Sound Pressure Level Converter
Our media sound & motion design calculator teaches sound pressure level step by step. Perfect for students, teachers, and self-learners.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
SPL (dB) = 20 log10(p / p_ref)
Where SPL is sound pressure level in decibels, p is the measured sound pressure in pascals, and p_ref is the reference pressure (20 micropascals in air). For distance calculations: SPL2 = SPL1 - 20 log10(d2/d1). For combining N identical sources: SPL_total = SPL + 10 log10(N).
Worked Examples
Example 1: Concert Speaker SPL at Different Distances
Problem:A speaker produces 110 dB SPL at 1 meter. What is the SPL at 10 meters and 50 meters?
Solution:Using the inverse square law: SPL2 = SPL1 - 20 log10(d2/d1)\nAt 10m: 110 - 20 log10(10/1) = 110 - 20 = 90 dB\nAt 50m: 110 - 20 log10(50/1) = 110 - 33.98 = 76 dB
Result:At 10m: 90 dB SPL | At 50m: 76 dB SPL
Example 2: Combining Multiple Identical Machines
Problem:A factory has 8 identical machines each producing 82 dB SPL. What is the combined SPL?
Solution:Combined SPL = Single SPL + 10 log10(N)\n= 82 + 10 log10(8)\n= 82 + 10 x 0.903\n= 82 + 9.03 = 91.03 dB
Result:Combined SPL: 91 dB (exceeds 85 dB safe exposure limit for 8 hours)
Frequently Asked Questions
What is sound pressure level (SPL) and how is it measured?
Sound pressure level (SPL) is a logarithmic measure of the effective pressure of a sound wave relative to a reference value, expressed in decibels (dB). The standard reference pressure in air is 20 micropascals, which corresponds roughly to the threshold of human hearing at 1 kHz. SPL is measured using a sound level meter that captures pressure variations in the air caused by sound waves. Because our ears perceive sound logarithmically rather than linearly, the decibel scale compresses an enormous range of pressures into manageable numbers, from 0 dB at the hearing threshold to around 194 dB at the theoretical maximum for undistorted sound in air.
How does the inverse square law affect sound pressure?
The inverse square law states that in a free field (no reflections), sound intensity decreases proportionally to the square of the distance from the source. This translates to a 6 dB reduction in SPL each time the distance from a point source doubles. For example, if a speaker produces 100 dB at 1 meter, it will be approximately 94 dB at 2 meters, 88 dB at 4 meters, and 82 dB at 8 meters. In practice, environmental factors such as reflections from walls, absorption by surfaces, and atmospheric conditions can cause deviations from this ideal relationship. Line sources like highways follow a different rule, losing only 3 dB per doubling of distance.
How do multiple sound sources combine in decibels?
Sound levels from multiple identical sources combine logarithmically rather than arithmetically. Two identical sources add 3 dB to the level of one source (10 log10 of 2 equals approximately 3). Ten identical sources add 10 dB, and one hundred identical sources add 20 dB. For non-identical sources, you must convert each dB value to intensity, sum the intensities, then convert back to dB. If two sources differ by more than 10 dB, the quieter source adds less than 0.5 dB to the louder one and can often be ignored for practical purposes. This principle is essential in acoustical engineering when designing sound systems or assessing noise from multiple machines.
How do I convert between sound pressure in pascals and SPL in decibels?
To convert from pressure to SPL: dB SPL = 20 times log base 10 of (measured pressure divided by reference pressure), where the reference pressure is 20 micropascals in air. To convert from SPL to pressure: pressure equals reference pressure times 10 raised to the power of (SPL divided by 20). For example, 94 dB SPL corresponds to 1 pascal of sound pressure. This relationship means that a 6 dB increase represents a doubling of sound pressure, while a 20 dB increase represents a tenfold increase in pressure. These conversions are fundamental in acoustics for translating between physical measurements and perceived loudness levels.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy