Sound Intensity Calculator

Convert sound intensity (W/m²) to decibels (dB) and back. Calculate sound pressure level (SPL), combine two sound sources, and apply inverse square law for distance attenuation.

W/m²
dB
Sound Level (dB)
—
Intensity I (W/m²) —
Sound Pressure (Pa) —
Extended More scenarios, charts & detailed breakdown ▾
W/m²
Sound Level (dB SPL)
—
Sound Pressure Level —
Sound Pressure (Pa) —
Professional Full parameters & maximum detail ▾
dB
m
m

Inverse Square Law

Level at r₂ —
Intensity at r₂ (W/m²) —
Distance Attenuation —
Sound Pressure at r₂ (Pa) —

How to Use This Calculator

  1. Select Intensity → dB to enter W/m² and get decibels, or dB → Intensity for the reverse.
  2. Use Add Two Sources tab to combine two sound sources correctly.
  3. Switch to Professional to apply the inverse square law at different distances.

Formula

dB = 10·log₁₀(I / I₀) where I₀ = 10⁻¹² W/m²

SPL = 20·log₁₀(P / P₀) where P₀ = 20 µPa

I₂ = I₁ × (r₁/r₂)² (inverse square law)

Example

Example: I = 10⁻⁶ W/m² → dB = 10·log₁₀(10⁻⁶ / 10⁻¹²) = 10·log₁₀(10⁶) = 60 dB.

Frequently Asked Questions

  • Sound intensity is the power of a sound wave per unit area (W/m²). It is related to decibels by: dB = 10·log₁₀(I/I₀) where I₀ = 10⁻¹² W/m² is the threshold of human hearing.
  • Sound intensity (I) measures power per unit area. Sound pressure level (SPL) measures pressure amplitude in Pascals, converted to dB as: SPL = 20·log₁₀(P/P₀) where P₀ = 20 µPa. For a plane wave in air, I ∝ P², so doubling pressure = +6 dB SPL.
  • You cannot add dB directly. Convert each to intensity: I = I₀ × 10^(dB/10). Sum the intensities: I_total = I₁ + I₂. Convert back: dB_total = 10·log₁₀(I_total/I₀). Two equal sources add ~3 dB.
  • By the inverse square law, intensity decreases as 1/r². Every time distance doubles, intensity drops by 6 dB. Formula: I₂ = I₁ × (r₁/r₂)².
  • The threshold of hearing is 0 dB (10⁻¹² W/m²). Uncomfortable levels start around 85–90 dB. The threshold of pain is approximately 130 dB (10 W/m²). Sound above 140 dB can cause immediate hearing damage.

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Sources & References (5) ▾
  1. Sound Intensity — HyperPhysics — Georgia State University HyperPhysics
  2. OSHA Noise Standards — 29 CFR 1910.95 — U.S. Occupational Safety and Health Administration
  3. University Physics Vol 1, Ch 17.3: Sound Intensity — OpenStax
  4. NIOSH — Sound Level Reference — National Institute for Occupational Safety and Health
  5. Acoustical Society of America — Sound Measurement — Acoustical Society of America