Sound Intensity Calculator — dB
Calculate sound intensity level in dB from intensity, and convert between intensity and dB.
What Is the Sound Intensity Calculator — dB?
The Sound Intensity Calculator converts between sound intensity in watts per square metre (W/m²) and sound level in decibels (dB), using the reference intensity of 10⁻¹² W/m² (the threshold of human hearing). It also computes how sound level changes with distance using the inverse square law.
Formula
How to Use
Enter either the sound intensity in W/m² or the sound level in dB. The calculator converts between the two. Optionally enter a distance ratio to compute how the sound level changes as you move further from the source (every doubling of distance reduces level by 6 dB).
Example Calculation
Intensity I = 10⁻⁶ W/m²: dB = 10×log₁₀(10⁻⁶/10⁻¹²) = 10×log₁₀(10⁶) = 10×6 = 60 dB (normal conversation). Moving from 1m to 2m from source: Level drops by 20×log₁₀(2) ≈ 6 dB.
Understanding Sound Intensity — dB
Sound intensity measures the power of a sound wave per unit area (W/m²), while sound level in decibels quantifies the same quantity on a logarithmic scale relative to the threshold of human hearing (10⁻¹² W/m²). The logarithmic scale is used because the ear responds to ratios of intensity, not absolute differences.
The decibel scale spans about 14 orders of magnitude from the threshold of hearing to the threshold of pain. A whisper at 30 dB has an intensity of 10⁻⁹ W/m² — one thousand times more intense than silence, yet quiet. A rock concert at 110 dB is 10¹¹ times more intense than silence, and prolonged exposure risks hearing damage.
Sound propagation outdoors follows the inverse square law: intensity decreases as the square of distance from the source. Engineering applications include acoustic design of concert halls, noise pollution assessment, industrial hearing protection, sonar, and ultrasound imaging. The dB scale is also used in electronics to express signal gains and losses.
Frequently Asked Questions
What is the decibel scale?
The decibel (dB) is a logarithmic unit used to measure sound intensity relative to a reference level. The human ear perceives loudness logarithmically, so the dB scale matches perception better than a linear intensity scale.
What are typical sound levels in dB?
Threshold of hearing: 0 dB. Whisper: 30 dB. Normal conversation: 60 dB. Traffic: 80 dB. Rock concert: 110 dB. Jet engine at 30m: 140 dB (pain threshold).
How much louder is 10 dB more?
An increase of 10 dB represents a 10× increase in intensity, but only sounds about twice as loud to human ears due to logarithmic perception.
How does distance affect sound level?
For a point source in free space, sound level decreases by 6 dB each time the distance doubles. This is the inverse square law: I ∝ 1/r².
Is this calculator free?
Yes, completely free with no sign-up required.
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