Sound Intensity Level Calculator
Enter a sound intensity in watts per square metre to get the sound intensity level in decibels — and see why the scale is logarithmic.
Intensity to decibels
Enter the sound intensity in W/m² and the calculator returns the sound intensity level in decibels using L = 10 · log₁₀(I / I₀).
Use W/m²
The intensity must be in watts per square metre. The reference I₀ = 1e-12 W/m² (the threshold of hearing) is built in, so 1e-12 W/m² maps to 0 dB.
What is sound intensity level?
Loudness on the decibel scale
The sound intensity level is how loud a sound is on the decibel (dB) scale, measured against the faintest sound a healthy ear can hear. The sound intensity level calculator takes the physical sound intensity in watts per square metre and compares it to the reference intensity I₀ = 1e-12 W/m², the threshold of hearing, then expresses the ratio in decibels. Because hearing spans a vast range of intensities, the scale is logarithmic — each 10 dB step is a tenfold change in intensity.
Enter a sound intensity in W/m² to get the sound intensity level in decibels instantly, with the threshold of hearing already set as the reference.
The sound intensity level is ten times the base-10 logarithm of the intensity divided by the reference intensity I₀ = 1e-12 W/m².
L = 10 × log₁₀(I / I₀)The ratio I / I₀ is dimensionless, so the result is in decibels. Because the logarithm is base 10, every tenfold rise in intensity adds exactly 10 dB: 1e-12 W/m² is 0 dB, 1e-11 W/m² is 10 dB, and 1 W/m² is 120 dB. That compression is what lets one scale cover everything from a rustling leaf to a jet engine.
Suppose a sound has an intensity of 0.000001 W/m² (1e-6 W/m²), about the level of normal conversation.
Divide by the reference
0.000001 / 1e-12 = 1,000,000 — the intensity is a million times the threshold of hearing.
Take the base-10 logarithm
log₁₀(1,000,000) = 6 — the power of ten in the ratio.
Multiply by ten
10 × 6 = 60 dB — the sound intensity level, the loudness of a normal conversation.
The decibel figure tells you where a sound sits between silence and pain. According to NIOSH and standard acoustics references, useful landmarks are a whisper near 30 dB, normal conversation around 60 dB, busy traffic about 80 dB, and the threshold of pain near 120 dB. Because the scale is logarithmic, the gaps are bigger than they look: 80 dB is not "a bit louder" than 60 dB but a hundred times the intensity, since each 10 dB is a tenfold jump. That is why prolonged exposure above roughly 85 dB risks hearing damage even though the number seems modest, and why doubling the perceived loudness takes about a 10 dB increase rather than twice the decibels.
The formula is exact, but a couple of practical points are worth keeping in mind.
Intensity level is not the same as perceived loudness
This calculator gives the physical sound intensity level in decibels relative to I₀ = 1e-12 W/m². It is not A-weighted (dBA) and does not model how the ear's sensitivity varies with frequency, so it is not a substitute for a calibrated sound-level meter for hearing-safety decisions. The input must be a strictly positive intensity in W/m²; an intensity of zero has no level on the decibel scale.