Decibel & Sound Intensity Level Calculator
Convert between sound intensity in W/m² and sound intensity level in decibels using the standard logarithmic formula.
Conversion direction
W/m²
Computed from intensity
- 1
Ratio I ÷ I₀
0 ÷ 0 = 1,000,000I₀ = 10⁻¹² W/m² is the reference threshold of hearing. - 2
Sound level L
10 × log₁₀(1,000,000) = 60
How does this calculator work?
Sound intensity level in decibels is L = 10·log10(I/I0), where I0 = 1e-12 W/m² is the hearing threshold. Enter an intensity to get its dB level, or a dB level to recover intensity via I = I0·10^(L/10). Each 10 dB step is a tenfold change in intensity.
Formula
How this is calculated
The sound intensity level L (in decibels) compares a measured acoustic intensity I to the reference threshold of human hearing I0 = 1×10⁻¹² W/m². Because the ear responds logarithmically over a huge dynamic range, the level is defined as L = 10·log10(I/I0). Every factor-of-10 increase in intensity adds 10 dB, and a doubling of intensity adds about 3 dB.
Pick a conversion direction. Given an intensity I (W/m²), the calculator returns L in dB. Given a level L (dB), it inverts the formula to I = I0·10^(L/10) to recover the intensity. Intensity must be a positive number, since log10 of zero or a negative value is undefined; the intensity input is therefore guarded against I ≤ 0.
The result is plotted on a 0–140 dB loudness scale with labeled bands: a quiet whisper near 30 dB, normal conversation around 60 dB, heavy traffic near 90 dB, and the threshold of pain approaching 130–140 dB. Levels are clamped to the 0–140 dB display range for the meter while the exact computed value is shown in the result card.
Frequently asked questions
I0 = 1×10⁻¹² W/m², the nominal threshold of human hearing at 1 kHz. It defines 0 dB on the sound intensity level scale.
Because the scale is logarithmic: 10·log10(2) ≈ 3.01 dB. A tenfold increase in intensity adds exactly 10 dB.
Yes. Intensities below the reference I0 give negative decibel values, meaning the sound is fainter than the 0 dB hearing threshold.
Also known as
TG we-Calculate Editorial Team. (2026). Decibel & Sound Intensity Level Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/decibel-sound-level-calculator
TG we-Calculate Editorial Team. "Decibel & Sound Intensity Level Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/decibel-sound-level-calculator.
TG we-Calculate Editorial Team, "Decibel & Sound Intensity Level Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/decibel-sound-level-calculator
@misc{wecalculate_decibel_sound_level_calculator, title = {Decibel & Sound Intensity Level Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/decibel-sound-level-calculator}}, year = {2026}, note = {TG we-Calculate} }
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