Decibel Calculator Formula

Understand the math behind the decibel calculator. Each variable explained with a worked example.

Use the Decibel Calculator

Formulas Used

Sound Level

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

Variables

VariableDescriptionDefault
intensitySound Intensity(W/m²)0.001

How It Works

Decibel Scale

The decibel scale expresses sound intensity on a logarithmic scale relative to a reference intensity.

Formula

dB = 10 * log10(I / I_0)

where I_0 = 10^-12 W/m². Every 10 dB increase represents a tenfold increase in intensity. A 3 dB increase doubles the intensity.

Worked Example

A sound with intensity 0.001 W/m².

intensity = 0.001
  1. 01dB = 10 * log10(I / I_0)
  2. 02dB = 10 * log10(0.001 / 1e-12)
  3. 03dB = 10 * log10(1e9)
  4. 04dB = 10 * 9 = 90 dB

Frequently Asked Questions

Why use a logarithmic scale for sound?

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

How loud is 60 dB?

About the level of normal conversation at 1 meter distance.

What does 0 dB mean?

Zero dB is the threshold of hearing, corresponding to an intensity of 10^-12 W/m². It does not mean no sound.

Ready to run the numbers?

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