Science & Engineering
Decibel Calculator - dB Conversion for Voltage, Power & SPL
Convert between decibels and voltage or power ratios. Calculate sound pressure level (dB SPL) from pressure in Pascals. Convert dB to amplitude ratios and back.
= 20.0000 dB
= 10.000000
Common dB Reference Levels
| dB SPL | Sound |
|---|---|
| 0 | Threshold of hearing |
| 30 | Quiet library |
| 60 | Normal conversation |
| 85 | Heavy traffic (safe limit ~8h) |
| 110 | Rock concert |
| 120 | Threshold of pain |
| 140 | Jet engine at 30 m |
How dB is calculated
Decibels are a logarithmic scale, not linear. For sound pressure level (SPL), the formula is:
dB SPL = 20 × log₁₀(P₁ / P₀)
- P₁: Measured sound pressure (pascals)
- P₀: Reference pressure = 20 µPa (micropascals), the threshold of human hearing
Why logarithmic? Human hearing perceives sound intensity logarithmically. A 10 dB increase sounds roughly "twice as loud" to our ears, but it's actually 10× the sound pressure. The log scale compresses the enormous range of human hearing (~1 trillion:1 in intensity) into a manageable 0–140 dB scale.
Relative vs. absolute dB scales
"dB" alone is always relative-a ratio with no absolute value. The suffix specifies the reference:
- dB SPL: Sound pressure level, reference = 20 µPa. Used for acoustics and hearing.
- dBm: Power relative to 1 milliwatt. Used in RF (radio frequency) and telecommunications.
- dBu: Voltage relative to 0.775 V RMS. Used in professional audio.
- dBFS: Decibels relative to digital full scale. 0 dBFS = maximum digital level; all other values are negative. Used in digital audio.
Hearing damage thresholds (NIOSH guidelines)
85 dB SPL is the threshold for occupational hearing protection. NIOSH recommends:
- 85 dB: Safe for 8 hours per day.
- Every 3 dB increase halves the safe exposure time. Examples:
- 88 dB: 4 hours safe
- 91 dB: 2 hours safe
- 94 dB: 1 hour safe
- 100 dB: 15 minutes safe (rock concert level)
- 115 dB: ~30 seconds safe (chainsaw, ambulance siren at close range)
- 120 dB: Threshold of pain. Immediate risk of hearing damage.
Permanent hearing loss is cumulative and irreversible. Use hearing protection (earplugs, earmuffs) in loud environments.