Sound Intensity & Decibel Calculator
Convert between sound intensity (W/m²), sound pressure (Pa), and decibel levels (dB). Calculate intensity levels, pressure levels, and combine multiple sound sources correctly.
Convert sound intensity and pressure into decibels
Enter a sound intensity or pressure and see its level in dB, or combine multiple sound sources correctly by summing their intensities instead of just adding decibel values.
Key Formulas
L_I = 10·log₁₀(I / I₀)
L_p = 20·log₁₀(p / p₀)
Standard Air References
I₀ = 10⁻¹² W/m²
p₀ = 20 μPa
Try converting 1×10⁻⁶ W/m² to dB, or combine two 60 dB sources
Understanding Sound Intensity and Decibels
What is a Decibel (dB)?
The decibel (dB) is a logarithmic unit used to express the ratio of a physical quantity (usually power or intensity) relative to a reference level. It's named after Alexander Graham Bell.
Because the decibel scale is logarithmic, it compresses a huge range of values into a manageable scale. Human hearing spans from about 10⁻¹² W/m² to about 1 W/m²—a ratio of one trillion! The decibel scale compresses this to 0-120 dB.
Intensity vs. Pressure
Sound Intensity (I) measures acoustic power flowing through a unit area (W/m²). Sound Pressure (p) measures local pressure deviation from atmospheric pressure (Pa).
Intensity Level: L = 10 · log₁₀(I/I₀)
Pressure Level: L = 20 · log₁₀(p/p₀)
The factor of 20 for pressure comes from intensity being proportional to pressure squared.
Reference Levels (Standard Air)
Reference Intensity:
I₀ = 10⁻¹² W/m²
Reference Pressure:
p₀ = 20 μPa = 2×10⁻⁵ Pa
These correspond to the threshold of human hearing at 1 kHz. When using these references, the result is called dB SPL.
Combining Multiple Sources
⚠️ You cannot simply add decibel values!
Convert to linear intensity, sum, then convert back:
- • Two identical sources: Total = L + 3 dB
- • Ten identical sources: Total = L + 10 dB
- • 80 dB + 80 dB = 83 dB (not 160 dB!)
- • 80 dB + 70 dB ≈ 80.4 dB
Power vs. Amplitude Ratios
Power/Intensity: ΔL = 10 · log₁₀(R)
Amplitude/Field: ΔL = 20 · log₁₀(R)
Common interpretations:
- +3 dB ≈ 2× power (1.41× amplitude)
- +6 dB ≈ 4× power (2× amplitude)
- +10 dB = 10× power (3.16× amplitude)
- +20 dB = 100× power (10× amplitude)
Hearing Safety Guidelines
Prolonged exposure to high sound levels can cause permanent hearing damage. OSHA/NIOSH guidelines:
| Level | Max Exposure |
|---|---|
| 85 dB | 8 hours |
| 88 dB | 4 hours |
| 94 dB | 1 hour |
| 100 dB | 15 minutes |
| 120 dB | Immediate risk |
Frequently Asked Questions
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