Sound intensity and decibel calculator
The decibel is a logarithm, so sound levels add strangely: two identical sources make 3 dB more, not twice as much.
dB
dB
Combined level
88.010dB
- Increase over the louder source
- 3.010 dB
- First source at the new distance
- 72.959 dB
- Sound pressure of the first source
- 0.355 656 Pa
- Sound intensity of the first source
- 0.000 316 228 W/m2
- Perceived loudness ratio
- 1.0000
Show the working
- First source level = 85
- Second source level = 85
- Reference distance = 1
- New distance = 4
- Combined level = 10 * log10(10^(85/10) + 10^(85/10)) = 88.0103
- Increase over the louder source = 88.0103 - max(85, 85) = 3.0103
- First source at the new distance = 85 - 20 * log10(4/1) = 72.9588
- Sound pressure of the first source = 0.00002 * 10^(85/20) = 0.355 656
- Sound intensity of the first source = 1e-12 * 10^(85/10) = 0.000 316 228
- Perceived loudness ratio = 2^((85 - 85)/10) = 1
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- combined = 10 log10(10^(L1/10) + 10^(L2/10))
- inverse square law: level falls 6 dB per doubling of distance
- reference: 20 micropascals and 1 picowatt per square metre
Two equal sources add to 3 dB more. Ten equal sources add 10 dB. Perceived loudness roughly doubles every 10 dB.
The inverse square law holds for a free field; indoors, reflections make it optimistic.