Sound Intensity Calculator
Get intensity and decibels from acoustic power and distance.
What it does
Sound spreads over growing spheres outdoors. One acoustic watt at ten meters spreads over 4 pi times 100 square meters, giving about 0.0008 W/m2. Decibels compress that span against the hearing threshold.
The tool above takes acoustic watts and distance and returns intensity, level dB, and small distance. The defaults 1 W at 10 m match the worked example, so the page opens showing 89 dB. Switch to imperial for feet.
Intensity I = P / (4 pi r2). Level L = 10 log10(I / 1e-12). Here 0.000796 over 1e-12 is 7.96e8, log 8.9009, times 10 is 89.0 dB. Doubling to 20 m quarters to 0.000199 and drops to 83 dB.
Free field spherical spreading is assumed. Rooms add reverberation, wind bends rays, and A weighting adjusts for hearing curves. Use this for order checks, not compliance surveys.
This page shows the formulas, one full hand checked example at 1 W and 10 m, a reference table, and practice checks that run through the tool in both unit systems.
How to use
- Pick Metric (m) or Imperial (ft).
- Type acoustic power in watts.
- Type distance in the active unit.
- Read Intensity in W/m2 or W/ft2.
- Read Level in dB re 1 pW/m2.
- Double distance to see minus 6 dB.
Formula
- P
- Acoustic watts.
- r
- Radius in meters.
- I0
- 1e-12 W/m2 reference.
Feet convert at 0.3048 m. Free field only. Near field and rooms need other models.
Worked example
Example: 1 W at 10 m
One acoustic watt ten meters away outdoors. Find level.
- Area: 4 x 3.14159 x 100 = 1256.64 m2.
- Intensity: 1 / 1256.64 = 0.000796 W/m2.
- Ratio: 0.000796 / 1e-12 = 796000000.
- Log: log10 is 8.9009.
- Times 10: 89.0 dB.
- Imperial mirror 32.8 ft gives same 89 dB.
Reference table
| Distance | Intensity | Level |
|---|---|---|
| 5 m | 0.003183 W/m2 | 95 dB |
| 10 m | 0.000796 W/m2 | 89 dB |
| 20 m | 0.000199 W/m2 | 83 dB |
Limits
- Free field spheres only. Rooms add reverb.
- Point source assumed. Large sources need integration.
- Unweighted dB here. A/C curves need filters.
- No wind or gradient bending.
Common mistakes
- Using diameter instead of radius in 4 pi r2.
- Forgetting square on distance.
- Mixing feet with meters in r2.
- Reading intensity W/m2 as dB.
- Expecting minus 3 dB per doubling (that is power halving, not distance).
Try it yourself
Quick checks. Answers sit tucked under each question.
10 W at 5 m?
Intensity 0.031831 W/m2, 105 dB.
1 W at 10 m in ft?
Same 89 dB, intensity 0.000074 W/ft2.
Questions
1 W at 10 m?
0.000796 W/m2, 89 dB.
Double distance?
Quarter intensity, minus 6 dB.
Reference?
1 picowatt per square meter.
A weighting?
Not here. Unweighted free field.
Rooms?
Reverb raises levels above free field.
W/ft2?
W/m2 over 10.7639.