Example 1
L = 0 dB -> I = 1e-12 W/m².
Sound intensity calculator
Here the unknown is I, not L. I = I0·10^(L/10). From an 85 dB label you return to about 3.16×10⁻⁴ W/m² at the 10⁻¹² threshold. 60 dB is 10⁻⁶ W/m², conversation.
Inverse, L from watts: L from I. Frequency shift in motion: Doppler f′. Wave period: T = 1/f.
Result
Level L (dB) and Reference I0 (W/m², blank = 1e-12). The result shows up here.
How it works
I = I0·10^(L/10) is the inverse of L = 10 log10(I/I0). From a decibel label you return to watts per square meter. 60 dB and default I0 = 10⁻¹² give I = 10⁻⁶ W/m². 0 dB is the threshold itself, 10⁻¹². 120 dB is 1 W/m². 85 dB is 10⁻¹²·10^8.5 ≈ 3.16×10⁻⁴ W/m².
The L field is in decibels and may be zero or negative. −10 dB means I is ten times below I0. Blank I0 means 10⁻¹² W/m². A typed I0 must be positive. The I you get is intensity I = P/A, power over area.
+10 dB multiplies I by exactly 10. +3 dB multiplies I by almost 2: 63 dB is about 2.0×10⁻⁶ W/m², twice the 60 dB conversation. L = 3 dB at I0 = 10⁻⁶ also gives I ≈ 2.0×10⁻⁶. 70 dB is 10⁻⁵, 110 dB is 0.1 W/m².
Units stay dB and W/m². Beside I the result is 10^(L/10), which is I/I0. A plot of I versus L is exponential: each +10 dB lifts I by a decade. Level uses the raw I/I0 ratio, with no A-weighting. dBA on a city meter is a different scale.
Type L, for example 60, leave I0 blank, click Calculate. The result is 1e-6 W/m². Check: open L from I, type 1e-6, and you return to 60 dB. 85 from a noise placard gives about 3.16e-4.
When you know power and area, compute I = P/A yourself and go to L from I. Come here when you only have a table number. Doppler and T = 1/f are about frequency, not this I.
How to use
- Type level L in decibels. Card examples: 0, 60, 85, 120. L may be zero or negative.
- You can leave I0 blank: the calculator uses 10⁻¹² W/m². Type your own I0 when L was measured against another threshold.
- Click Calculate. 60 dB gives I = 10⁻⁶ W/m². 85 dB gives about 3.16×10⁻⁴. 63 dB gives about 2.0×10⁻⁶.
- +10 dB multiplies I by 10. +3 dB almost doubles I. A typed I0 must be positive.
- To return to decibels, open L from I and type the I you got. T = 1/f and Doppler do not turn dB into watts.
Formula
I = I0 · 10L/10
Blank I0 = 10−12 W/m². L any finite value. Unit of I: W/m².
Letters in I = I0·10^(L/10)
Here the unknown is I, not L. From an 85 dB label at I0 = 10⁻¹² you return to ≈ 3.16×10⁻⁴ W/m²; 60 dB is 10⁻⁶.
- I
- Intensity recovered from decibels. 85 dB is 10⁻¹²·10^8.5 ≈ 3.16×10⁻⁴ W/m²; 120 dB is 1 W/m².
- I0
- The same 10⁻¹² reference when the field is blank. 0 dB then means I = I0, the threshold itself.
- L
- Level from a label, in dB. Typed 60 here inverts to 10⁻⁶ W/m², the reverse of L from I.
Real-life examples
Example 2
L = 20 dB -> I = 1e-10 W/m².
Example 3
L = 60 dB -> I = 1e-6 W/m².
Example 4
L = 70 dB -> I = 1e-5 W/m².
Example 5
L = 110 dB -> I = 0.1 W/m².
Example 6
L = 120 dB -> I = 1 W/m².
Example 7
L = 63 dB -> I ≈ 2.0e-6 W/m².
Example 8
L = 3 dB, I0 = 1e-6 -> I ≈ 2.0e-6 W/m².
Ways to use this calculator
- From an 85 dB label you read I at the 10⁻¹² threshold: about 3.16×10⁻⁴ W/m².
- You type 63 dB and see that I is almost twice 1e-6.
- You compute I, go back to L from I, and check that L returns.
Frequently asked questions
What I at 60 dB and blank I0?
I = 10⁻⁶ W/m². 0 dB is 10⁻¹². 120 dB is 1 W/m². 20 dB is 10⁻¹⁰.
What I at 85 dB?
About 3.16×10⁻⁴ W/m² at I0 = 10⁻¹². That is 10^8.5 times the threshold.
How is I different from P/A?
I is P/A. Here you get I from L. Power P = I·A is a separate step once you know the area.
What do +3 dB and +10 dB do?
+10 dB is ×10 in I. +3 dB is almost ×2: 63 dB ≈ 2.0×10⁻⁶, twice 60 dB.
Can L be negative?
Yes. −10 dB means I is ten times smaller than I0. 0 dB means I = I0.
What is blank I0?
10⁻¹² W/m². If L was taken against 10⁻⁶, type that I0 and 3 dB gives ≈ 2.0×10⁻⁶.
How do I check the inverse?
Open L from I and type the I you got. 10⁻⁶ should return 60 dB.
What I at 110 dB and 70 dB?
110 dB is 0.1 W/m². 70 dB is 10⁻⁵ W/m². Each 10 dB is a factor of ten in I.
Is this dBA?
No. The formula has no A-weighting. A street dBA placard is a different number than this I.
Can I type 63 as 63.0?
Yes. 63 and 63.0 give the same I ≈ 2.0e-6 at blank I0.
Knowledge sources
The formula is the school one. Units follow SI; NIST SP 330 and BIPM define the measures, not your result.
Page updated in 2026.