From a measured sound pressure level to the source's sound power level
A sound pressure level Lp depends on where it is measured, while the sound power level Lw characterises the source itself. This converter takes an Lp measured at a distance r from a machine, together with the directivity factor Q of the source, and returns an estimate of Lw using the free-field approximation.
The relation assumes a spherical wave in a free field:
Lw = Lp + 20·log10(r) + 11 − 10·log10(Q)
Here r is in metres, and 11 dB is the constant for r in metres; a distance typed in feet is converted first with 1 ft = 0.3048 m. Q = 1 means the source radiates equally in all directions.
The correction for atmospheric temperature and pressure is neglected, as it is for most steady industrial sources. For example, Lp = 90 dB measured at 6 ft from a source with Q = 2 gives Lw = 103.23 dB; the source's worked example rounds this to 103 dB.
How to use the converter
- Enter the sound pressure level Lp in dB. Negative values are accepted; the allowed range is −50 to 250 dB.
- Enter the distance r from the source to the measurement point and choose m or ft in the length menu. Changing the unit keeps the number you typed and reads it in the new unit.
- Enter the directivity factor Q, a number above 0. Leave it at 1 for a source that radiates equally in all directions.
- Read Lw in dB and the formula with your values substituted. The result updates as you type, and the Calculate button recomputes it on demand.
Frequently asked questions
What does this converter calculate?
It estimates the sound power level Lw of a source from a sound pressure level Lp measured at a distance r, using the free-field relation Lw = Lp + 20 log10(r) + 11 - 10 log10(Q), where r is in metres and Q is the directivity factor.
What is the directivity factor Q?
Q describes how the source directs its sound. Q = 1 means the source radiates equally in all directions. Enter any number above 0; the default is 1.
Can I enter the distance in feet?
Yes. Choose ft in the length menu. The distance is converted to metres with 1 ft = 0.3048 m before the calculation, because the 11 dB constant applies to r in metres. Changing the unit does not alter the number you typed; it changes the unit that number is read in.
Why is the atmospheric correction not included?
The correction for atmospheric temperature and pressure is neglected, as it is for most steady industrial sources. The result is therefore an estimate based on a spherical wave in a free field.