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MotionLab
A logarithmic scale because our ears perceive loudness logarithmically.
Human hearing spans an enormous range — from the threshold of hearing (10⁻¹² W/m²) to the threshold of pain (about 1 W/m²), a factor of 10¹². The decibel scale compresses this trillion-fold range into a manageable 0–120 dB span by using logarithms.
A 10 dB increase represents a 10× increase in intensity but is perceived as roughly double the loudness — so 80 dB (busy traffic) sounds about twice as loud as 70 dB (normal conversation), even though it carries 10 times more acoustic energy.
Sound level (dB)
90
dB = 10 × log₁₀(I / I₀)
What you entered
Intensity ratio
1.00e-3 ÷ 1.00e-12= 1000000000dB = 10 × log₁₀(I ÷ I₀)
10 × log₁₀(1000000000)= 90 dBResult
Sound level (dB): 90
An intensity of 1.00e-3 W/m² is 90 dB relative to the reference of 1.00e-12 W/m².