Sound Intensity Level Calculator Formula

Understand the math behind the sound intensity level calculator. Each variable explained with a worked example.

Use the Sound Intensity Level Calculator

Formulas Used

Sound Intensity Level

level_db = 10 * log10(intensity / 1e-12)

Variables

VariableDescriptionDefault
intensitySound Intensity(W/m2)0.001

How It Works

Sound Intensity Level

The decibel scale expresses sound intensity relative to the threshold of human hearing.

Formula

L = 10 log10(I / I0)

  • *I* = sound intensity (W/m2)
  • *I0* = 10^-12 W/m2 (reference threshold)

    • Every 10 dB increase corresponds to a tenfold increase in intensity. Normal conversation is about 60 dB; a rock concert about 110 dB.

    Worked Example

    Sound intensity of 0.001 W/m2.

    intensity = 0.001
    1. 01L = 10 log10(I / I0)
    2. 02L = 10 log10(0.001 / 1e-12)
    3. 03L = 10 log10(1e9)
    4. 04L = 10 * 9 = 90 dB

    Frequently Asked Questions

    Why use a logarithmic scale?

    Human hearing spans an enormous range of intensities (a factor of about 10^12). The logarithmic decibel scale compresses this into a manageable range of about 0 to 120 dB.

    What is the threshold of pain?

    About 120 to 130 dB, corresponding to 1 to 10 W/m2. Prolonged exposure above 85 dB can cause hearing damage.

    How does distance affect intensity level?

    For a point source, intensity decreases as 1/r^2. Doubling the distance reduces the level by about 6 dB.

    Ready to run the numbers?

    Open Sound Intensity Level Calculator