Decibel Formula
Convert sound intensity to decibels.
Understand and compare loudness levels on the logarithmic decibel scale.
The Formula
dB = 10 × log₁₀(I / I₀)
The decibel scale measures sound intensity on a logarithmic scale. Every 10 dB increase represents a tenfold increase in sound intensity.
Variables
| Symbol | Meaning |
|---|---|
| dB | Sound level in decibels |
| I | Sound intensity being measured (W/m²) |
| I₀ | Reference intensity — threshold of hearing (10⁻¹² W/m²) |
| log₁₀ | Common logarithm (base 10) |
Example 1
A sound has intensity 10⁻⁶ W/m². What is its decibel level?
dB = 10 × log₁₀(10⁻⁶ / 10⁻¹²)
dB = 10 × log₁₀(10⁶) = 10 × 6
dB = 60 dB (normal conversation level)
Example 2
How many decibels is a sound 1,000 times more intense than another at 50 dB?
Additional dB = 10 × log₁₀(1,000) = 10 × 3 = 30
New level = 50 + 30 = 80 dB
When to Use It
Use the decibel formula when:
- Measuring and comparing sound levels
- Assessing noise exposure for safety standards
- Designing audio systems and soundproofing
- Converting between linear intensity and the logarithmic dB scale