What is the reference intensity I0 and why is it 10^-12 W/m^2?

I0 = 10^-12 W/m^2 is the threshold of human hearing — the quietest sound a healthy young person can detect at 1 kHz. Setting this as the reference makes 0 dB correspond to the hearing threshold.

If I double the sound intensity, how many dB does the level increase?

An intensity doubling gives an increase of 10*log10(2) approximately 3 dB. A tenfold intensity increase gives +10 dB. A perceived doubling of loudness requires roughly +10 dB.

Can dB values be negative?

Yes. A negative dB value means the sound intensity is below the reference level — quieter than the threshold of hearing. In practice this means the sound is inaudible to most people.

Decibel Level Calculator

Convert sound intensity to decibels using dB = 10 log10(I / I0). Enter the sound intensity and reference intensity (default 10⁻¹² W/m²) to find the sound level in dB SPL.

By AbraCalc Editorial Team · Reviewed by AbraCalc Methodology Review · Last reviewed: 2026-06-25

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How to use this tool

Enter sound intensity (i) and reference intensity (i₀) in the fields above.
Results update instantly as you type — or click Calculate.
Read your sound level and the full breakdown beneath it.

Formula

L = 10 log10(I / I₀)

How it works

Take the base-10 logarithm of the intensity ratio and multiply by 10.

Worked example

Common mistakes to avoid

Using the pressure amplitude formula (20*log10) when intensity values are intended — the intensity formula is 10*log10(I/I0); using 20 instead of 10 doubles the dB result.
Entering intensity in milliwatts per square metre instead of watts per square metre, shifting the result by about 30 dB.
Forgetting the reference intensity I0 = 10^-12 W/m^2 for sound in air and using 1 W/m^2 instead, shifting every result by 120 dB.

Key terms

Frequently asked questions

What is the reference intensity I0 and why is it 10^-12 W/m^2?: I0 = 10^-12 W/m^2 is the threshold of human hearing — the quietest sound a healthy young person can detect at 1 kHz. Setting this as the reference makes 0 dB correspond to the hearing threshold.
If I double the sound intensity, how many dB does the level increase?: An intensity doubling gives an increase of 10*log10(2) approximately 3 dB. A tenfold intensity increase gives +10 dB. A perceived doubling of loudness requires roughly +10 dB.
Can dB values be negative?: Yes. A negative dB value means the sound intensity is below the reference level — quieter than the threshold of hearing. In practice this means the sound is inaudible to most people.