Decibel Calculator
Calculate decibel difference between sound levels using dB = 10 log10(P2/P1).
Converts dB to intensity ratios and perceived loudness changes.
Decibels (dB) express ratios between power or intensity levels using a logarithmic scale. Because our hearing perceives loudness on an exponential curve, decibels align more naturally with human perception than linear measurements.
Power-based dB formula:
dB = 10 × log₁₀(P₁ / P₂)
Amplitude / voltage / pressure formula:
dB = 20 × log₁₀(A₁ / A₂)
Reverse — dB to ratio:
- Power ratio:
Ratio = 10^(dB / 10) - Amplitude ratio:
Ratio = 10^(dB / 20)
Worked example — power: Amplifier output increases from 10W to 100W:
- dB gain = 10 × log₁₀(100/10) = 10 × 1 = +10 dB
Worked example — sound pressure: Microphone signal doubles in amplitude:
- dB change = 20 × log₁₀(2) = 20 × 0.301 = +6.02 dB
Key dB relationships to memorize:
| Change | Power Effect | Perceived Loudness |
|---|---|---|
| +3 dB | ×2 power | Slightly louder |
| +6 dB | ×4 power | Noticeably louder |
| +10 dB | ×10 power | Twice as loud (perceptual) |
| −10 dB | ÷10 power | Half as loud |
Common sound pressure levels:
- 0 dB: Threshold of hearing (reference)
- 30 dB: Library whisper
- 60 dB: Normal conversation at 3 feet
- 85 dB: Heavy traffic (prolonged exposure causes hearing damage)
- 110 dB: Live music concert
- 130 dB: Threshold of pain
- 194 dB: Theoretical maximum in Earth’s atmosphere
OSHA exposure limits: At 90 dB, maximum safe exposure without protection is 8 hours. Every +5 dB halves the allowable exposure time.