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Help with SPL calculation
Help with SPL calculation
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Old 2nd August 2019, 08:42 PM   #1
Conrad Hoffman is offline Conrad Hoffman  United States
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Default Help with SPL calculation

From another thread, you can calculate SPL from driver diameter and peak excursion. (I also divide by 4, 2, 1 and .5 to account for radiation space due to baffle and wavelength.):


p=Sd*Xmax*f^2*pi*rho0/(r*sqrt(2))

where p=sound pressure in Pa, Sd=eqv. piston area in m², Xmax=max peak excursion in m, f=frequency in Hz, rho0=1.2kg/m3, r=speaker-to-mic distance in m.

The sound pressure p can be converted to sound pressure level:
SPL=20*log10(p/0,00002) dB. Note that 0.00002 Pa = 0.0002 dynes/cm²

I had access to a laser vibrometer and tested the equation with an actual driver. The results were within 1 dB, which is easily within the error of my meter and setup.

What I don't understand is that the driver excursion is peak, one half of the peak to peak value, but the 0 dB reference is an RMS number, as is the SPL. How can unit be mixed like that? Can anybody explain why this equation works? Or should the driver excursion really be RMS?
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Old 3rd August 2019, 11:55 PM   #2
PRR is offline PRR  United States
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Too sticky here tonight to think (even bark), but asking.......

What does the "sqrt(2)" in the bottom of the fraction do?

Obviously "x/1.414" converts a Peak to an RMS. But I have not gone through the full formula to grok what it does.
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Old 4th August 2019, 12:28 AM   #3
rayma is offline rayma  United States
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The physical units are the same whether peak or rms, so either could appear in a formula in that sense.
In this case, the (1/sqrt 2) factor does convert the Xmax peak value to rms in the SPL formula.

Last edited by rayma; 4th August 2019 at 12:39 AM.
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Old 4th August 2019, 04:00 AM   #4
Conrad Hoffman is offline Conrad Hoffman  United States
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Ah, OK, simple enough. For some reason I though it was doing something else- thanks!
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