Reviewed By: Patrick Myers (BSME)

Enter the RMS sound pressure and reference pressure into the calculator to determine the sound pressure level (SPL) in decibels (dB).

Sound Pressure Level Calculator

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Sound Pressure Level Formula

The following equation is used to calculate a sound pressure level (SPL).

SPL = 20 \log_{10}\left(\frac{p_{rms}}{p_{ref}}\right)

Where SPL is the sound pressure level in decibels (dB) relative to a reference pressure
p_rms is the RMS sound pressure (pascals)
p_ref is the reference sound pressure (pascals), commonly 20 µPa in air (and commonly 1 µPa in water)

To calculate the sound pressure level, divide the RMS sound pressure by the reference pressure, take the base-10 logarithm (log₁₀) of the ratio, then multiply by 20.

Sound Pressure Level Definition

Sound pressure level (SPL) is a logarithmic measure of the RMS (effective) sound pressure relative to a specified reference pressure, expressed in decibels (dB).

Sound Pressure Example

How to calculate a sound pressure level?

First, determine the sound pressure (RMS).
Measure the fluctuating (AC) sound pressure about ambient and use its RMS value.
Next, determine the reference pressure.
Use the appropriate reference pressure for your medium (commonly 20 µPa in air, and commonly 1 µPa in water).
Finally, calculate the sound pressure level.
Calculate SPL in decibels using the equation above.

FAQ

What is the significance of the reference pressure in calculating sound pressure level?

The reference pressure is crucial because it sets the baseline pressure for the dB scale (SPL is a ratio, not an absolute pressure). The most common reference is 20 µPa in air (and commonly 1 µPa in water). Using atmospheric pressure (~101,325 Pa) as a reference is not standard for SPL and will not produce meaningful SPL values.

How does the sound pressure level relate to the perceived loudness of a sound?

The sound pressure level, measured in decibels, correlates with perceived loudness: higher dB generally sounds louder. However, the human ear’s response depends strongly on frequency and is not linear, so equal changes in SPL do not always sound equally loud.

Can sound pressure levels be harmful to human hearing?

Yes. Prolonged exposure to high levels can damage hearing. As a common guideline, long exposures at or above about 85 dB can increase the risk of hearing loss, and very high levels (roughly 120–140 dB, depending on duration and conditions) can cause pain and potentially immediate damage. Use hearing protection when appropriate.