Decibel Calculator (β = 10 log₁₀(I/I₀))
Decibel Calculator (β = 10 log₁₀(I/I₀))
Sound intensity level in decibels is a logarithmic measure of how a sound's intensity compares to the threshold of human hearing (I₀ = 1×10⁻¹² W/m²) - logarithmic because human hearing itself responds to loudness roughly logarithmically, and because sound intensities in nature span an enormous range. Enter either the intensity or the decibel level, and this calculator converts between them.
- β = 10 × log₁₀(I / I₀), where I₀ = 1×10⁻¹² W/m² is the threshold of hearing - so an intensity of 1×10⁻⁶ W/m² gives β = 10 × log₁₀(10⁶) = 60 dB.
- Every 10 dB increase means 10× the intensity - a 70 dB sound (busy street traffic) is 10 times more intense than a 60 dB sound (normal conversation), and 100 times more intense than a 50 dB sound (quiet office).
- The decibel scale exists because sound intensities vary enormously - from the threshold of hearing (0 dB) to a jet engine at close range (~140 dB, a factor of 10¹⁴ in raw intensity) - a linear scale would be unworkable.
How do I convert sound intensity to decibels?
Use β = 10 × log₁₀(I / I₀), where I₀ = 1×10⁻¹² W/m². An intensity of 1×10⁻⁶ W/m² gives β = 10 × log₁₀(10⁶) = 60 dB.
Why is 0 dB not "no sound"?
0 dB is defined as the threshold of human hearing (I = I₀), not zero intensity - sounds quieter than this are technically negative decibels, though inaudible in practice.
Decibel Calculator (β = 10 log₁₀(I/I₀))
Sound intensity level in decibels is a logarithmic measure of how a sound's intensity compares to the threshold of human hearing (I₀ = 1×10⁻¹² W/m²) - logarithmic because human hearing itself responds to loudness roughly logarithmically, and because sound intensities in nature span an enormous range. Enter either the intensity or the decibel level, and this calculator converts between them.
- β = 10 × log₁₀(I / I₀), where I₀ = 1×10⁻¹² W/m² is the threshold of hearing - so an intensity of 1×10⁻⁶ W/m² gives β = 10 × log₁₀(10⁶) = 60 dB.
- Every 10 dB increase means 10× the intensity - a 70 dB sound (busy street traffic) is 10 times more intense than a 60 dB sound (normal conversation), and 100 times more intense than a 50 dB sound (quiet office).
- The decibel scale exists because sound intensities vary enormously - from the threshold of hearing (0 dB) to a jet engine at close range (~140 dB, a factor of 10¹⁴ in raw intensity) - a linear scale would be unworkable.
How do I convert sound intensity to decibels?
Use β = 10 × log₁₀(I / I₀), where I₀ = 1×10⁻¹² W/m². An intensity of 1×10⁻⁶ W/m² gives β = 10 × log₁₀(10⁶) = 60 dB.
Why is 0 dB not "no sound"?
0 dB is defined as the threshold of human hearing (I = I₀), not zero intensity - sounds quieter than this are technically negative decibels, though inaudible in practice.