quietest sound a healthy young ear can detect at 1 kHz.

Formula table

Worked example

A normal conversation at about one metre produces an intensity of roughly $10^{-6}\ \text{W/m}^2$. The sound level is

The reference threshold

The reference $I_0 = 1\times10^{-12}\ \text{W/m}^2$ defines 0 dB as the threshold of human hearing. At this intensity, the eardrum displacement is smaller than the diameter of a hydrogen atom. Common reference points on the decibel scale:

Key rules of the decibel scale

Adding 10 dB multiplies intensity by 10. Because $\log_{10}(10I/I_0) = \log_{10}(I/I_0) + 1$, each additional 10 dB corresponds to a tenfold increase in physical intensity, not a tenfold increase in perceived loudness.

Adding 3 dB doubles the intensity. A factor of 2 in intensity gives $10\log_{10}(2) \approx 3\ \text{dB}$. This means two identical sound sources playing together produce a level 3 dB higher than either source alone — the intensities add, not the decibel values.

Decibels cannot be added directly. To combine two levels $L_1$ and $L_2$, convert each back to intensity, sum, then take the logarithm:

Hearing damage thresholds

Sustained exposure above about 85 dB damages the hair cells in the cochlea. Regulatory bodies including the US OSHA and the EU Noise at Work Directive set the action level at 85 dB for an 8-hour working day, with mandatory hearing protection above 90 dB. Each 3 dB increase halves the permissible exposure time under these rules because the intensity doubles.

Limits of this calculation

This calculator computes the intensity level, which is defined in terms of acoustic power per unit area. The related but distinct quantity sound pressure level (SPL) is defined from the ratio of root-mean-square pressure to a reference pressure; in a plane wave the two measures are numerically equal, but they differ in reverberant or multi-source fields.

A-weighting (dBA) adjusts for the frequency dependence of human hearing sensitivity and is the standard for occupational noise assessment; the unweighted intensity level computed here does not apply A-weighting. For precision acoustic measurements, consider the frequency spectrum of the source and apply the appropriate weighting.