Sound intensity level
dB
Relative to I₀ = 10⁻¹² W/m².
Physics · Acoustics
Sound intensity level calculator
Convert sound intensity in W/m² to an intensity level in decibels, or reverse the calculation. The conventional air reference is I₀ = 10⁻¹² W/m².
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Sound intensity
W/m²
Physical power crossing one square metre.
Reference intensity
W/m²
Conventional air reference.
Relation and numerical substitution
β = 10 × log₁₀(I / I₀)—
The input is sound intensity magnitude. Both intensities use the same units; the fixed reference is for sound intensity level in air.
01Formulas and symbols
Formulas used
I₀
I₀ = 10⁻¹²Conventional reference intensity in W/m².β
β = 10 × log₁₀(I / I₀)Ten times the base-10 logarithm of the intensity ratio.I
I = I₀ × 10^(β / 10)Inverse logarithmic relation.02Assumptions and limits
Scope of validity
- The input is sound intensity magnitude. Both intensities use the same units; the fixed reference is for sound intensity level in air.
03Validation example
Reference numerical case
- Given I = 10⁻⁶ W/m², β = 10 log₁₀(10⁻⁶ / 10⁻¹²) = 60 dB. Conversely, β = 80 dB gives I = 10⁻¹² × 10⁸ = 10⁻⁴ W/m².
04References
Technical references
FAQ
Can decibels be negative?
Yes. A negative intensity level means I is below I₀; it does not mean negative physical intensity.
Does 0 dB mean no sound?
No. Here 0 dB means I equals 10⁻¹² W/m². Zero intensity would lead to a logarithmic singularity.
05How it works
Adding 10 dB multiplies intensity by ten. Doubling intensity adds about 3 dB. The diagram marks decades of I/I₀, not subjective loudness or a danger threshold.
06Model limits
Intensity level is not sound pressure level or perceived loudness. This calculator does not apply A-weighting, combine sources, or assess exposure, hearing risk or safety.
07Common mistakes
Use 10 log₁₀ for intensity ratios. The 20 log₁₀ rule for pressure amplitudes belongs to a different quantity and reference. Zero intensity has no finite decibel level.