What is the reference intensity I₀?

I₀ = 10⁻¹² W/m² is the internationally agreed threshold of human hearing at 1 kHz. All decibel sound-intensity levels are defined relative to this value.

Why is the scale logarithmic?

Human hearing perceives loudness logarithmically. A 10 dB increase sounds roughly twice as loud, but represents a tenfold increase in physical intensity. A linear scale would span 13 orders of magnitude from silence to a jet engine.

What is the difference between sound intensity and sound pressure level?

Intensity (W/m²) is the power per unit area flowing through the medium. Sound pressure level (SPL) is measured in pascals and uses a pressure reference of 20 µPa. For a plane wave in free field they are numerically the same in dB, but they are different physical quantities.

How do I add two sound sources together in dB?

Convert each dB level back to intensity (I = I₀ · 10^(L/10)), add the intensities, then convert the sum back to dB. Two identical 70 dB sources combine to ~73 dB, not 140 dB.

What intensity corresponds to the pain threshold?

The pain threshold is roughly 130 dB, which corresponds to an intensity of 10 W/m². Prolonged exposure above 85 dB (3.16 × 10⁻⁴ W/m²) can cause hearing damage.

Sound Intensity Level Calculator

Convert sound intensity (W/m²) to decibels or reverse — using the standard reference I₀ = 10⁻¹² W/m².

Conversion Direction

Sound Intensity (W/m²)

Scientific notation: enter 1e-6 for 10⁻⁶ W/m²

Reference I₀ = 10⁻¹² W/m²

Common Reference Levels

Source	dB	W/m²

Result

Enter a value and press Calculate

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Summary

Sound intensity level measures the power of sound relative to a standard reference intensity I₀ = 10⁻¹² W/m² (the threshold of human hearing). The decibel scale is logarithmic: L = 10 · log₁₀(I / I₀). This calculator converts intensity in watts per square meter to dB, or back from dB to W/m², and displays the full formula with substituted values.

How it works

Select the conversion direction: intensity → dB, or dB → intensity.
Enter the intensity in W/m² (scientific notation supported) or the dB level.
The tool applies L = 10 · log₁₀(I / I₀) or its inverse I = I₀ · 10^(L/10).
Results display the numeric answer alongside the worked formula.
Use the common reference table to identify everyday sound levels.

Use cases

Physics homework and acoustics coursework.
Engineering noise assessments and occupational health checks.
Audio equipment specification comparisons.
Environmental noise monitoring and reporting.
Understanding how dB levels relate to physical power.
Verifying manual decibel calculations.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu