Sound Pressure Level Converter (dB, Pa, W/m²)

dB SPL to pascals to sound intensity and back, with the 20 µPa and 1 pW/m² references spelt out — including the 0.14 dB the two of them disagree by, because air is 413 rayl and the references assume 400.

The two references, and the air between them

The pressure scale, from the reference to the ceiling

What the air temperature actually does

The A-weighting function against the standard’s own table

The decibel with an absolute reference

A decibel is a ratio, so an acoustic decibel needs something to be a ratio of. That something is 20 micropascals for pressure and one picowatt per square metre for intensity, and the moment you know those two numbers the decibel stops being relative and starts being a unit. SPL = 20 log₁₀(p / 20 µPa) and the factor 20 rather than 10 is because pressure is an amplitude, not a power.

The two references do not quite agree with each other, and that is the interesting part. They were chosen together in 1932, and they are consistent only if the characteristic impedance of air is exactly 400 rayl: (20 × 10⁻⁶)² ÷ 400 is exactly 10⁻¹², to the last digit. Air is not 400 rayl. Compute it from the ideal gas law and √(γRT) and at 20 °C it is 413.3, at 0 °C 428.2, at 25 °C 409.8 — which is the figure the National Physical Laboratory quote, at their own standard temperature. So a sound pressure level and a sound intensity level describing exactly the same plane wave are not the same number: at 20 °C they differ by 0.142 dB. It is a seventh of a decibel and nobody’s ears care, but it is a systematic offset rather than scatter, and the temperature box on this page is there so you can watch it move. It reaches zero at about 39.8 °C: the 400-rayl assumption behind the standard references is exact in a foundry and wrong in a cold room.

Intensity from pressure needs an assumption the page states. I = p²/ρc is true for a plane progressive wave, in which pressure and particle velocity rise and fall together. Near a source, inside a standing wave, or anywhere in a reverberant room they do not, and the real intensity can be a small fraction of what the pressure implies — in an ideal standing wave it is zero while the pressure is at its largest. Every intensity row on this page carries that assumption. It is also why a real sound intensity measurement needs a two-microphone probe rather than a sound level meter.

Distance, honestly. A point source in a free field loses 20 log₁₀(d₂/d₁) decibels, which is 6.02 dB per doubling; a long line source loses half that because the wave spreads in two dimensions instead of three; a plane wave in a duct loses nothing geometrically at all. Those three options are the whole of what the distance rows here do. They are geometric divergence and nothing else: no ground reflection, no air absorption, no barrier, no wind gradient, no room. Outdoors over any real distance the answer is ISO 9613-2’s, not this one. Indoors, past the reverberation radius, the level simply stops falling.

And dB(A) is not a unit conversion. A-weighting is a filter with a shape, and turning a broadband sound pressure level into an A-weighted one requires knowing how that sound’s energy is distributed across frequency — information a single dB SPL figure does not contain. What this page offers instead is the weighting at one stated frequency, computed from the four-pole function of IEC 61672-1 and checked against all thirty-four tabulated values in that standard to better than 0.05 dB. Use it to see the shape of the curve, not to convert a measurement. For occupational noise, where the A-weighted level is the legally relevant quantity, the noise exposure dose calculator takes A-weighted levels and hours and gives you a dose under each regime. The electronics section’s decibel calculator handles the decibel as a pure ratio of electrical quantities, which is the same logarithm and a different subject.

Frequently asked questions

Related calculators

References

1. ISO 1683:2015, Acoustics — Preferred reference values for acoustical and vibratory levels. Fixes the reference sound pressure at 20 µPa and the reference sound intensity at 1 pW/m². Copyrighted and cited, not reproduced; both reference values are also stated in the NPL guide below.
2. National Physical Laboratory. Sound Pressure Level and Intensity Level, NPL acoustics technical guide, resource.npl.co.uk. States both reference values, that they were chosen together in 1932, and that “a 20 µPa acoustic pressure in air gives a 1 pW/m² intensity if the impedance is 400 Rayls” — which is the sentence this page’s temperature input exists because of. NPL quote 409 rayl for air; that is the 25 °C value, and 413 is the 20 °C one.
3. Picard A, Davis RS, Gläser M, Fujii K. Revised formula for the density of moist air (CIPM-2007). Metrologia 45:149–155 (2008). Source of the specific gas constant used for dry air, 287.0528 J kg^-1 K^-1, from which the density and hence the characteristic impedance on this page are computed rather than quoted. The speed of sound follows as √(γRT), which returns 331.32 m/s at 0 °C — the published figure — and 343.2 m/s at 20 °C.
4. IEC 61672-1:2013, Electroacoustics — Sound level meters — Part 1: Specifications, clause 5.4 and Table 3. The frequency weightings are defined in the standard by a table of values with tolerances, not by a formula; the standard is copyrighted and its table is NOT reproduced here. The analytic four-pole function this page uses was checked against all 34 tabulated A-weighting values and reproduces every one to better than 0.05 dB, inside the table’s own 0.1 dB rounding.
5. Rimell AN, Mansfield NJ, Paddan GS. Design of digital filters for frequency weightings (A and C) required for risk assessments of workers exposed to noise. Industrial Health 53(1):21–27 (2015). Open access. Source of the four pole frequencies of the A-weighting transfer function — 20.598 997, 107.652 65, 737.862 23 and 12 194.217 Hz — and of the statement that the standard defines the weightings by table rather than by function.
6. ISO 9613-2:1996, Acoustics — Attenuation of sound during propagation outdoors — Part 2: General method of calculation. The 6 dB per doubling of distance used here is geometric divergence from a point source in a free field and nothing else: this standard’s method adds ground effect, atmospheric absorption, barriers and foliage, all of which this page leaves out and says so.