SPL from Pressure

SPL = 20 × log₁₀(p / p_ref)

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Result
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Formula

SPL = 20 × log₁₀(p / 20 µPa)

Description

Sound pressure level in decibels is defined relative to the threshold of human hearing at 20 micropascals (20 µPa). This reference was chosen because it represents the quietest sound a healthy young person can perceive at 1 kHz. The logarithmic scale compresses the enormous range of pressures the ear can handle: from the threshold of hearing (0 dB SPL, 20 µPa) to the threshold of pain (130 dB SPL, about 63 Pa), a ratio of over 3 million to one in pressure. Each 20 dB increase represents a 10× increase in sound pressure.

Variables

  • SPL — Sound pressure level (dB SPL)
  • p — RMS sound pressure (Pa)

Practical Notes

Normal conversation is about 60-65 dB SPL (0.02 Pa), a lawnmower at 1 meter is about 90 dB SPL (0.63 Pa), and a jet engine at 30 meters is about 140 dB SPL (200 Pa). Occupational noise exposure limits are typically 85 dB SPL for 8 hours. A-weighting (dBA) applies a frequency-dependent correction to match human hearing sensitivity.

Related Formulas

Audio Crossover Frequency SPL from Power & Sensitivity Audio Cable High-Frequency Rolloff Crest Factor Reverberation Time (RT60) Total Harmonic Distortion

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