SoupCalc

Sound Intensity Level Calculator — Watts per Square Metre to dB

Sound Intensity Level Calculator

This calculator converts a sound intensity and reference intensity into a relative level in decibels (dB). Both inputs use watts per square metre (W/m²).

It calculates an intensity level from numbers you already have. It does not measure sound through the device microphone and is not a replacement for a calibrated sound-level meter.

Formula used

The calculator applies:

Lᵢ = 10 × log₁₀(I ÷ I₀)

where:

  • Lᵢ is the sound intensity level in decibels;
  • I is the measured or specified intensity in W/m²;
  • I₀ is the reference intensity in W/m².

For airborne sound, a commonly used reference is 1 × 10⁻¹² W/m². Both intensity values must be positive. Because the calculation uses a ratio, the result has no meaning unless both values describe the same physical quantity in the same units.

Worked example

For I = 1 × 10⁻⁹ W/m² and I₀ = 1 × 10⁻¹² W/m²:

  1. Intensity ratio: (1 × 10⁻⁹) ÷ (1 × 10⁻¹²) = 1,000
  2. Base-10 logarithm: log₁₀(1,000) = 3
  3. Level: 10 × 3 = 30 dB

SoupCalc therefore displays 30.00 dB.

An intensity ten times the reference gives 10 dB; 100 times the reference gives 20 dB. Doubling intensity increases the level by about 3.01 dB, not by a factor of two in the displayed decibel value.

Intensity level is not the same as every “dB” value

Decibel notation is used for several different ratios. Sound pressure level normally uses a 20-micropascal pressure reference and an equivalent 20 × log₁₀ expression. Sound power level uses power in watts. This page specifically uses sound intensity in W/m² and the 10 × log₁₀ formula.

Likewise, dBA is an A-weighted sound-pressure measurement intended to approximate human hearing sensitivity across frequency. An unweighted intensity calculation from this page cannot be treated automatically as a dBA workplace or listening exposure.

Hearing-risk context and limitations

Hearing risk depends on measured level, frequency, duration, repetition, distance, environment, and individual susceptibility. NIOSH recommends an occupational exposure limit of 85 dBA averaged over eight hours and uses a 3 dB exchange rate, meaning recommended exposure time is halved for each 3 dB increase. That guidance applies to properly measured A-weighted workplace exposure, not directly to every result produced by this intensity-ratio calculator.

Use calibrated equipment and the standards applicable to your workplace or jurisdiction for safety decisions. If sound causes pain, ringing, muffled hearing, or requires shouting at close range, move away from the source and seek appropriate safety or medical guidance rather than relying on an online conversion.

Sources

Editorial record

Written and manually reviewed by the SoupCalc Editorial Team. The formula and worked example were checked against the current calculator implementation. Last reviewed: August 10, 2026. This page remains unavailable for indexing and advertising until all approved localizations pass review.