Decibel Calculator

Calculate and understand sound level changes in decibels (dB), including conversions between intensity ratios and power ratios. This calculator helps audio professionals, acousticians, and anyone working with sound measurements.

Why Use This Calculator?

Convert between decibels and power/intensity ratios
Understand the logarithmic nature of sound levels
Calculate combined sound levels from multiple sources
Determine sound level changes and differences
Evaluate acoustic measurements and specifications

How It Works

The calculator uses logarithmic relationships to convert between decibels and ratios:

Intensity Level (dB): 10 × log₁₀(I₁/I₂)
Power Level (dB): 20 × log₁₀(P₁/P₂)
Combined Levels: Uses logarithmic addition

Understanding the Results

Decibel Scale Characteristics

+3 dB: Represents doubling of sound power
+10 dB: Perceived as roughly twice as loud
+20 dB: 100 times more powerful
-6 dB: Half the sound pressure level

Common Reference Levels

0 dB: Threshold of human hearing
30 dB: Quiet whisper
60 dB: Normal conversation
85 dB: OSHA workplace safety limit
120 dB: Pain threshold

Common Use Cases

Audio Engineering
- Signal level changes
- Gain staging
- Equipment specifications
Noise Control
- Sound reduction requirements
- Barrier effectiveness
- Environmental impact assessment
Acoustic Design
- Room acoustics
- Sound system design
- Noise isolation

Technical Notes

Calculations use standard logarithmic formulas
Results are rounded to one decimal place
Valid for both sound power and pressure ratios
Accounts for different reference levels

Frequently Asked Questions

What’s the difference between power and intensity ratios?

Power ratios use 10 × log₁₀, while intensity (pressure) ratios use 20 × log₁₀. This is because sound pressure is proportional to the square root of power.

Why are decibels logarithmic?

Human hearing perceives sound logarithmically. A logarithmic scale better matches our perception of loudness changes and allows for a more manageable range of numbers.

How do I combine multiple sound sources?

Multiple sound sources are combined using logarithmic addition: Total dB = 10 × log₁₀(10^(dB₁/10) + 10^(dB₂/10))

What’s a significant change in decibels?

1 dB: Barely perceptible
3 dB: Noticeable change
5 dB: Clearly noticeable
10 dB: Perceived as twice/half as loud