Last updated: 2026-06-16

Sound pressure level

Sound pressure level (SPL) is a logarithmic measure of the RMS acoustic pressure of a sound wave relative to a fixed reference pressure. It is the quantity that sound-level meters and calibrated microphones measure directly, and it is expressed in decibels (dB). The formula is

where $p$ is the root-mean-square acoustic pressure and $p_0$ is the reference pressure. In air, the standard reference is $p_0 = 20\,\mu\text{Pa}$ (2×10⁻⁵ Pa), roughly the quietest tone a healthy human ear can detect at 1 kHz. At that pressure the level is 0 dB by definition.

Why the factor 20

The decibel was originally defined for power ratios as $L = 10\log_{10}(P/P_0)$. Acoustic intensity — power per unit area — is proportional to the square of the pressure:

Substituting into the power-ratio formula gives

Using the factor 20 keeps the decibel scale consistent: doubling the pressure adds $20\log_{10}(2) \approx 6\,\text{dB}$, and doubling the intensity adds $10\log_{10}(2) \approx 3\,\text{dB}$ — the same ratio on the same scale.

Formula reference

Worked example

A sound wave has an RMS pressure of 0.2 Pa. With the standard reference $p_0 = 2\times10^{-5}\,\text{Pa}$:

A level of 80 dB corresponds roughly to a busy restaurant or a vacuum cleaner at one metre.

The 20 µPa reference

The reference pressure $p_0 = 20\,\mu\text{Pa}$ is defined by ISO 1683 as the standard for sound in air and corresponds approximately to the threshold of human hearing at 1 kHz. It was chosen so that 0 dB represents the quietest audible sound under ideal conditions.

For underwater acoustics a different reference is used — 1 µPa — so SPL values in water cannot be compared directly with SPL values in air without adjusting for the different reference.

Relation to sound intensity level

Sound intensity level (SIL) is defined as $L_I = 10\log_{10}(I/I_0)$ with $I_0 = 10^{-12}\,\text{W/m}^2$. For a plane wave in free air the two references are thermodynamically consistent, so $L_p$ and $L_I$ give the same numerical value in decibels. In enclosed rooms, near reflecting surfaces, or in reactive fields, intensity and pressure can decouple and the two levels diverge.

Typical hearing thresholds

Limits of the model

The SPL formula assumes a single sinusoidal or broadband RMS pressure reading. It does not account for frequency weighting (A-weighting, C-weighting), which adjust for the varying sensitivity of human hearing across frequencies. Measurements for health and safety assessment are typically A-weighted (dB(A)), whereas this calculator uses unweighted broadband pressure. The formula also treats the sound field as a scalar pressure and does not model interference, directivity, or the acoustic environment.