Sound Pressure Level Calculator: dB and Pa Converter

Sound pressure level (SPL) is a logarithmic measure of the effective sound pressure of a sound relative to a reference value, expressed in decibels (dB). The formula is SPL = 20 x log10(p / p_ref), where p is the measured root-mean-square sound pressure and p_ref is the reference pressure of 20 micropascals (20 µPa), which is approximately the threshold of human hearing at 1 kHz. Because the decibel scale is logarithmic, an increase of 10 dB represents a tenfold increase in pressure squared (or acoustic intensity), and a doubling of perceived loudness is approximately 10 dB.

The reference sound pressure for airborne sound is 20 micropascals (20 µPa or 2 x 10^-5 Pa). This value was chosen because it corresponds closely to the threshold of human hearing at 1 kHz for a young person with normal hearing. At this reference, 0 dB SPL represents the quietest sound most people can detect. This reference is standardised in ISO 1683 and ANSI S1.1. Note that underwater acoustics uses a different reference pressure of 1 µPa.

For a point source in a free field (no reflections), sound pressure level decreases by 6 dB each time the distance from the source doubles. The formula is: SPL at distance d2 = SPL at distance d1 minus 20 x log10(d2 / d1). For example, if SPL is 90 dB at 1 metre, it will be 84 dB at 2 metres, 78 dB at 4 metres, and so on. This approximation applies best in open outdoor conditions. Indoors, reflections add reverberant energy, so actual decay is slower than the inverse square law predicts.

Prolonged exposure to sounds at or above 85 dB SPL can cause permanent hearing damage. NIOSH (National Institute for Occupational Safety and Health) sets the recommended exposure limit at 85 dB(A) for 8 hours per day, with the permissible dose halving for every 3 dB increase. OSHA sets the action level at 85 dB(A) and the permissible exposure limit at 90 dB(A) for 8 hours. Brief exposures to sounds above 120 dB can cause immediate damage; impulse sounds above 140 dB (such as gunshots) can cause instantaneous hearing damage.

dB SPL is a flat (unweighted) measure of sound pressure level using the reference of 20 µPa. dB(A), or A-weighted decibels, applies a frequency-weighting filter that approximates the sensitivity of the human ear, which is less sensitive to very low and very high frequencies. A-weighting attenuates low frequencies significantly. Most occupational noise regulations and environmental noise standards specify dB(A) rather than dB SPL because it better correlates with perceived loudness and hearing damage risk. C-weighting (dB(C)) attenuates less at low frequencies and is used for peak measurements.