Sound Power Level Calculator
Sound power level rates how much acoustic energy a source radiates, a property of the machine itself rather than of where you measure. Sound pressure level, by contrast, is the local reading that falls off with distance. This calculator converts a measured sound pressure level at a known distance into the source's sound power level using the free-field relation, accounting for how the source radiates through its directivity factor Q. Use it to derive a machine's Lw rating from a field measurement, or to compare equipment on a distance-independent basis. Enter the level, distance and Q.
Sound power level formula
Lw = Lp + 20 * log10(r) + 11 - 10 * log10(Q)
(11 dB = 10 * log10(4 * pi), full-space radiation)
Q = 1 free space, 2 half space, 4 edge, 8 corner
The reverse relation Lp = Lw - 20 * log10(r) - 11 + 10 * log10(Q) predicts the pressure level from a rated source at any free-field distance.
Power vs pressure context
- Lw is a source property; Lp depends on distance, room and direction.
- Equipment is rated by Lw so noise is comparable across installations.
- Q = 2 (half space) applies to a source on a hard floor.
- This free-field relation ignores room reverberation.
- Higher Q concentrates power, raising local pressure for the same Lw.
Sound power level: frequently asked questions
What is the difference between sound power and sound pressure?
Sound power level (Lw) is a property of the source itself, the total acoustic energy it radiates per second, independent of where you stand. Sound pressure level (Lp) is what a microphone or ear measures at a particular point and depends on distance, room and direction. Lw is the source rating used to compare machines; Lp is the local effect.
How do I convert Lp to Lw in a free field?
For a point source in a free field, Lw = Lp + 20 * log10(r) + 11 - 10 * log10(Q), where r is the distance in meters and Q is the directivity factor. The 11 dB term is 10 * log10(4 * pi) for full-space spherical radiation. For a source on a hard floor radiating into a half space, Q = 2.
What is the directivity factor Q here?
Q describes the solid angle the source radiates into: Q = 1 for full-space (free) radiation, Q = 2 for a source on a reflecting plane (half space), Q = 4 at a two-plane edge, and Q = 8 in a three-plane corner. A higher Q concentrates the same power into a smaller angle, so the measured pressure is higher and the inferred power lower.
Why does sound power level matter?
Manufacturers rate equipment such as fans, pumps and appliances by sound power level because, unlike sound pressure, it does not depend on the test room or microphone position. This lets engineers predict the noise a machine will produce in any installation and compare products fairly. Many regulations and labels specify a maximum Lw.
Can I get Lp back from Lw?
Yes. Rearranging the free-field relation gives Lp = Lw - 20 * log10(r) - 11 + 10 * log10(Q). This calculator focuses on deriving Lw from a measured Lp at a known distance, but the same equation predicts the pressure level a rated source will produce at any distance in a free field.
Official sources
- NIOSH (CDC): Noise and Occupational Hearing Loss.
- NIST: National Institute of Standards and Technology.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.