๐ Sound Level Converter
* Calculated relative to the standard hearing threshold reference (20 micropascals = 0 dB SPL).
Convert between a sound's physical pressure (in pascals) and its sound pressure level relative to human hearing (decibels, dB SPL). Uses a logarithmic calculation based on the standard hearing threshold reference (20 micropascals) โ useful for acoustics or noise-measurement studies.
How to use
- Choose a direction: "dB โ Pa" or "Pa โ dB".
- Enter the value you want to convert.
- The converted result is shown automatically.
How the calculation works
Sound pressure level (dB SPL) expresses sound pressure (in pascals) relative to a reference pressure on a logarithmic scale: Lp = 20 ร logโโ(p รท pโ). The reference pโ is 20 micropascals (0.00002 Pa), set as roughly the quietest sound a healthy person can just hear around 1 kHz โ that is 0 dB. Audible sound spans an enormous range: the loudest sounds before pain are about a million times the pressure of the quietest. Handling that directly would mean unwieldy numbers, so the logarithm compresses it into a manageable 0 to roughly 120 dB. The factor is 20 because sound intensity (energy) is proportional to the square of pressure. Ten times the pressure is +20 dB; double the pressure is about +6 dB.
Worked example
A sound pressure of 1 Pa as a level 20 ร logโโ(1 รท 0.00002) = 20 ร logโโ(50,000) โ 94.0 dB 94 dB is a level commonly used by sound level meter calibrators. Going the other way, 60 dB corresponds to 0.00002 ร 10^(60 รท 20) = 0.00002 ร 1,000 = 0.02 Pa.
Things to be aware of
- This calculates unweighted sound pressure level (dB SPL). Readings in A-weighted dB(A), common on noise meters, will differ.
- Decibels are logarithmic, so the levels of two sounds cannot simply be added together.
- The 20 ยตPa reference applies to sound in air; underwater acoustics uses a 1 ยตPa reference.
- Prolonged exposure to loud sound can damage hearing. Assess noise against the relevant professional standards.
FAQ
Why does decibel use a logarithm instead of a simple ratio?
Human hearing perceives loudness logarithmically relative to physical sound pressure. The decibel is a logarithmic scale designed to match how we actually perceive sound.
What's the 20 micropascal reference value?
It's based on the quietest sound pressure a healthy human ear can detect (the threshold of hearing), which is defined as 0 dB SPL.
Does this support A-weighting, like dB(A)?
No โ this tool only calculates plain sound pressure level (dB SPL) and doesn't apply frequency-weighting curves like A-weighting.