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Sound Intensity Level Calculator

Convert sound intensity into a decibel level.

Result

70.00 dB

How it is calculated

The tool converts a physical intensity in watts per square metre into a level in decibels: L = 10 × log10(I ÷ I0), with the fixed reference I0 = 10-12 W/m². The answer is rounded to two decimals.

Intensity must be greater than zero; zero and negative values give no result, because the logarithm of zero is undefined. Because the scale is logarithmic, every factor of 10 in intensity adds 10 dB, and doubling the intensity adds about 3 dB. The input is intensity (power per area), not sound pressure in pascals, and it is not a weighted figure such as dB(A). A reading from a sound level meter cannot be reconstructed from this alone.

Worked example

The sound intensity is 0.00001 W/m², which is 10-5 W/m².

Ratio to the reference: 10-5 ÷ 10-12 = 107. Logarithm: log10(107) = 7. Level: 10 × 7 = 70.00 dB. Doubling the intensity to 0.00002 W/m² gives 73.01 dB, only about 3 dB higher.

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Common mistakes

  • Entering sound pressure in pascals or a value in dB. The field takes intensity in W/m², and the pressure formula uses 20 × log10, not 10.
  • Writing the intensity in scientific notation incorrectly, for example typing 10-5 instead of 0.00001 or 1e-5.
  • Assuming that doubling the intensity doubles the decibels. It adds only about 3 dB.
  • Adding decibel values arithmetically. Two 70 dB sources together give about 73 dB, not 140 dB; add the intensities first.
  • Expecting a value for zero intensity. There is no result, as the log of zero is undefined.

Sources

About this calculator

This calculator converts an acoustic intensity I (in watts per square meter) into a sound intensity level in decibels using L = 10·log₁₀(I/I₀), where I₀ = 10⁻¹² W/m² is the standard reference intensity, approximately the threshold of human hearing at 1 kHz. Because decibels are logarithmic, a 10 dB increase corresponds to a 10-fold increase in intensity but is perceived as roughly a doubling of loudness.

Acoustic engineers, audiologists, and occupational health and safety professionals use this to assess noise exposure against workplace limits (e.g., OSHA's 85-90 dB thresholds), while audio and architectural acoustics students use it to relate raw physical intensity to the decibel scale used on sound level meters.

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Comments (1)

  • Editorial team

    To work backwards from a decibel target, use I = 10⁻¹² × 10^(dB/10). A level of 85 dB corresponds to about 3.16e-4 W/m², and entering 0.000316 returns 85.00 dB. This is physical intensity, so it will not reproduce a reading from a handheld sound level meter, which typically reports a pressure-based, often A-weighted value. Which noise limit or sound source are you trying to translate into watts per square metre?

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