Sound Intensity Level Calculator
Convert a sound intensity in W/m² to a decibel level relative to the threshold of hearing.
How it works
L = 10 · log₁₀(I ÷ I₀) · I₀ = 1×10⁻¹² W/m²
Human hearing spans about twelve orders of magnitude in intensity, so we compress it onto a logarithmic decibel scale referenced to the faintest audible sound, I₀ = 10⁻¹² W/m². Every factor-of-10 increase in intensity adds 10 dB, and a doubling of intensity adds about 3 dB. Because the scale is logarithmic, a small dB change represents a large change in actual acoustic energy.
Worked example
A sound of 10⁻⁶ W/m² compared with I₀ = 10⁻¹² W/m² gives L = 10 × log₁₀(10⁻⁶ / 10⁻¹²) = 10 × log₁₀(10⁶) = 60 dB — normal conversation level.
Sources: Sound intensity level — HyperPhysics
Frequently asked questions
Why is the decibel scale logarithmic?
The ear responds to an enormous range of intensities — from 10⁻¹² to over 1 W/m². A logarithmic scale compresses that huge range into a manageable 0–120+ dB and roughly matches how loudness is perceived.
How much louder is 10 dB?
Each 10 dB step is a tenfold increase in sound intensity. Perceived loudness roughly doubles every 10 dB, while a barely noticeable change is about 3 dB (a doubling of intensity).
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This calculator is for educational purposes. Double-check important results before acting on them.