dB Calculator
Calculate decibel levels from sound pressure and intensity measurements using logarithmic scales
Calculate Decibel Levels
Sound wave pressure amplitude
Decibel Calculation Results
Formulas used:
SPL = 20 × log₁₀(P/P₀), where P₀ = 0.00002 Pa
SIL = 10 × log₁₀(I/I₀), where I₀ = 1e-12 W/m²
Decibel Scale Analysis
Example Calculation
Normal Conversation SPL
Scenario: Person speaking at normal conversation level
Sound pressure: 0.02 Pa (20 mPa)
Reference pressure: 0.00002 Pa (20 μPa)
Application: Daily communication, office environment
Calculation
SPL = 20 × log₁₀(P/P₀)
SPL = 20 × log₁₀(0.02/0.00002)
SPL = 20 × log₁₀(1000)
SPL = 20 × 3
SPL = 60 dB
Result: Normal conversation produces about 60 dB SPL, which is a comfortable listening level.
dB Reference Scale
Decibel Facts
Decibel is a logarithmic unit measuring sound intensity
Every 10 dB increase represents 10× more intensity
SPL uses 20 μPa as reference pressure
SIL uses 10⁻¹² W/m² as reference intensity
Hearing damage possible above 85 dB prolonged exposure
Understanding Decibels and Sound Measurement
What are Decibels?
Decibels (dB) are a logarithmic unit used to express the ratio of two values of a physical quantity. In acoustics, decibels measure sound pressure level (SPL) and sound intensity level (SIL) relative to reference values that correspond to the threshold of human hearing.
Why Use Logarithmic Scale?
- •Human hearing spans an enormous range (10¹² times)
- •Logarithmic scale compresses this range into manageable numbers
- •Matches human perception of sound intensity
- •Makes calculations and comparisons easier
dB Calculation Formulas
SPL = 20 × log₁₀(P/P₀)
Sound Pressure Level
SIL = 10 × log₁₀(I/I₀)
Sound Intensity Level
P₀: Reference pressure = 20 μPa
I₀: Reference intensity = 10⁻¹² W/m²
Factor 20: For pressure (amplitude quantity)
Factor 10: For intensity (power quantity)
Sound Intensity and Distance
I = P/(4πR²)
Intensity decreases with square of distance
Sound intensity follows the inverse square law - as you double the distance from a sound source, the intensity decreases by a factor of 4 (6 dB decrease). This is because the same acoustic power is distributed over a larger spherical surface area.
Applications and Safety
Acoustics & Audio
Sound level measurements for concert halls, recording studios, and audio equipment calibration use dB scales.
Environmental Monitoring
Noise pollution assessment, urban planning, and environmental impact studies rely on dB measurements.
Occupational Safety
Workplace noise exposure limits and hearing protection requirements are based on dB levels and exposure time.