Sound Power to Pressure Calculator
Sound power level (Lw) is how much acoustic energy a source radiates in total; sound pressure level (Lp) is what you actually hear at a given spot, which drops with distance. This calculator converts Lw to Lp at a chosen distance in a free field, accounting for source directivity Q. In free space each doubling of distance loses 6 decibels by the inverse-square law. The result assumes no reflections, so it suits outdoor or near-field estimates rather than reverberant rooms.
Power to pressure formula
distance attenuation = 20 * log10(r) + 11
directivity gain = 10 * log10(Q)
Lp = Lw - 20 * log10(r) - 11 + 10 * log10(Q)
doubling distance lowers Lp by about 6 dB
The constant 11 is 10 log10(4 pi), from spreading over a sphere. The minus 20 log10(r) term is the inverse-square law. Directivity Q raises the on-axis level for a focused source.
Sound level facts
- Doubling distance in a free field drops Lp by 6 decibels.
- Q = 1 omnidirectional, 2 on a floor, 4 at an edge, 8 in a corner.
- Lw is a fixed property of the source; Lp depends on where you measure.
- Indoors beyond the critical distance, the reverberant field sets Lp.
- The reference for both levels is the standard 1 picowatt and 20 micropascal.
Power to pressure: frequently asked questions
What is the difference between sound power and sound pressure?
Sound power level (Lw) is the total acoustic energy a source emits, independent of where you stand. Sound pressure level (Lp) is what a microphone or ear measures at a point, which falls with distance. Lw is a property of the source; Lp depends on distance, directivity and the room.
How do you convert sound power level to pressure level?
In a free field, Lp = Lw + 10 log10(Q / (4 pi r squared)), where r is the distance and Q the directivity factor. Written out, Lp = Lw minus 20 log10(r) minus 11 plus 10 log10(Q), with r in metres.
What is the inverse square law here?
Each doubling of distance from a point source in a free field reduces sound pressure level by 6 decibels, because the same power spreads over four times the area. The minus 20 log10(r) term captures this inverse-square spreading.
What is the directivity factor Q?
Q describes how the source concentrates its energy. Q = 1 is omnidirectional in free space; mounting on a hard floor gives 2, a wall-floor edge 4, and a corner 8. Higher Q raises the pressure level on axis for the same power.
When does this free-field formula break down?
It assumes a free field with no reflections. Indoors, beyond the critical distance the reverberant field dominates and pressure no longer falls with distance, so the free-field result underestimates the actual level. Use it outdoors or close to the source.
Official sources
- International Organization for Standardization: ISO 3744 sound power determination.
- Acoustical Society of America: sound level references.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.